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    <link:label id="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsLineItems_16416a0f-7edf-4887-b61a-7f8e866f1e64_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt and Equity Securities, FV-NI [Line Items]</link:label>
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    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
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    <link:label id="lab_us-gaap_DebtSecuritiesTradingRealizedGainLoss_01603683-e86b-44f5-b5af-e686dbcf1a6f_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesTradingRealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, Trading, Realized Gain (Loss)</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesTradingRealizedGainLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesTradingRealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Trading, Realized Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesTradingRealizedGainLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtSecuritiesTradingRealizedGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesTradingRealizedGainLoss" xlink:to="lab_us-gaap_DebtSecuritiesTradingRealizedGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_terseLabel_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement does not require Recovery</link:label>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_label_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Does Not Require Recovery [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_RestatementDoesNotRequireRecoveryTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:to="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessDescriptionAndBasisOfPresentationTextBlock_e7943011-7ea2-49b7-a178-ce91386c14a4_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessDescriptionAndBasisOfPresentationTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Background and Business Description</link:label>
    <link:label id="lab_us-gaap_BusinessDescriptionAndBasisOfPresentationTextBlock_label_en-US" xlink:label="lab_us-gaap_BusinessDescriptionAndBasisOfPresentationTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Description and Basis of Presentation [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessDescriptionAndBasisOfPresentationTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_BusinessDescriptionAndBasisOfPresentationTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessDescriptionAndBasisOfPresentationTextBlock" xlink:to="lab_us-gaap_BusinessDescriptionAndBasisOfPresentationTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_DeterminationDateAxis_abe90670-2122-4f5d-9a47-afa44f79ee07_terseLabel_en-US" xlink:label="lab_ambc_DeterminationDateAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Determination Date [Axis]</link:label>
    <link:label id="lab_ambc_DeterminationDateAxis_label_en-US" xlink:label="lab_ambc_DeterminationDateAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Determination Date [Axis]</link:label>
    <link:label id="lab_ambc_DeterminationDateAxis_documentation_en-US" xlink:label="lab_ambc_DeterminationDateAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Determination Date [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_DeterminationDateAxis" xlink:href="ambc-20240630.xsd#ambc_DeterminationDateAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_DeterminationDateAxis" xlink:to="lab_ambc_DeterminationDateAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThan25AndWithin30YearsFromBalanceSheetDate_984d370a-55f6-4b23-a0e7-5e915013cba6_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThan25AndWithin30YearsFromBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Future expected premiums to be earned, net of reinsurance, December 31, 2050</link:label>
    <link:label id="lab_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThan25AndWithin30YearsFromBalanceSheetDate_label_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThan25AndWithin30YearsFromBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Guarantee Insurance Contract, Premium Revenue to be Recognized, after Year 25 Through 30</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThan25AndWithin30YearsFromBalanceSheetDate" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThan25AndWithin30YearsFromBalanceSheetDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThan25AndWithin30YearsFromBalanceSheetDate" xlink:to="lab_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThan25AndWithin30YearsFromBalanceSheetDate" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_FairValueInputsMaturity_35e863d6-3ee0-42c7-b4a1-6c1c9e63d202_terseLabel_en-US" xlink:label="lab_ambc_FairValueInputsMaturity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Inputs Maturity</link:label>
    <link:label id="lab_ambc_FairValueInputsMaturity_label_en-US" xlink:label="lab_ambc_FairValueInputsMaturity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Inputs Maturity</link:label>
    <link:label id="lab_ambc_FairValueInputsMaturity_documentation_en-US" xlink:label="lab_ambc_FairValueInputsMaturity" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair value inputs maturity.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_FairValueInputsMaturity" xlink:href="ambc-20240630.xsd#ambc_FairValueInputsMaturity"/>
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    <link:label id="lab_us-gaap_VariableInterestEntityLineItems_b4ed0700-1a5a-4796-acd6-5326cb853290_verboseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityLineItems" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Variable Interest Entity [Line Items]</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityLineItems_70afaccb-6b39-4b9b-8497-e8870bc8e627_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Interest Entities [Line Items]</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityLineItems_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_VariableInterestEntityLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableInterestEntityLineItems" xlink:to="lab_us-gaap_VariableInterestEntityLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_BusinessCombinationPercentageOwnershipRetainedByRolloverShareholders_72400445-6762-4f92-805e-ccdb022a5ef2_terseLabel_en-US" xlink:label="lab_ambc_BusinessCombinationPercentageOwnershipRetainedByRolloverShareholders" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Percentage Ownership Retained by Rollover Shareholders</link:label>
    <link:label id="lab_ambc_BusinessCombinationPercentageOwnershipRetainedByRolloverShareholders_label_en-US" xlink:label="lab_ambc_BusinessCombinationPercentageOwnershipRetainedByRolloverShareholders" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Percentage Ownership Retained by Rollover Shareholders</link:label>
    <link:label id="lab_ambc_BusinessCombinationPercentageOwnershipRetainedByRolloverShareholders_documentation_en-US" xlink:label="lab_ambc_BusinessCombinationPercentageOwnershipRetainedByRolloverShareholders" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Percentage Ownership Retained by Rollover Shareholders</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_BusinessCombinationPercentageOwnershipRetainedByRolloverShareholders" xlink:href="ambc-20240630.xsd#ambc_BusinessCombinationPercentageOwnershipRetainedByRolloverShareholders"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_BusinessCombinationPercentageOwnershipRetainedByRolloverShareholders" xlink:to="lab_ambc_BusinessCombinationPercentageOwnershipRetainedByRolloverShareholders" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReportingUnitDomain_48fc3b05-80a2-4b69-8d6b-da96aaaf2108_terseLabel_en-US" xlink:label="lab_us-gaap_ReportingUnitDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reporting Unit [Domain]</link:label>
    <link:label id="lab_us-gaap_ReportingUnitDomain_label_en-US" xlink:label="lab_us-gaap_ReportingUnitDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reporting Unit [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReportingUnitDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ReportingUnitDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReportingUnitDomain" xlink:to="lab_us-gaap_ReportingUnitDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PremiumReceivableAllowanceForCreditLossTableTextBlock_4845a280-7bf9-402b-a189-4b366deeba70_terseLabel_en-US" xlink:label="lab_us-gaap_PremiumReceivableAllowanceForCreditLossTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Premium Receivable, Allowance for Credit Loss [Table Text Block]</link:label>
    <link:label id="lab_us-gaap_PremiumReceivableAllowanceForCreditLossTableTextBlock_label_en-US" xlink:label="lab_us-gaap_PremiumReceivableAllowanceForCreditLossTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Premium Receivable, Allowance for Credit Loss [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumReceivableAllowanceForCreditLossTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PremiumReceivableAllowanceForCreditLossTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PremiumReceivableAllowanceForCreditLossTableTextBlock" xlink:to="lab_us-gaap_PremiumReceivableAllowanceForCreditLossTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_AmortizedCostAndFairValueDebtSecuritiesAbstract_ace33c11-f34e-47da-95e3-b250d481adf6_terseLabel_en-US" xlink:label="lab_ambc_AmortizedCostAndFairValueDebtSecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortized Cost And Fair Value Debt Securities [Abstract]</link:label>
    <link:label id="lab_ambc_AmortizedCostAndFairValueDebtSecuritiesAbstract_label_en-US" xlink:label="lab_ambc_AmortizedCostAndFairValueDebtSecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortized Cost And Fair Value Debt Securities [Abstract]</link:label>
    <link:label id="lab_ambc_AmortizedCostAndFairValueDebtSecuritiesAbstract_documentation_en-US" xlink:label="lab_ambc_AmortizedCostAndFairValueDebtSecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Amortized Cost and Fair Value Debt Securities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_AmortizedCostAndFairValueDebtSecuritiesAbstract" xlink:href="ambc-20240630.xsd#ambc_AmortizedCostAndFairValueDebtSecuritiesAbstract"/>
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    <link:label id="lab_us-gaap_DeferredFederalIncomeTaxExpenseBenefit_d649f9b9-fcb9-4a9d-8f94-a4663c7638b5_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredFederalIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred Federal Income Tax Expense (Benefit)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredFederalIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DeferredFederalIncomeTaxExpenseBenefit"/>
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    <link:label id="lab_ambc_DerivativeAndOtherAssets_912f2fc0-bd4c-4560-8374-20294b71c03f_terseLabel_en-US" xlink:label="lab_ambc_DerivativeAndOtherAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative and other assets</link:label>
    <link:label id="lab_ambc_DerivativeAndOtherAssets_label_en-US" xlink:label="lab_ambc_DerivativeAndOtherAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative and other assets</link:label>
    <link:label id="lab_ambc_DerivativeAndOtherAssets_documentation_en-US" xlink:label="lab_ambc_DerivativeAndOtherAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative and other assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_DerivativeAndOtherAssets" xlink:href="ambc-20240630.xsd#ambc_DerivativeAndOtherAssets"/>
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    <link:label id="lab_us-gaap_PreferredStockValue_74ddf8e3-4686-476b-8dbe-fea2841707ea_verboseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, par value $0.01 per share; 20,000,000 shares authorized; issued and outstanding shares&#8212;none</link:label>
    <link:label id="lab_us-gaap_PreferredStockValue_label_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PreferredStockValue"/>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTypeDomain" xlink:to="lab_us-gaap_SubsequentEventTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InformationByCategoryOfDebtSecurityAxis_a4a57488-2814-44d6-9d4d-f83802e6b2b2_terseLabel_en-US" xlink:label="lab_us-gaap_InformationByCategoryOfDebtSecurityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Security Category [Axis]</link:label>
    <link:label id="lab_us-gaap_InformationByCategoryOfDebtSecurityAxis_label_en-US" xlink:label="lab_us-gaap_InformationByCategoryOfDebtSecurityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Security Category [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InformationByCategoryOfDebtSecurityAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InformationByCategoryOfDebtSecurityAxis"/>
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    <link:label id="lab_ambc_BusinessCombinationValueOfSharesIssuedForBeatAcquisition_eeea73d1-789c-4abd-bf99-f4357aad3310_terseLabel_en-US" xlink:label="lab_ambc_BusinessCombinationValueOfSharesIssuedForBeatAcquisition" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Value of Shares Issued for Beat Acquisition</link:label>
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    <link:label id="lab_ambc_BusinessCombinationValueOfSharesIssuedForBeatAcquisition_documentation_en-US" xlink:label="lab_ambc_BusinessCombinationValueOfSharesIssuedForBeatAcquisition" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Value of Shares Issued for Beat Acquisition</link:label>
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    <link:label id="lab_us-gaap_SupplementalCashFlowElementsAbstract_00897362-b914-401a-8bd3-b59fbcaf75b7_terseLabel_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowElementsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Supplemental Cash Flow Elements [Abstract]</link:label>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossFinancialLiabilityFairValueOptionUnrealizedGainLossArisingDuringPeriodAfterTax_bd543aa1-0ae6-49b5-a344-7e9ce3a67412_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossFinancialLiabilityFairValueOptionUnrealizedGainLossArisingDuringPeriodAfterTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Financial Liability, Fair Value Option, Unrealized Gain (Loss) Arising During Period, after Tax</link:label>
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    <link:label id="lab_us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount_5b07a015-76a5-425a-ac2e-2f435cec1a43_terseLabel_en-US" xlink:label="lab_us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redeemable Noncontrolling Interest, Equity, Carrying Amount</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount"/>
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    <link:label id="lab_dei_TradingSymbol_bec926bb-eda0-46be-ab51-49cc143d2187_terseLabel_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
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    <link:label id="lab_us-gaap_LettersOfCreditOutstandingAmount_2f06ac8d-5bab-4a8e-a07c-52ad5588ed4f_terseLabel_en-US" xlink:label="lab_us-gaap_LettersOfCreditOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Letters of Credit Outstanding, Amount</link:label>
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    <link:label id="lab_ambc_LoansUnpaidPrincipalBalance_documentation_en-US" xlink:label="lab_ambc_LoansUnpaidPrincipalBalance" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">This represents the amount of principal outstanding on loans receivable that are presented on the balance sheet at fair value, whether such presentation is as a separate caption or parenthetical disclosure.</link:label>
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    <link:label id="lab_us-gaap_ContractWithCustomerLiability_e22bf6ed-7038-4df6-b7ba-6607dd3d39b6_terseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contract with Customer, Liability</link:label>
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    <link:label id="lab_ambc_AllTransMember_e44197a1-d38f-442f-a3cf-a6538d3f11b6_terseLabel_en-US" xlink:label="lab_ambc_AllTransMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Trans</link:label>
    <link:label id="lab_ambc_AllTransMember_label_en-US" xlink:label="lab_ambc_AllTransMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Trans [Member]</link:label>
    <link:label id="lab_ambc_AllTransMember_documentation_en-US" xlink:label="lab_ambc_AllTransMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">All Trans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_AllTransMember" xlink:href="ambc-20240630.xsd#ambc_AllTransMember"/>
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    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_eec72d13-0a51-49a9-bcef-daaf301b2509_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Earnings Per Share, Basic and Diluted</link:label>
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    <link:label id="lab_us-gaap_SecuritiesFinancingTransactionTypeDomain_label_en-US" xlink:label="lab_us-gaap_SecuritiesFinancingTransactionTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Securities Financing Transaction [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuritiesFinancingTransactionTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SecuritiesFinancingTransactionTypeDomain"/>
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    <link:label id="lab_ambc_EstimatedFuturePremiumPaymentsWeightedAverageDiscountedRate_documentation_en-US" xlink:label="lab_ambc_EstimatedFuturePremiumPaymentsWeightedAverageDiscountedRate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Weighted average discounted rate of estimated future premium payments to be paid by the VIEs.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_EstimatedFuturePremiumPaymentsWeightedAverageDiscountedRate" xlink:href="ambc-20240630.xsd#ambc_EstimatedFuturePremiumPaymentsWeightedAverageDiscountedRate"/>
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    <link:label id="lab_ambc_AmbacAssuranceMember_documentation_en-US" xlink:label="lab_ambc_AmbacAssuranceMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Ambac assurance.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_AmbacAssuranceMember" xlink:href="ambc-20240630.xsd#ambc_AmbacAssuranceMember"/>
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    <link:label id="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember_1c3d972d-aed9-4986-9676-47074b8ef4e6_terseLabel_en-US" xlink:label="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reported Value Measurement [Member]</link:label>
    <link:label id="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember_5d46d32d-da44-4d1e-a5bf-c2a0359dde93_verboseLabel_en-US" xlink:label="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Priced Through Pricing Vendors [Member]</link:label>
    <link:label id="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reported Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CarryingReportedAmountFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:to="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_currency_GBP_8d34adf6-d69e-4b5b-bb44-0885512f4ac1_terseLabel_en-US" xlink:label="lab_currency_GBP" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">United Kingdom, Pounds</link:label>
    <link:label id="lab_currency_GBP_label_en-US" xlink:label="lab_currency_GBP" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">United Kingdom, Pounds</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_currency_GBP" xlink:href="https://xbrl.sec.gov/currency/2023/currency-2023.xsd#currency_GBP"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_currency_GBP" xlink:to="lab_currency_GBP" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HedgeFundsMultistrategyMember_205def48-125f-48de-8081-0a7f6b532f03_terseLabel_en-US" xlink:label="lab_us-gaap_HedgeFundsMultistrategyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hedge Funds, Multi-strategy [Member]</link:label>
    <link:label id="lab_us-gaap_HedgeFundsMultistrategyMember_label_en-US" xlink:label="lab_us-gaap_HedgeFundsMultistrategyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedge Funds, Multi-strategy [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HedgeFundsMultistrategyMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_HedgeFundsMultistrategyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HedgeFundsMultistrategyMember" xlink:to="lab_us-gaap_HedgeFundsMultistrategyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_db3783f0-3376-473b-b4ef-2c4c41a299b7_terseLabel_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementEquityComponentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementEquityComponentsAxis" xlink:to="lab_us-gaap_StatementEquityComponentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_522a586d-ddb1-4fb4-9da4-fabe67fe2619_terseLabel_en-US" xlink:label="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instruments [Domain]</link:label>
    <link:label id="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_label_en-US" xlink:label="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instruments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:to="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Additional402vDisclosureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_Additional402vDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional 402(v) Disclosure</link:label>
    <link:label id="lab_ecd_Additional402vDisclosureTextBlock_label_en-US" xlink:label="lab_ecd_Additional402vDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional 402(v) Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Additional402vDisclosureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_Additional402vDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Additional402vDisclosureTextBlock" xlink:to="lab_ecd_Additional402vDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherCreditDerivativesMember_c0b899c1-c50c-4053-86bf-f8f3d72033f6_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherCreditDerivativesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other Derivatives [Member]</link:label>
    <link:label id="lab_us-gaap_OtherCreditDerivativesMember_label_en-US" xlink:label="lab_us-gaap_OtherCreditDerivativesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Credit Derivatives [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherCreditDerivativesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherCreditDerivativesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherCreditDerivativesMember" xlink:to="lab_us-gaap_OtherCreditDerivativesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentTypeAxis_ccba2584-7b34-4188-94e6-591b99af254f_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Type [Axis]</link:label>
    <link:label id="lab_us-gaap_InvestmentTypeAxis_label_en-US" xlink:label="lab_us-gaap_InvestmentTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InvestmentTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentTypeAxis" xlink:to="lab_us-gaap_InvestmentTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseClaimsPaidCurrentYear1_331d668c-60e7-42d8-9807-85a820c06715_negatedLabel_en-US" xlink:label="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseClaimsPaidCurrentYear1" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Claim and loss expense payments, net of subrogation and reinsurance</link:label>
    <link:label id="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseClaimsPaidCurrentYear1_label_en-US" xlink:label="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseClaimsPaidCurrentYear1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Unpaid Claims and Claims Adjustment Expense, Claims Paid, Current Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseClaimsPaidCurrentYear1" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseClaimsPaidCurrentYear1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseClaimsPaidCurrentYear1" xlink:to="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseClaimsPaidCurrentYear1" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntitySmallBusiness_d2153691-8454-4c03-9bbb-ffa4ec3e9898_terseLabel_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:label id="lab_dei_EntitySmallBusiness_label_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntitySmallBusiness" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntitySmallBusiness"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntitySmallBusiness" xlink:to="lab_dei_EntitySmallBusiness" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_SummaryOfCededParAndNetUnsecuredReinsuranceRecoverableLineItems_de14b004-11b6-4e3a-b13e-67e7dd2c15df_terseLabel_en-US" xlink:label="lab_ambc_SummaryOfCededParAndNetUnsecuredReinsuranceRecoverableLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Ceded Par and Net Unsecured Reinsurance Recoverable [Line Items]</link:label>
    <link:label id="lab_ambc_SummaryOfCededParAndNetUnsecuredReinsuranceRecoverableLineItems_label_en-US" xlink:label="lab_ambc_SummaryOfCededParAndNetUnsecuredReinsuranceRecoverableLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Summary Of Ceded Par And Net Unsecured Reinsurance Recoverable [Line Items]</link:label>
    <link:label id="lab_ambc_SummaryOfCededParAndNetUnsecuredReinsuranceRecoverableLineItems_documentation_en-US" xlink:label="lab_ambc_SummaryOfCededParAndNetUnsecuredReinsuranceRecoverableLineItems" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Summary of Ceded Par and Net Unsecured Reinsurance Recoverable [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_SummaryOfCededParAndNetUnsecuredReinsuranceRecoverableLineItems" xlink:href="ambc-20240630.xsd#ambc_SummaryOfCededParAndNetUnsecuredReinsuranceRecoverableLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_SummaryOfCededParAndNetUnsecuredReinsuranceRecoverableLineItems" xlink:to="lab_ambc_SummaryOfCededParAndNetUnsecuredReinsuranceRecoverableLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentTypeCategorizationMember_ca690814-ed91-478d-bbbf-3d95046a30b0_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentTypeCategorizationMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments [Domain]</link:label>
    <link:label id="lab_us-gaap_InvestmentTypeCategorizationMember_label_en-US" xlink:label="lab_us-gaap_InvestmentTypeCategorizationMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeCategorizationMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InvestmentTypeCategorizationMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentTypeCategorizationMember" xlink:to="lab_us-gaap_InvestmentTypeCategorizationMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LocalPhoneNumber_86d67f65-7aca-472d-b48f-e3e3e37eeef9_terseLabel_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:label id="lab_dei_LocalPhoneNumber_label_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_LocalPhoneNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LocalPhoneNumber" xlink:to="lab_dei_LocalPhoneNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RecoveryOfErrCompDisclosureLineItems_label_en-US" xlink:label="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Recovery of Erroneously Awarded Compensation Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_RecoveryOfErrCompDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:to="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeNotionalAmount_f335716f-52e6-4201-a4b5-effcd144af5b_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Notional outstanding</link:label>
    <link:label id="lab_us-gaap_DerivativeNotionalAmount_8d0d55a9-cf7f-4b1c-a96a-d4873d2303c0_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative products, Notional Amount</link:label>
    <link:label id="lab_us-gaap_DerivativeNotionalAmount_label_en-US" xlink:label="lab_us-gaap_DerivativeNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Notional Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeNotionalAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeNotionalAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeNotionalAmount" xlink:to="lab_us-gaap_DerivativeNotionalAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationDiscountOnGrossClaimLiability_ca146ca5-2dce-435c-9e15-0bfcceb3c343_negatedLabel_en-US" xlink:label="lab_ambc_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationDiscountOnGrossClaimLiability" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Discount, gross claim liability</link:label>
    <link:label id="lab_ambc_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationDiscountOnGrossClaimLiability_label_en-US" xlink:label="lab_ambc_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationDiscountOnGrossClaimLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule Of Insured Financial Obligations With Credit Deterioration Discount On Gross Claim Liability</link:label>
    <link:label id="lab_ambc_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationDiscountOnGrossClaimLiability_documentation_en-US" xlink:label="lab_ambc_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationDiscountOnGrossClaimLiability" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">This element represents the discounting on the gross claim liability for financial guarantee insurance contracts presented in the context of each surveillance grouping or category used by management to monitor and track potential deterioration in the credit worthiness of the insured party's ability to meet its financial obligations related to the contracts underlying financial guarantee insurance contracts the entity has issued.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationDiscountOnGrossClaimLiability" xlink:href="ambc-20240630.xsd#ambc_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationDiscountOnGrossClaimLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationDiscountOnGrossClaimLiability" xlink:to="lab_ambc_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationDiscountOnGrossClaimLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan30AndWithin35YearsFromBalanceSheetDate_95ade07f-3251-4ad5-863c-65a94fffee97_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan30AndWithin35YearsFromBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Future premiums expected to be collected, December 31, 2055</link:label>
    <link:label id="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan30AndWithin35YearsFromBalanceSheetDate_label_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan30AndWithin35YearsFromBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Guarantee Insurance Contract, Premium Receivable, to be Collected, after Year 30 Through 35</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan30AndWithin35YearsFromBalanceSheetDate" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan30AndWithin35YearsFromBalanceSheetDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan30AndWithin35YearsFromBalanceSheetDate" xlink:to="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan30AndWithin35YearsFromBalanceSheetDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByMeasurementFrequencyAxis_089c49cc-d062-4a26-a3d9-0112e66df18f_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Frequency [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByMeasurementFrequencyAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Frequency [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueByMeasurementFrequencyAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:to="lab_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_InvestorOwnedAndPublicUtilitiesMember_3debb861-2660-46d0-824f-a12d9db64ee3_terseLabel_en-US" xlink:label="lab_ambc_InvestorOwnedAndPublicUtilitiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investor Owned And Public Utilities [Member]</link:label>
    <link:label id="lab_ambc_InvestorOwnedAndPublicUtilitiesMember_label_en-US" xlink:label="lab_ambc_InvestorOwnedAndPublicUtilitiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investor Owned And Public Utilities [Member]</link:label>
    <link:label id="lab_ambc_InvestorOwnedAndPublicUtilitiesMember_documentation_en-US" xlink:label="lab_ambc_InvestorOwnedAndPublicUtilitiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investor Owned and Public Utilities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_InvestorOwnedAndPublicUtilitiesMember" xlink:href="ambc-20240630.xsd#ambc_InvestorOwnedAndPublicUtilitiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_InvestorOwnedAndPublicUtilitiesMember" xlink:to="lab_ambc_InvestorOwnedAndPublicUtilitiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedCashAndCashEquivalentsAtCarryingValue_3c50afe2-2417-4bd5-988f-d0e7f3e2ac4e_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedCashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted Cash and Cash Equivalents, Current</link:label>
    <link:label id="lab_us-gaap_RestrictedCashAndCashEquivalentsAtCarryingValue_label_en-US" xlink:label="lab_us-gaap_RestrictedCashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Cash and Cash Equivalents, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedCashAndCashEquivalentsAtCarryingValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RestrictedCashAndCashEquivalentsAtCarryingValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedCashAndCashEquivalentsAtCarryingValue" xlink:to="lab_us-gaap_RestrictedCashAndCashEquivalentsAtCarryingValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetirementPlanTypeDomain_89959c27-d070-4883-9663-a20b38e685cc_terseLabel_en-US" xlink:label="lab_us-gaap_RetirementPlanTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Retirement Plan Type [Domain]</link:label>
    <link:label id="lab_us-gaap_RetirementPlanTypeDomain_label_en-US" xlink:label="lab_us-gaap_RetirementPlanTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retirement Plan Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetirementPlanTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RetirementPlanTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetirementPlanTypeDomain" xlink:to="lab_us-gaap_RetirementPlanTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedStockUnitsRSUMember_e67e09ca-bbf9-43c4-b3e0-c43341fbc979_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted Stock Units (RSUs) [Member]</link:label>
    <link:label id="lab_us-gaap_RestrictedStockUnitsRSUMember_label_en-US" xlink:label="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Stock Units (RSUs) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedStockUnitsRSUMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RestrictedStockUnitsRSUMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedStockUnitsRSUMember" xlink:to="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt"/>
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    <link:label id="lab_ambc_ComponentsofVIEGainLossTableTextBlock_d6f694f4-61c0-4cfc-b216-6cc4df667e2c_terseLabel_en-US" xlink:label="lab_ambc_ComponentsofVIEGainLossTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Components of VIE Gain (Loss) [Table Text Block]</link:label>
    <link:label id="lab_ambc_ComponentsofVIEGainLossTableTextBlock_label_en-US" xlink:label="lab_ambc_ComponentsofVIEGainLossTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Components of VIE Gain (Loss) [Table Text Block]</link:label>
    <link:label id="lab_ambc_ComponentsofVIEGainLossTableTextBlock_documentation_en-US" xlink:label="lab_ambc_ComponentsofVIEGainLossTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">[Table Text Block] for Components of VIE Gain (Loss) [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_ComponentsofVIEGainLossTableTextBlock" xlink:href="ambc-20240630.xsd#ambc_ComponentsofVIEGainLossTableTextBlock"/>
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    <link:label id="lab_us-gaap_Depreciation_77b068cd-047e-43dd-ba6c-36d0d51a4afe_terseLabel_en-US" xlink:label="lab_us-gaap_Depreciation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation</link:label>
    <link:label id="lab_us-gaap_Depreciation_label_en-US" xlink:label="lab_us-gaap_Depreciation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Depreciation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Depreciation" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_Depreciation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Depreciation" xlink:to="lab_us-gaap_Depreciation" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_NumberOfAdmittedCarriersOwned_049cf73c-894a-4201-b7d0-4de8e7cedb76_terseLabel_en-US" xlink:label="lab_ambc_NumberOfAdmittedCarriersOwned" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of Admitted Carriers Owned</link:label>
    <link:label id="lab_ambc_NumberOfAdmittedCarriersOwned_label_en-US" xlink:label="lab_ambc_NumberOfAdmittedCarriersOwned" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Admitted Carriers Owned</link:label>
    <link:label id="lab_ambc_NumberOfAdmittedCarriersOwned_documentation_en-US" xlink:label="lab_ambc_NumberOfAdmittedCarriersOwned" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number of Admitted Carriers Owned</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_NumberOfAdmittedCarriersOwned" xlink:href="ambc-20240630.xsd#ambc_NumberOfAdmittedCarriersOwned"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_NumberOfAdmittedCarriersOwned" xlink:to="lab_ambc_NumberOfAdmittedCarriersOwned" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PostemploymentBenefitsPeriodExpense_ee05187d-b0e0-4be4-8ae2-9604b2f59f36_terseLabel_en-US" xlink:label="lab_us-gaap_PostemploymentBenefitsPeriodExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Postemployment Benefits, Period Expense</link:label>
    <link:label id="lab_us-gaap_PostemploymentBenefitsPeriodExpense_label_en-US" xlink:label="lab_us-gaap_PostemploymentBenefitsPeriodExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Postemployment Benefits, Period Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PostemploymentBenefitsPeriodExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PostemploymentBenefitsPeriodExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PostemploymentBenefitsPeriodExpense" xlink:to="lab_us-gaap_PostemploymentBenefitsPeriodExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ReportableGeographicalComponentsMember_9b6f97f5-018d-4bea-9b32-5fead575b06f_terseLabel_en-US" xlink:label="lab_srt_ReportableGeographicalComponentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reportable Geographical Components [Member]</link:label>
    <link:label id="lab_srt_ReportableGeographicalComponentsMember_label_en-US" xlink:label="lab_srt_ReportableGeographicalComponentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reportable Geographical Components [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ReportableGeographicalComponentsMember" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_ReportableGeographicalComponentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ReportableGeographicalComponentsMember" xlink:to="lab_srt_ReportableGeographicalComponentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThan20AndWithin25YearsFromBalanceSheetDate_650a4f51-2a5b-42f7-8f60-4bf2edd97a2a_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThan20AndWithin25YearsFromBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Future expected premiums to be earned, net of reinsurance, December 31, 2045</link:label>
    <link:label id="lab_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThan20AndWithin25YearsFromBalanceSheetDate_label_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThan20AndWithin25YearsFromBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Guarantee Insurance Contract, Premium Revenue to be Recognized, after Year 20 Through 25</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThan20AndWithin25YearsFromBalanceSheetDate" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThan20AndWithin25YearsFromBalanceSheetDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThan20AndWithin25YearsFromBalanceSheetDate" xlink:to="lab_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThan20AndWithin25YearsFromBalanceSheetDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember_db616ca7-185d-4b78-8d33-62f9b472b4da_terseLabel_en-US" xlink:label="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Portion at Fair Value Measurement [Member]</link:label>
    <link:label id="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Portion at Fair Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PortionAtFairValueFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:to="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceRecoverablesOnUnpaidLossesAllowance_89e4fd2d-a1c4-4d68-8546-9f50649c5642_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverablesOnUnpaidLossesAllowance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverables on Unpaid Losses, Allowance</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRecoverablesOnUnpaidLossesAllowance_label_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverablesOnUnpaidLossesAllowance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverables on Unpaid Losses, Allowance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverablesOnUnpaidLossesAllowance" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ReinsuranceRecoverablesOnUnpaidLossesAllowance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceRecoverablesOnUnpaidLossesAllowance" xlink:to="lab_us-gaap_ReinsuranceRecoverablesOnUnpaidLossesAllowance" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CededCreditRiskAxis_afe57b77-d18a-49bd-ae77-37c2a8033e8b_terseLabel_en-US" xlink:label="lab_us-gaap_CededCreditRiskAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ceded Credit Risk, Reinsurer [Axis]</link:label>
    <link:label id="lab_us-gaap_CededCreditRiskAxis_label_en-US" xlink:label="lab_us-gaap_CededCreditRiskAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurer, Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededCreditRiskAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CededCreditRiskAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CededCreditRiskAxis" xlink:to="lab_us-gaap_CededCreditRiskAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationLineItems_07220f74-4e92-4d5f-8257-9dc0c4d091bd_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Insured Financial Obligations with Credit Deterioration [Line Items]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationLineItems_label_en-US" xlink:label="lab_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Insured Financial Obligations with Credit Deterioration [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationLineItems" xlink:to="lab_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsTextBlock_13270d7c-6c42-4a20-adf7-bac723b1ce49_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Method Investments [Table Text Block]</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsTextBlock_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investments [Table Text Block]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentsTextBlock" xlink:to="lab_us-gaap_EquityMethodInvestmentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_VariableInterestEntityNonconsolidatedCarryingAmountDerivativeNetAssetsOrLiabilities_234bd6bb-4037-4921-9f94-eb622ffb8b17_terseLabel_en-US" xlink:label="lab_ambc_VariableInterestEntityNonconsolidatedCarryingAmountDerivativeNetAssetsOrLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Liabilities</link:label>
    <link:label id="lab_ambc_VariableInterestEntityNonconsolidatedCarryingAmountDerivativeNetAssetsOrLiabilities_label_en-US" xlink:label="lab_ambc_VariableInterestEntityNonconsolidatedCarryingAmountDerivativeNetAssetsOrLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity Nonconsolidated Carrying Amount Derivative Net Assets Or Liabilities</link:label>
    <link:label id="lab_ambc_VariableInterestEntityNonconsolidatedCarryingAmountDerivativeNetAssetsOrLiabilities_documentation_en-US" xlink:label="lab_ambc_VariableInterestEntityNonconsolidatedCarryingAmountDerivativeNetAssetsOrLiabilities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The net carrying amount of derivative assets or liabilities in the reporting entity's statement of financial position that relate to the entity's variable interests in Variable Interest Entities (VIEs) where the VIEs are not consolidated.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_VariableInterestEntityNonconsolidatedCarryingAmountDerivativeNetAssetsOrLiabilities" xlink:href="ambc-20240630.xsd#ambc_VariableInterestEntityNonconsolidatedCarryingAmountDerivativeNetAssetsOrLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_VariableInterestEntityNonconsolidatedCarryingAmountDerivativeNetAssetsOrLiabilities" xlink:to="lab_ambc_VariableInterestEntityNonconsolidatedCarryingAmountDerivativeNetAssetsOrLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThanOneAndWithinTwoYearsFromBalanceSheetDate_05bd8b2d-ab84-4bbe-b68f-edcbc891cca0_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThanOneAndWithinTwoYearsFromBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Future premiums expected to be collected, December 31, 2022</link:label>
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    <link:label id="lab_us-gaap_AccountsPayableCurrentAndNoncurrent_2b029a9c-23d9-4e08-8d2d-94484634655e_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Estimated Future Premium Payments Maximum Discounted Rate</link:label>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax_7b6c1a4a-acc2-43a3-b2db-8b2aa14879d8_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive income before reclassifications</link:label>
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    <link:label id="lab_us-gaap_EmployeeStockOptionMember_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Employee Stock Option</link:label>
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    <link:label id="lab_srt_MaximumMember_e3f30049-de5d-4c32-9fcf-5823352d70a7_terseLabel_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum [Member]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_srt_MaximumMember" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_MaximumMember"/>
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    <link:label id="lab_dei_DocumentType_f112c8b0-b732-45a2-a4be-1af298cd95c4_terseLabel_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
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    <link:label id="lab_us-gaap_GoodwillAcquiredDuringPeriod_a58e2846-d52b-426e-845e-b5da8326c623_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillAcquiredDuringPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill, Acquired During Period</link:label>
    <link:label id="lab_us-gaap_GoodwillAcquiredDuringPeriod_label_en-US" xlink:label="lab_us-gaap_GoodwillAcquiredDuringPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill, Acquired During Period</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTable"/>
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    <link:label id="lab_us-gaap_BenefitsLossesAndExpenses_9e23de4a-a97f-45a2-b98b-8f455f752c7e_totalLabel_en-US" xlink:label="lab_us-gaap_BenefitsLossesAndExpenses" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total expenses</link:label>
    <link:label id="lab_us-gaap_BenefitsLossesAndExpenses_0024a17d-2f35-4bf1-a37f-b9f594c781e8_terseLabel_en-US" xlink:label="lab_us-gaap_BenefitsLossesAndExpenses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Benefits, Losses and Expenses</link:label>
    <link:label id="lab_us-gaap_BenefitsLossesAndExpenses_label_en-US" xlink:label="lab_us-gaap_BenefitsLossesAndExpenses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Benefits, Losses and Expenses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BenefitsLossesAndExpenses" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_BenefitsLossesAndExpenses"/>
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    <link:label id="lab_us-gaap_CurrencySwapMember_eaddc3d8-5f44-4592-8672-905cb37aa302_terseLabel_en-US" xlink:label="lab_us-gaap_CurrencySwapMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Currency Swaps [Member]</link:label>
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    <link:label id="lab_us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount_b12ebf62-8d45-4ebf-a487-2180da38ec61_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum Exposure To Loss</link:label>
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    <link:label id="lab_us-gaap_AntidilutiveSecuritiesNameDomain_9d221614-f1e0-4b2c-9fcf-2cd5c7936021_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities, Name [Domain]</link:label>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodTax_e4385201-24a2-4fc0-b713-b2900e681caf_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized (loss) gain on securities, taxes</link:label>
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    <link:label id="lab_ambc_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition_26af567d-024a-49f9-992b-84b6b60d8778_terseLabel_en-US" xlink:label="lab_ambc_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities , Available for sale, Continuous Unrealized Loss Position,</link:label>
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    <link:label id="lab_us-gaap_ExternalCreditRatingNonInvestmentGradeMember_dbeb17a3-922d-41ac-9127-9d821ecc5ced_terseLabel_en-US" xlink:label="lab_us-gaap_ExternalCreditRatingNonInvestmentGradeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">External Credit Rating, Non Investment Grade [Member]</link:label>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleTable_d2dce80a-c07c-4829-a19f-3d37290ad743_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Available-for-sale Securities [Table]</link:label>
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    <link:label id="lab_us-gaap_OtherAssetsMember_695723b0-faae-41c7-922f-7945fcfb0a8a_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssetsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Assets [Member]</link:label>
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    <link:label id="lab_dei_EntityIncorporationStateCountryCode_label_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems"/>
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    <link:label id="lab_us-gaap_InternalCreditAssessmentDomain_003b7cae-1b21-44e0-a1dc-a121b25de7d0_terseLabel_en-US" xlink:label="lab_us-gaap_InternalCreditAssessmentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment [Domain]</link:label>
    <link:label id="lab_us-gaap_InternalCreditAssessmentDomain_label_en-US" xlink:label="lab_us-gaap_InternalCreditAssessmentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InternalCreditAssessmentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InternalCreditAssessmentDomain"/>
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    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonStockSharesOutstanding"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherInvestments"/>
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    <link:label id="lab_us-gaap_InvestmentsMember_10234772-9f2b-40bf-811e-670b4aae7f02_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments [Member]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InvestmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentsMember" xlink:to="lab_us-gaap_InvestmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoMember_terseLabel_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO</link:label>
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    <link:label id="lab_us-gaap_OtherCostAndExpenseOperating_5ce41f0a-ef7a-445b-a768-fa88089d0a0b_terseLabel_en-US" xlink:label="lab_us-gaap_OtherCostAndExpenseOperating" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Cost and Expense, Operating</link:label>
    <link:label id="lab_us-gaap_OtherCostAndExpenseOperating_label_en-US" xlink:label="lab_us-gaap_OtherCostAndExpenseOperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Cost and Expense, Operating</link:label>
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    <link:label id="lab_ambc_OtherInternationalMember_a03c4655-b47f-4bc8-990f-776d18add890_terseLabel_en-US" xlink:label="lab_ambc_OtherInternationalMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other International [Member]</link:label>
    <link:label id="lab_ambc_OtherInternationalMember_label_en-US" xlink:label="lab_ambc_OtherInternationalMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other International [Member]</link:label>
    <link:label id="lab_ambc_OtherInternationalMember_documentation_en-US" xlink:label="lab_ambc_OtherInternationalMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other international.</link:label>
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    <link:label id="lab_ambc_LossReservesClaimLiabilityMember_f759c0b9-3b37-4cd4-96fc-3f9bf18fa77d_terseLabel_en-US" xlink:label="lab_ambc_LossReservesClaimLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss Reserves [Member]</link:label>
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    <link:label id="lab_ambc_LossReservesClaimLiabilityMember_documentation_en-US" xlink:label="lab_ambc_LossReservesClaimLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loss Reserves Claim Liability [Member]</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable_127912c4-00a4-4d1e-b661-24fc2727593a_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Variable Interest Entities [Table]</link:label>
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    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_c5fafef1-20db-4b16-92f4-75f17994c926_netLabel_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Par value of common stock issued</link:label>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Par or Stated Value Per Share</link:label>
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    <link:label id="lab_ambc_UncollateralizedCreditExposureSupoortedByUnlimitedUncappedIndemnity_dc2a05b4-44fd-43d5-8553-bf1ede24b2fe_terseLabel_en-US" xlink:label="lab_ambc_UncollateralizedCreditExposureSupoortedByUnlimitedUncappedIndemnity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Uncollateralized Credit Exposure Supoorted by Unlimited Uncapped Indemnity</link:label>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_7541bcf3-c726-4ff6-ba82-4c7b1ec43a8a_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash provided by (used in) investing activities</link:label>
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    <link:label id="lab_us-gaap_InterestRateSwapMember_9ab0b5a2-5d1c-4aa4-839d-bddb038a3bb7_terseLabel_en-US" xlink:label="lab_us-gaap_InterestRateSwapMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Rate Swap [Member]</link:label>
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    <link:label id="lab_us-gaap_DebtInstrumentAxis_90d005a3-b981-468f-9592-3e9cb54bb64c_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
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    <link:label id="lab_ambc_PublicFinanceMember_documentation_en-US" xlink:label="lab_ambc_PublicFinanceMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Public Finance [Member]</link:label>
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    <link:label id="lab_us-gaap_Liabilities_0517eeca-064e-46e2-85ac-2b8c234d9400_verboseLabel_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total liabilities</link:label>
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    <link:label id="lab_us-gaap_InvestmentIncomeMember_d9cc2226-5d23-45d9-aa75-7f9f2f17b874_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net Investment Income [Member]</link:label>
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    <link:label id="lab_us-gaap_FairValueMeasurementFrequencyDomain_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementFrequencyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Frequency [Domain]</link:label>
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    <link:label id="lab_us-gaap_AssumedPremiumsEarned_aaa60059-1e17-49e0-8946-3c3f5db29718_terseLabel_en-US" xlink:label="lab_us-gaap_AssumedPremiumsEarned" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assumed Reinsurance Premiums Earned</link:label>
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    <link:label id="lab_srt_ExternalCreditRatingMoodysMember_78f27c2b-1f32-4cc5-aff0-f02b0c9a4864_terseLabel_en-US" xlink:label="lab_srt_ExternalCreditRatingMoodysMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">External Credit Rating, Moody's [Domain]</link:label>
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    <link:label id="lab_us-gaap_ContractWithCustomerReceivableAfterAllowanceForCreditLoss_34d37551-9b09-485e-b498-db328a60e4f2_terseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerReceivableAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contract with Customer, Receivable, after Allowance for Credit Loss</link:label>
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    <link:label id="lab_us-gaap_OtherLiabilities_366897d8-5954-494c-86b9-77498e19e558_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilities_60f3344d-379a-4e89-b3d7-5051cb419098_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other Liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilities_label_en-US" xlink:label="lab_us-gaap_OtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilities" xlink:to="lab_us-gaap_OtherLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock_d514e122-b145-4f92-b575-84d695aca7ea_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill and Intangible Assets Disclosure</link:label>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill and Intangible Assets Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:to="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan10AndWithin15YearsFromBalanceSheetDate_f3447b01-7791-4a6b-bbae-25cc66a562e3_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan10AndWithin15YearsFromBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Future premiums expected to be collected, December 31, 2035</link:label>
    <link:label id="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan10AndWithin15YearsFromBalanceSheetDate_label_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan10AndWithin15YearsFromBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Guarantee Insurance Contract, Premium Receivable, to be Collected, after Year 10 Through 15</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan10AndWithin15YearsFromBalanceSheetDate" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan10AndWithin15YearsFromBalanceSheetDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan10AndWithin15YearsFromBalanceSheetDate" xlink:to="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan10AndWithin15YearsFromBalanceSheetDate" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_SurveillanceCategoryOneaMember_bfdf0e35-0735-4d38-9ba6-7ad884195d82_terseLabel_en-US" xlink:label="lab_ambc_SurveillanceCategoryOneaMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">IA [Member]</link:label>
    <link:label id="lab_ambc_SurveillanceCategoryOneaMember_label_en-US" xlink:label="lab_ambc_SurveillanceCategoryOneaMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Surveillance Category Onea [Member]</link:label>
    <link:label id="lab_ambc_SurveillanceCategoryOneaMember_documentation_en-US" xlink:label="lab_ambc_SurveillanceCategoryOneaMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Surveillance Category OneA [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_SurveillanceCategoryOneaMember" xlink:href="ambc-20240630.xsd#ambc_SurveillanceCategoryOneaMember"/>
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    <link:label id="lab_us-gaap_SalvageAndSubrogationRecoveriesValue_0dd49344-24ab-4b6b-8a07-6c697f9a6791_terseLabel_en-US" xlink:label="lab_us-gaap_SalvageAndSubrogationRecoveriesValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subrogation recoverable</link:label>
    <link:label id="lab_us-gaap_SalvageAndSubrogationRecoveriesValue_dd243acd-2a23-4e94-87e6-82846f01a196_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_SalvageAndSubrogationRecoveriesValue" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Subrogation recoverable</link:label>
    <link:label id="lab_us-gaap_SalvageAndSubrogationRecoveriesValue_3fa2dd2d-8e12-47a6-bc3a-3ae27e214891_negatedLabel_en-US" xlink:label="lab_us-gaap_SalvageAndSubrogationRecoveriesValue" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Subrogation recoverable</link:label>
    <link:label id="lab_us-gaap_SalvageAndSubrogationRecoveriesValue_label_en-US" xlink:label="lab_us-gaap_SalvageAndSubrogationRecoveriesValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Salvage and Subrogation Recoveries, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SalvageAndSubrogationRecoveriesValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SalvageAndSubrogationRecoveriesValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SalvageAndSubrogationRecoveriesValue" xlink:to="lab_us-gaap_SalvageAndSubrogationRecoveriesValue" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_CapacityMarineMember_6d1870eb-9387-4664-949a-bef90b96be46_terseLabel_en-US" xlink:label="lab_ambc_CapacityMarineMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capacity Marine</link:label>
    <link:label id="lab_ambc_CapacityMarineMember_label_en-US" xlink:label="lab_ambc_CapacityMarineMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Capacity Marine [Member]</link:label>
    <link:label id="lab_ambc_CapacityMarineMember_documentation_en-US" xlink:label="lab_ambc_CapacityMarineMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Capacity Marine</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_CapacityMarineMember" xlink:href="ambc-20240630.xsd#ambc_CapacityMarineMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_CapacityMarineMember" xlink:to="lab_ambc_CapacityMarineMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock_bbd18865-eed6-4474-86e4-73af72a9aea7_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Changes in Balances of Each Component of Accumulated Other Comprehensive Income</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Accumulated Other Comprehensive Income (Loss) [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InsuranceCommissionsAndFees_768c86fe-377e-45e2-b254-c7f050000e62_terseLabel_en-US" xlink:label="lab_us-gaap_InsuranceCommissionsAndFees" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insurance Commissions and Fees</link:label>
    <link:label id="lab_us-gaap_InsuranceCommissionsAndFees_label_en-US" xlink:label="lab_us-gaap_InsuranceCommissionsAndFees" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insurance Commissions and Fees</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InsuranceCommissionsAndFees" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InsuranceCommissionsAndFees"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InsuranceCommissionsAndFees" xlink:to="lab_us-gaap_InsuranceCommissionsAndFees" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Investments_abf2bf7c-d37e-4214-929f-4c7076b84f32_totalLabel_en-US" xlink:label="lab_us-gaap_Investments" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total investments (net of allowance for credit losses of $3 and $3)</link:label>
    <link:label id="lab_us-gaap_Investments_label_en-US" xlink:label="lab_us-gaap_Investments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Investments" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_Investments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Investments" xlink:to="lab_us-gaap_Investments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems_19cbb157-5ffc-4045-9564-acf100687426_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Inputs, Assets, Quantitative Information [Line Items] (Deprecated 2018-01-31)</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems"/>
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    <link:label id="lab_us-gaap_USTreasuryAndGovernmentMember_f9139fed-c97f-48ba-a782-e8e063e9677d_terseLabel_en-US" xlink:label="lab_us-gaap_USTreasuryAndGovernmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">US Treasury and Government</link:label>
    <link:label id="lab_us-gaap_USTreasuryAndGovernmentMember_label_en-US" xlink:label="lab_us-gaap_USTreasuryAndGovernmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">US Treasury and Government [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_USTreasuryAndGovernmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_USTreasuryAndGovernmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_USTreasuryAndGovernmentMember" xlink:to="lab_us-gaap_USTreasuryAndGovernmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_PercentageOfInvestmentPortfolioValuedUsingExternalPricingServices_aba0e5d4-9356-42bb-b5a5-5cd2ff2f235e_terseLabel_en-US" xlink:label="lab_ambc_PercentageOfInvestmentPortfolioValuedUsingExternalPricingServices" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percentage of investment portfolio valued using external pricing services</link:label>
    <link:label id="lab_ambc_PercentageOfInvestmentPortfolioValuedUsingExternalPricingServices_label_en-US" xlink:label="lab_ambc_PercentageOfInvestmentPortfolioValuedUsingExternalPricingServices" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Percentage Of Investment Portfolio Valued Using External Pricing Services</link:label>
    <link:label id="lab_ambc_PercentageOfInvestmentPortfolioValuedUsingExternalPricingServices_documentation_en-US" xlink:label="lab_ambc_PercentageOfInvestmentPortfolioValuedUsingExternalPricingServices" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Percentage of investment portfolio valued using external pricing services.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_PercentageOfInvestmentPortfolioValuedUsingExternalPricingServices" xlink:href="ambc-20240630.xsd#ambc_PercentageOfInvestmentPortfolioValuedUsingExternalPricingServices"/>
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    <link:label id="lab_us-gaap_OtherPostretirementBenefitPlansDefinedBenefitMember_d71a88f2-0ff5-49a4-84a5-c743a45a15dc_terseLabel_en-US" xlink:label="lab_us-gaap_OtherPostretirementBenefitPlansDefinedBenefitMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Postretirement Benefits Plan [Member]</link:label>
    <link:label id="lab_us-gaap_OtherPostretirementBenefitPlansDefinedBenefitMember_label_en-US" xlink:label="lab_us-gaap_OtherPostretirementBenefitPlansDefinedBenefitMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Postretirement Benefits Plan [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherPostretirementBenefitPlansDefinedBenefitMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherPostretirementBenefitPlansDefinedBenefitMember"/>
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    <link:label id="lab_us-gaap_AssetBackedSecuritiesMember_339c2370-3c78-4e6b-a406-5fee9b38400a_terseLabel_en-US" xlink:label="lab_us-gaap_AssetBackedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset-backed Securities [Member]</link:label>
    <link:label id="lab_us-gaap_AssetBackedSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_AssetBackedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset-Backed Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetBackedSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssetBackedSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetBackedSecuritiesMember" xlink:to="lab_us-gaap_AssetBackedSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_OtherIncomeItems_a2821ab0-c9c9-461c-8dff-03d6f773fc49_terseLabel_en-US" xlink:label="lab_ambc_OtherIncomeItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other income Items</link:label>
    <link:label id="lab_ambc_OtherIncomeItems_label_en-US" xlink:label="lab_ambc_OtherIncomeItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other income Items</link:label>
    <link:label id="lab_ambc_OtherIncomeItems_documentation_en-US" xlink:label="lab_ambc_OtherIncomeItems" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other income Items</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_OtherIncomeItems" xlink:href="ambc-20240630.xsd#ambc_OtherIncomeItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_OtherIncomeItems" xlink:to="lab_ambc_OtherIncomeItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_281bd48f-861a-47b9-a46c-640a5ab95a3c_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Operating Activities, Total</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Operating Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities"/>
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    <link:label id="lab_ambc_DebtSecuritiesAvailableForSaleUnrealizedLossMeasuredAsAPercentOfAmortizedCost_2d6a15ed-f594-46c2-8517-a0003d3ece66_terseLabel_en-US" xlink:label="lab_ambc_DebtSecuritiesAvailableForSaleUnrealizedLossMeasuredAsAPercentOfAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities Available for Sale Unrealized Loss Measured as a Percent of Amortized Cost</link:label>
    <link:label id="lab_ambc_DebtSecuritiesAvailableForSaleUnrealizedLossMeasuredAsAPercentOfAmortizedCost_label_en-US" xlink:label="lab_ambc_DebtSecuritiesAvailableForSaleUnrealizedLossMeasuredAsAPercentOfAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities Available for Sale Unrealized Loss Measured as a Percent of Amortized Cost</link:label>
    <link:label id="lab_ambc_DebtSecuritiesAvailableForSaleUnrealizedLossMeasuredAsAPercentOfAmortizedCost_documentation_en-US" xlink:label="lab_ambc_DebtSecuritiesAvailableForSaleUnrealizedLossMeasuredAsAPercentOfAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities Available for Sale Unrealized Loss Measured as a Percent of Amortized Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_DebtSecuritiesAvailableForSaleUnrealizedLossMeasuredAsAPercentOfAmortizedCost" xlink:href="ambc-20240630.xsd#ambc_DebtSecuritiesAvailableForSaleUnrealizedLossMeasuredAsAPercentOfAmortizedCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_DebtSecuritiesAvailableForSaleUnrealizedLossMeasuredAsAPercentOfAmortizedCost" xlink:to="lab_ambc_DebtSecuritiesAvailableForSaleUnrealizedLossMeasuredAsAPercentOfAmortizedCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementClassOfStockAxis_e05defba-7653-4785-af56-d7a35dfcae91_terseLabel_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementClassOfStockAxis_label_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementClassOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementClassOfStockAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementClassOfStockAxis" xlink:to="lab_us-gaap_StatementClassOfStockAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_UnsecuredReinsuranceRecoverables_ea35fd69-228a-4395-91ad-418581097bc1_terseLabel_en-US" xlink:label="lab_ambc_UnsecuredReinsuranceRecoverables" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unsecured Reinsurance Recoverables</link:label>
    <link:label id="lab_ambc_UnsecuredReinsuranceRecoverables_label_en-US" xlink:label="lab_ambc_UnsecuredReinsuranceRecoverables" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unsecured Reinsurance Recoverables</link:label>
    <link:label id="lab_ambc_UnsecuredReinsuranceRecoverables_documentation_en-US" xlink:label="lab_ambc_UnsecuredReinsuranceRecoverables" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents reinsurance recoverables on paid and unpaid losses and deferred ceded premiums, net of ceded premiums payables due to reinsurers, letters of credit, and collateral posted for the benefit of the cedant.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_UnsecuredReinsuranceRecoverables" xlink:href="ambc-20240630.xsd#ambc_UnsecuredReinsuranceRecoverables"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_UnsecuredReinsuranceRecoverables" xlink:to="lab_ambc_UnsecuredReinsuranceRecoverables" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntitiesTable_53a8a3ca-caf5-477d-b48a-09280193a4a1_terseLabel_en-US" xlink:label="lab_dei_EntitiesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entities [Table]</link:label>
    <link:label id="lab_dei_EntitiesTable_label_en-US" xlink:label="lab_dei_EntitiesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entities [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntitiesTable" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntitiesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntitiesTable" xlink:to="lab_dei_EntitiesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompRecoveryTable_terseLabel_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery</link:label>
    <link:label id="lab_ecd_ErrCompRecoveryTable_label_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompRecoveryTable" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_ErrCompRecoveryTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompRecoveryTable" xlink:to="lab_ecd_ErrCompRecoveryTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_InsuranceLinkedMember_d4e9dd81-fd0d-45c3-aaf4-e75f1f5570a0_terseLabel_en-US" xlink:label="lab_ambc_InsuranceLinkedMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insurance Linked [Member]</link:label>
    <link:label id="lab_ambc_InsuranceLinkedMember_label_en-US" xlink:label="lab_ambc_InsuranceLinkedMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insurance Linked [Member]</link:label>
    <link:label id="lab_ambc_InsuranceLinkedMember_documentation_en-US" xlink:label="lab_ambc_InsuranceLinkedMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Insurance Linked [Member] [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_InsuranceLinkedMember" xlink:href="ambc-20240630.xsd#ambc_InsuranceLinkedMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_InsuranceLinkedMember" xlink:to="lab_ambc_InsuranceLinkedMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherOperatingIncomeExpenseNet_8812d77c-bee6-4c05-b06f-547d2187f1c5_terseLabel_en-US" xlink:label="lab_us-gaap_OtherOperatingIncomeExpenseNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Operating Income (Expense), Net</link:label>
    <link:label id="lab_us-gaap_OtherOperatingIncomeExpenseNet_label_en-US" xlink:label="lab_us-gaap_OtherOperatingIncomeExpenseNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Operating Income (Expense), Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherOperatingIncomeExpenseNet" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherOperatingIncomeExpenseNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherOperatingIncomeExpenseNet" xlink:to="lab_us-gaap_OtherOperatingIncomeExpenseNet" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_AwardTmgHowMnpiCnsdrdTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:to="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_ScheduleOfEarningsPerShareLineItems_b45983dc-cfae-43c0-9001-85cb871e5369_terseLabel_en-US" xlink:label="lab_ambc_ScheduleOfEarningsPerShareLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule Of Earnings Per Share [Line Items]</link:label>
    <link:label id="lab_ambc_ScheduleOfEarningsPerShareLineItems_label_en-US" xlink:label="lab_ambc_ScheduleOfEarningsPerShareLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule Of Earnings Per Share [Line Items]</link:label>
    <link:label id="lab_ambc_ScheduleOfEarningsPerShareLineItems_documentation_en-US" xlink:label="lab_ambc_ScheduleOfEarningsPerShareLineItems" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule Of Earnings Per Share [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_ScheduleOfEarningsPerShareLineItems" xlink:href="ambc-20240630.xsd#ambc_ScheduleOfEarningsPerShareLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_ScheduleOfEarningsPerShareLineItems" xlink:to="lab_ambc_ScheduleOfEarningsPerShareLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeAssetAmountNotOffsetAgainstCollateral_f007ff8b-2a1a-4325-a7da-61cfa249bd1f_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeAssetAmountNotOffsetAgainstCollateral" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Asset, Fair Value, Amount Not Offset Against Collateral</link:label>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeAssetAmountNotOffsetAgainstCollateral_label_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeAssetAmountNotOffsetAgainstCollateral" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject to Master Netting Arrangement, before Offset of Collateral</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeFairValueOfDerivativeAssetAmountNotOffsetAgainstCollateral" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeFairValueOfDerivativeAssetAmountNotOffsetAgainstCollateral"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeFairValueOfDerivativeAssetAmountNotOffsetAgainstCollateral" xlink:to="lab_us-gaap_DerivativeFairValueOfDerivativeAssetAmountNotOffsetAgainstCollateral" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityInformationLineItems_f18dd999-b64e-43c8-862a-049ae4c8971c_terseLabel_en-US" xlink:label="lab_dei_EntityInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Information [Line Items]</link:label>
    <link:label id="lab_dei_EntityInformationLineItems_label_en-US" xlink:label="lab_dei_EntityInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Information [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityInformationLineItems" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityInformationLineItems" xlink:to="lab_dei_EntityInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PostemploymentBenefitsAbstract_label_en-US" xlink:label="lab_us-gaap_PostemploymentBenefitsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Postemployment Benefits [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PostemploymentBenefitsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PostemploymentBenefitsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PostemploymentBenefitsAbstract" xlink:to="lab_us-gaap_PostemploymentBenefitsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedGain_e528da1c-d02c-497b-bc32-6688f7c74e70_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedGain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-sale, Realized Gain</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedGain_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedGain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Realized Gain</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleRealizedGain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtSecuritiesAvailableForSaleRealizedGain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleRealizedGain" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedGain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NotesReceivableNet_ecc59b36-892f-4134-9495-64a5424d95e5_terseLabel_en-US" xlink:label="lab_us-gaap_NotesReceivableNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, after Allowance for Credit Loss</link:label>
    <link:label id="lab_us-gaap_NotesReceivableNet_2b41761c-c643-4e1c-9ced-8a916fad7cff_verboseLabel_en-US" xlink:label="lab_us-gaap_NotesReceivableNet" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Loans</link:label>
    <link:label id="lab_us-gaap_NotesReceivableNet_label_en-US" xlink:label="lab_us-gaap_NotesReceivableNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, after Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NotesReceivableNet" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NotesReceivableNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NotesReceivableNet" xlink:to="lab_us-gaap_NotesReceivableNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumReceivableProceedsFromPremiumsReceived_3dece860-561a-4e66-8efa-2571d774a0c2_negatedLabel_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumReceivableProceedsFromPremiumsReceived" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Premium receipts</link:label>
    <link:label id="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumReceivableProceedsFromPremiumsReceived_label_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumReceivableProceedsFromPremiumsReceived" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Guarantee Insurance Contracts, Premium Receivable, Proceeds from Premiums Received</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialGuaranteeInsuranceContractsPremiumReceivableProceedsFromPremiumsReceived" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancialGuaranteeInsuranceContractsPremiumReceivableProceedsFromPremiumsReceived"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialGuaranteeInsuranceContractsPremiumReceivableProceedsFromPremiumsReceived" xlink:to="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumReceivableProceedsFromPremiumsReceived" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidationItemsAxis_6c38f8bf-a5c3-4891-8338-118e57cf634e_terseLabel_en-US" xlink:label="lab_srt_ConsolidationItemsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidation Items [Axis]</link:label>
    <link:label id="lab_srt_ConsolidationItemsAxis_label_en-US" xlink:label="lab_srt_ConsolidationItemsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation Items [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsAxis" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_ConsolidationItemsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidationItemsAxis" xlink:to="lab_srt_ConsolidationItemsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_NumberOfReinsurersCoveringMajority_809dffd4-25c1-4572-9e6e-944c2b510f3f_terseLabel_en-US" xlink:label="lab_ambc_NumberOfReinsurersCoveringMajority" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of Reinsurers Covering Majority</link:label>
    <link:label id="lab_ambc_NumberOfReinsurersCoveringMajority_label_en-US" xlink:label="lab_ambc_NumberOfReinsurersCoveringMajority" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Reinsurers Covering Majority</link:label>
    <link:label id="lab_ambc_NumberOfReinsurersCoveringMajority_documentation_en-US" xlink:label="lab_ambc_NumberOfReinsurersCoveringMajority" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number of Reinsurers Covering Majority</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_NumberOfReinsurersCoveringMajority" xlink:href="ambc-20240630.xsd#ambc_NumberOfReinsurersCoveringMajority"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_NumberOfReinsurersCoveringMajority" xlink:to="lab_ambc_NumberOfReinsurersCoveringMajority" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillImpairmentLoss_e1e83ce0-56c0-4105-998a-293e2d49cfe5_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillImpairmentLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill, Impairment Loss</link:label>
    <link:label id="lab_us-gaap_GoodwillImpairmentLoss_label_en-US" xlink:label="lab_us-gaap_GoodwillImpairmentLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill, Impairment Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillImpairmentLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_GoodwillImpairmentLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillImpairmentLoss" xlink:to="lab_us-gaap_GoodwillImpairmentLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerLiabilityRevenueRecognized_410cb0e1-3b77-4d2d-9abf-e762e88b9ecf_terseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiabilityRevenueRecognized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contract with Customer, Liability, Revenue Recognized</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerLiabilityRevenueRecognized_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiabilityRevenueRecognized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract with Customer, Liability, Revenue Recognized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerLiabilityRevenueRecognized" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ContractWithCustomerLiabilityRevenueRecognized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerLiabilityRevenueRecognized" xlink:to="lab_us-gaap_ContractWithCustomerLiabilityRevenueRecognized" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Foreign Currency Transaction and Translation Adjustment, Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_DeterminationDateDomain_4deaf539-00ca-4e5b-80e3-6a3b2877eecc_terseLabel_en-US" xlink:label="lab_ambc_DeterminationDateDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Determination Date [Domain]</link:label>
    <link:label id="lab_ambc_DeterminationDateDomain_label_en-US" xlink:label="lab_ambc_DeterminationDateDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Determination Date [Domain]</link:label>
    <link:label id="lab_ambc_DeterminationDateDomain_documentation_en-US" xlink:label="lab_ambc_DeterminationDateDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">[Domain] for Determination Date [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_DeterminationDateDomain" xlink:href="ambc-20240630.xsd#ambc_DeterminationDateDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_DeterminationDateDomain" xlink:to="lab_ambc_DeterminationDateDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_ProvisionforIncomeTaxesTable_4e48121d-b5de-416d-9dcd-9dd0fa0475fe_terseLabel_en-US" xlink:label="lab_ambc_ProvisionforIncomeTaxesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Provision for Income Taxes [Table]</link:label>
    <link:label id="lab_ambc_ProvisionforIncomeTaxesTable_label_en-US" xlink:label="lab_ambc_ProvisionforIncomeTaxesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Provision for Income Taxes [Table]</link:label>
    <link:label id="lab_ambc_ProvisionforIncomeTaxesTable_documentation_en-US" xlink:label="lab_ambc_ProvisionforIncomeTaxesTable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Provision for Income Taxes [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_ProvisionforIncomeTaxesTable" xlink:href="ambc-20240630.xsd#ambc_ProvisionforIncomeTaxesTable"/>
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    <link:label id="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThanFourAndWithinFiveYearsFromBalanceSheetDate_d2b87760-7814-4daf-a422-973276b2d303_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThanFourAndWithinFiveYearsFromBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Future premiums expected to be collected, December 31, 2025</link:label>
    <link:label id="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThanFourAndWithinFiveYearsFromBalanceSheetDate_label_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThanFourAndWithinFiveYearsFromBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Guarantee Insurance Contract, Premium Receivable, to be Collected, Year Five</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThanFourAndWithinFiveYearsFromBalanceSheetDate" xlink:to="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThanFourAndWithinFiveYearsFromBalanceSheetDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedGainLossFinancialLiabilityFairValueOptionIncludingPortionAttributableToNoncontrollingInterestMember_cc2dabca-d828-42d2-8ca7-38959cab4e75_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedGainLossFinancialLiabilityFairValueOptionIncludingPortionAttributableToNoncontrollingInterestMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Gain (Loss), Financial Liability, Fair Value Option, Including Portion Attributable to Noncontrolling Interest [Member]</link:label>
    <link:label id="lab_us-gaap_AccumulatedGainLossFinancialLiabilityFairValueOptionIncludingPortionAttributableToNoncontrollingInterestMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedGainLossFinancialLiabilityFairValueOptionIncludingPortionAttributableToNoncontrollingInterestMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Gain (Loss), Financial Liability, Fair Value Option, Including Portion Attributable to Noncontrolling Interest [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedGainLossFinancialLiabilityFairValueOptionIncludingPortionAttributableToNoncontrollingInterestMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccumulatedGainLossFinancialLiabilityFairValueOptionIncludingPortionAttributableToNoncontrollingInterestMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedGainLossFinancialLiabilityFairValueOptionIncludingPortionAttributableToNoncontrollingInterestMember" xlink:to="lab_us-gaap_AccumulatedGainLossFinancialLiabilityFairValueOptionIncludingPortionAttributableToNoncontrollingInterestMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationTable_3d1f226b-b9d2-4f13-882a-23f9ec88c3a1_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Insured Financial Obligations with Credit Deterioration [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Insured Financial Obligations with Credit Deterioration [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationTable" xlink:to="lab_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestment90DaysPastDueAndStillAccruing_c9389741-ef19-446a-ada0-5aec4bc98cb0_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestment90DaysPastDueAndStillAccruing" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, 90 Days or More Past Due, Still Accruing</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestment90DaysPastDueAndStillAccruing_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestment90DaysPastDueAndStillAccruing" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, 90 Days or More Past Due, Still Accruing</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableRecordedInvestment90DaysPastDueAndStillAccruing" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancingReceivableRecordedInvestment90DaysPastDueAndStillAccruing"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableRecordedInvestment90DaysPastDueAndStillAccruing" xlink:to="lab_us-gaap_FinancingReceivableRecordedInvestment90DaysPastDueAndStillAccruing" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesIssued_c3380e2d-2110-4272-8fa9-0b5737192da5_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Issued</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PreferredStockSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesIssued" xlink:to="lab_us-gaap_PreferredStockSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_BusinessDisposalLifeOfWarrantsIssuedInConnectionWithAACDisposal_9b9643b0-c0fa-4275-a31e-ea9686168a27_terseLabel_en-US" xlink:label="lab_ambc_BusinessDisposalLifeOfWarrantsIssuedInConnectionWithAACDisposal" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Disposal, Life of Warrants Issued in Connection with AAC Disposal</link:label>
    <link:label id="lab_ambc_BusinessDisposalLifeOfWarrantsIssuedInConnectionWithAACDisposal_label_en-US" xlink:label="lab_ambc_BusinessDisposalLifeOfWarrantsIssuedInConnectionWithAACDisposal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Disposal, Life of Warrants Issued in Connection with AAC Disposal</link:label>
    <link:label id="lab_ambc_BusinessDisposalLifeOfWarrantsIssuedInConnectionWithAACDisposal_documentation_en-US" xlink:label="lab_ambc_BusinessDisposalLifeOfWarrantsIssuedInConnectionWithAACDisposal" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Disposal, Life of Warrants Issued in Connection with AAC Disposal</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_BusinessDisposalLifeOfWarrantsIssuedInConnectionWithAACDisposal" xlink:href="ambc-20240630.xsd#ambc_BusinessDisposalLifeOfWarrantsIssuedInConnectionWithAACDisposal"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_BusinessDisposalLifeOfWarrantsIssuedInConnectionWithAACDisposal" xlink:to="lab_ambc_BusinessDisposalLifeOfWarrantsIssuedInConnectionWithAACDisposal" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_aaf3cfdf-6247-4bb9-bced-a26af1f279f6_terseLabel_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_label_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityEmergingGrowthCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityEmergingGrowthCompany" xlink:to="lab_dei_EntityEmergingGrowthCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_country_GB_cdae5e3b-e052-4c83-b452-96c8e361df1e_terseLabel_en-US" xlink:label="lab_country_GB" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">United Kingdom [Member]</link:label>
    <link:label id="lab_country_GB_label_en-US" xlink:label="lab_country_GB" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">UNITED KINGDOM</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_country_GB" xlink:href="https://xbrl.sec.gov/country/2023/country-2023.xsd#country_GB"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_country_GB" xlink:to="lab_country_GB" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill_65cff1e6-db7c-48da-a734-80c74511c8e8_terseLabel_en-US" xlink:label="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible assets, less accumulated amortization</link:label>
    <link:label id="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill_label_en-US" xlink:label="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Assets, Net (Excluding Goodwill)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IntangibleAssetsNetExcludingGoodwill"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:to="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumReceivablePremiumExpectedToBeCollected_5c0d1a12-3e55-418a-ad6e-0bfd9edd8c43_totalLabel_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumReceivablePremiumExpectedToBeCollected" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Future premiums expected to be collected, Total</link:label>
    <link:label id="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumReceivablePremiumExpectedToBeCollected_label_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumReceivablePremiumExpectedToBeCollected" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Guarantee Insurance Contracts, Premium Receivable, Premium Expected to be Collected</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialGuaranteeInsuranceContractsPremiumReceivablePremiumExpectedToBeCollected" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancialGuaranteeInsuranceContractsPremiumReceivablePremiumExpectedToBeCollected"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialGuaranteeInsuranceContractsPremiumReceivablePremiumExpectedToBeCollected" xlink:to="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumReceivablePremiumExpectedToBeCollected" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_OtherStructuredFinanceMember_82a45efb-a67a-455a-962a-71f2a77a8a86_terseLabel_en-US" xlink:label="lab_ambc_OtherStructuredFinanceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Structured Finance [Member]</link:label>
    <link:label id="lab_ambc_OtherStructuredFinanceMember_label_en-US" xlink:label="lab_ambc_OtherStructuredFinanceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Structured Finance [Member]</link:label>
    <link:label id="lab_ambc_OtherStructuredFinanceMember_documentation_en-US" xlink:label="lab_ambc_OtherStructuredFinanceMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Structured Finance [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_OtherStructuredFinanceMember" xlink:href="ambc-20240630.xsd#ambc_OtherStructuredFinanceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_OtherStructuredFinanceMember" xlink:to="lab_ambc_OtherStructuredFinanceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateFundsMember_4fe9b3ee-0056-4996-b031-88376ab77f19_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateFundsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate Funds</link:label>
    <link:label id="lab_us-gaap_RealEstateFundsMember_label_en-US" xlink:label="lab_us-gaap_RealEstateFundsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Funds [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateFundsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RealEstateFundsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateFundsMember" xlink:to="lab_us-gaap_RealEstateFundsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_NoncontrollingInterestPolicyPolicyTextBlock_896a7373-51f9-4b44-ae96-697a05c17e9d_terseLabel_en-US" xlink:label="lab_ambc_NoncontrollingInterestPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest Policy</link:label>
    <link:label id="lab_ambc_NoncontrollingInterestPolicyPolicyTextBlock_label_en-US" xlink:label="lab_ambc_NoncontrollingInterestPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest Policy [Policy Text Block]</link:label>
    <link:label id="lab_ambc_NoncontrollingInterestPolicyPolicyTextBlock_documentation_en-US" xlink:label="lab_ambc_NoncontrollingInterestPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest Policy</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_NoncontrollingInterestPolicyPolicyTextBlock" xlink:href="ambc-20240630.xsd#ambc_NoncontrollingInterestPolicyPolicyTextBlock"/>
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    <link:label id="lab_ecd_PvpTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure, Table</link:label>
    <link:label id="lab_ecd_PvpTableTextBlock_label_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_PvpTableTextBlock"/>
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    <link:label id="lab_us-gaap_OtherInvestmentNotReadilyMarketableFairValue_d6dbf8d7-43f2-4f27-a3a2-8be53bc1c2f2_terseLabel_en-US" xlink:label="lab_us-gaap_OtherInvestmentNotReadilyMarketableFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Investment Not Readily Marketable, Fair Value</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherInvestmentNotReadilyMarketableFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherInvestmentNotReadilyMarketableFairValue"/>
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    <link:label id="lab_ambc_DocumentAndEntityInformationAbstract_771526b2-4fcd-4104-8ca6-59f19656c241_terseLabel_en-US" xlink:label="lab_ambc_DocumentAndEntityInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document And Entity Information [Abstract]</link:label>
    <link:label id="lab_ambc_DocumentAndEntityInformationAbstract_label_en-US" xlink:label="lab_ambc_DocumentAndEntityInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document And Entity Information [Abstract]</link:label>
    <link:label id="lab_ambc_DocumentAndEntityInformationAbstract_documentation_en-US" xlink:label="lab_ambc_DocumentAndEntityInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Document and Entity Information [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_DocumentAndEntityInformationAbstract" xlink:href="ambc-20240630.xsd#ambc_DocumentAndEntityInformationAbstract"/>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax_5327c5ec-2fc5-4bf8-b5f9-c631a353d1ab_totalLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total other comprehensive income (loss), net of income tax</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherComprehensiveIncomeLossNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_69db583e-31ae-4c13-b2f7-e6d621efc85c_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementOfCashFlowsAbstract"/>
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    <link:label id="lab_us-gaap_AssetsAbstract_073d0fdc-65ed-4837-a8e8-6bb3641ae564_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets:</link:label>
    <link:label id="lab_us-gaap_AssetsAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsAbstract" xlink:to="lab_us-gaap_AssetsAbstract" xlink:type="arc" order="1"/>
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    <link:label id="lab_ambc_MarineMember_6be21671-6f39-42b8-a618-6f44eeb15698_terseLabel_en-US" xlink:label="lab_ambc_MarineMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Marine</link:label>
    <link:label id="lab_ambc_MarineMember_label_en-US" xlink:label="lab_ambc_MarineMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Marine [Member]</link:label>
    <link:label id="lab_ambc_MarineMember_documentation_en-US" xlink:label="lab_ambc_MarineMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Marine</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_MarineMember" xlink:href="ambc-20240630.xsd#ambc_MarineMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_MarineMember" xlink:to="lab_ambc_MarineMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseIncurredClaims1_29cd8ece-e86b-405a-9096-0421540c237a_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseIncurredClaims1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liability for Unpaid Claims and Claims Adjustment Expense, Incurred Claims</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseIncurredClaims1" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseIncurredClaims1"/>
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    <link:label id="lab_ambc_BusinessDisposalTerminationFee_a877770d-2bef-4e3f-8665-741732bebe5d_terseLabel_en-US" xlink:label="lab_ambc_BusinessDisposalTerminationFee" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Disposal, Termination Fee</link:label>
    <link:label id="lab_ambc_BusinessDisposalTerminationFee_label_en-US" xlink:label="lab_ambc_BusinessDisposalTerminationFee" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Disposal, Termination Fee</link:label>
    <link:label id="lab_ambc_BusinessDisposalTerminationFee_documentation_en-US" xlink:label="lab_ambc_BusinessDisposalTerminationFee" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Disposal, Termination Fee</link:label>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue_e185406d-504d-4877-bbf7-a8012d5882a3_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Estimated Fair Value, Due after ten years</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Fair Value, Maturity, Allocated and Single Maturity Date, after Year 10</link:label>
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    <link:label id="lab_us-gaap_ForeignCurrencyTransactionGainLossBeforeTax_045b3534-a457-49f0-baf7-74bee5bd9649_verboseLabel_en-US" xlink:label="lab_us-gaap_ForeignCurrencyTransactionGainLossBeforeTax" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Foreign Currency Transaction Gain (Loss), before Tax</link:label>
    <link:label id="lab_us-gaap_ForeignCurrencyTransactionGainLossBeforeTax_51c9110c-095d-4c86-bf18-938229c26962_terseLabel_en-US" xlink:label="lab_us-gaap_ForeignCurrencyTransactionGainLossBeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign exchange (losses) gains</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignCurrencyTransactionGainLossBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ForeignCurrencyTransactionGainLossBeforeTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ForeignCurrencyTransactionGainLossBeforeTax" xlink:to="lab_us-gaap_ForeignCurrencyTransactionGainLossBeforeTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation_8ff5dd0a-62ad-4d48-b161-7f8ba2fe494a_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Tax payments related to shares withheld for share-based compensation plans</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation"/>
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    <link:label id="lab_us-gaap_LiabilitiesAbstract_ac052624-cdc3-4e2d-a9e1-87520dc50764_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities:</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LiabilitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAbstract" xlink:to="lab_us-gaap_LiabilitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherThanTemporaryImpairmentCreditLossesRecognizedInEarningsLineItems_540cb27a-8b0a-448f-b95c-887a87181284_terseLabel_en-US" xlink:label="lab_us-gaap_OtherThanTemporaryImpairmentCreditLossesRecognizedInEarningsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other than Temporary Impairment, Credit Losses Recognized in Earnings [Line Items]</link:label>
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    <link:label id="lab_ambc_InterestRateSwapOneMember_cdf31079-ee98-4fcb-a8b1-c63e7869dce5_terseLabel_en-US" xlink:label="lab_ambc_InterestRateSwapOneMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Rate Swaps-Pay-Fixed/Receive-Variable [Member]</link:label>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_28af0055-4637-4028-9aa9-36776cac04bf_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash used in financing activities</link:label>
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    <link:label id="lab_us-gaap_RetirementPlanTypeAxis_c7d80326-6e25-4abf-8b00-56f8606b1189_terseLabel_en-US" xlink:label="lab_us-gaap_RetirementPlanTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Retirement Plan Type [Axis]</link:label>
    <link:label id="lab_us-gaap_RetirementPlanTypeAxis_label_en-US" xlink:label="lab_us-gaap_RetirementPlanTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retirement Plan Type [Axis]</link:label>
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    <link:label id="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities_a529ae9d-3692-40f5-805b-aa0a875726e1_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Other, net</link:label>
    <link:label id="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities_label_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments for (Proceeds from) Other Investing Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PaymentsForProceedsFromOtherInvestingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:to="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireInterestInSubsidiariesAndAffiliates_322097bb-a342-4762-8d01-60a071130540_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireInterestInSubsidiariesAndAffiliates" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payments to Acquire Interest in Subsidiaries and Affiliates</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireInterestInSubsidiariesAndAffiliates_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireInterestInSubsidiariesAndAffiliates" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Interest in Subsidiaries and Affiliates</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireInterestInSubsidiariesAndAffiliates" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PaymentsToAcquireInterestInSubsidiariesAndAffiliates"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireInterestInSubsidiariesAndAffiliates" xlink:to="lab_us-gaap_PaymentsToAcquireInterestInSubsidiariesAndAffiliates" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired_534e95ff-e47e-490d-821e-c2d4da68da0a_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Acquisition, Percentage of Voting Interests Acquired</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Acquisition, Percentage of Voting Interests Acquired</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired"/>
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    <link:label id="lab_us-gaap_RetainedEarningsMember_8a1ad4d8-8217-4dfb-8a06-49f027199630_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Retained Earnings [Member]</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsMember_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RetainedEarningsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsMember" xlink:to="lab_us-gaap_RetainedEarningsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InsuredFinancialObligationsWithCreditDeteriorationRemainingWeightedAverageContractPeriod_c8fbce9f-35c5-42ab-878d-caa2d94f793c_terseLabel_en-US" xlink:label="lab_us-gaap_InsuredFinancialObligationsWithCreditDeteriorationRemainingWeightedAverageContractPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Remaining weighted-average contract period (in years)</link:label>
    <link:label id="lab_us-gaap_InsuredFinancialObligationsWithCreditDeteriorationRemainingWeightedAverageContractPeriod_label_en-US" xlink:label="lab_us-gaap_InsuredFinancialObligationsWithCreditDeteriorationRemainingWeightedAverageContractPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insured Financial Obligations with Credit Deterioration, Remaining Weighted Average Contract Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InsuredFinancialObligationsWithCreditDeteriorationRemainingWeightedAverageContractPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InsuredFinancialObligationsWithCreditDeteriorationRemainingWeightedAverageContractPeriod"/>
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    <link:label id="lab_us-gaap_FixedIncomeInvestmentsMember_8dcc1420-2c34-4f3e-901b-5db99612fc9b_terseLabel_en-US" xlink:label="lab_us-gaap_FixedIncomeInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fixed Income Investments [Member]</link:label>
    <link:label id="lab_us-gaap_FixedIncomeInvestmentsMember_label_en-US" xlink:label="lab_us-gaap_FixedIncomeInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Income Investments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FixedIncomeInvestmentsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FixedIncomeInvestmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FixedIncomeInvestmentsMember" xlink:to="lab_us-gaap_FixedIncomeInvestmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote</link:label>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_AdjToNonPeoNeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:to="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_DeferredCededPremiumsAndReinsuranceRecoverables_f768e8be-c86f-4dc1-ab1c-79b56d436598_terseLabel_en-US" xlink:label="lab_ambc_DeferredCededPremiumsAndReinsuranceRecoverables" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred Ceded Premiums And Reinsurance Recoverables</link:label>
    <link:label id="lab_ambc_DeferredCededPremiumsAndReinsuranceRecoverables_label_en-US" xlink:label="lab_ambc_DeferredCededPremiumsAndReinsuranceRecoverables" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Ceded Premiums And Reinsurance Recoverables</link:label>
    <link:label id="lab_ambc_DeferredCededPremiumsAndReinsuranceRecoverables_documentation_en-US" xlink:label="lab_ambc_DeferredCededPremiumsAndReinsuranceRecoverables" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Includes the unexpired portion of financial guarantee premiums ceded on policies as of the balance sheet date and reinsurance recoverables on claims or claim adjustment expense paid by the ceding insurer.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_DeferredCededPremiumsAndReinsuranceRecoverables" xlink:href="ambc-20240630.xsd#ambc_DeferredCededPremiumsAndReinsuranceRecoverables"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_DeferredCededPremiumsAndReinsuranceRecoverables" xlink:to="lab_ambc_DeferredCededPremiumsAndReinsuranceRecoverables" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ExternalCreditRatingByGroupingDomain_5b78e4b2-9810-4d2b-ac65-416a9fa843b6_terseLabel_en-US" xlink:label="lab_us-gaap_ExternalCreditRatingByGroupingDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">External Credit Rating by Grouping [Domain]</link:label>
    <link:label id="lab_us-gaap_ExternalCreditRatingByGroupingDomain_label_en-US" xlink:label="lab_us-gaap_ExternalCreditRatingByGroupingDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">External Credit Rating by Grouping [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ExternalCreditRatingByGroupingDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ExternalCreditRatingByGroupingDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ExternalCreditRatingByGroupingDomain" xlink:to="lab_us-gaap_ExternalCreditRatingByGroupingDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_723693ea-6610-42ac-89a3-54a6ac6f29b7_verboseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_a88b2c60-25eb-482b-a81c-c03c61c39e5a_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EarningsPerShareBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareBasic" xlink:to="lab_us-gaap_EarningsPerShareBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_9ba0ed6e-505e-47ae-a2a5-38f501fc9a4f_terseLabel_en-US" xlink:label="lab_us-gaap_AccountingPoliciesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounting Policies [Abstract]</link:label>
    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_label_en-US" xlink:label="lab_us-gaap_AccountingPoliciesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounting Policies [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountingPoliciesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccountingPoliciesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountingPoliciesAbstract" xlink:to="lab_us-gaap_AccountingPoliciesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis</link:label>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_label_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompAnalysisTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_ErrCompAnalysisTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompAnalysisTextBlock" xlink:to="lab_ecd_ErrCompAnalysisTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_XchangeMember_2abe8359-4eff-49f0-bfd3-e29e0bc56dfc_terseLabel_en-US" xlink:label="lab_ambc_XchangeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Xchange</link:label>
    <link:label id="lab_ambc_XchangeMember_label_en-US" xlink:label="lab_ambc_XchangeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Xchange [Member]</link:label>
    <link:label id="lab_ambc_XchangeMember_documentation_en-US" xlink:label="lab_ambc_XchangeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Xchange</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_XchangeMember" xlink:href="ambc-20240630.xsd#ambc_XchangeMember"/>
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    <link:label id="lab_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccounts_16a29582-24d7-40d0-8b69-2442a96a45dd_terseLabel_en-US" xlink:label="lab_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccounts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Premium Receivable, Allowance for Credit Loss</link:label>
    <link:label id="lab_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccounts_eafaf56c-5185-4273-b520-90485828d250_verboseLabel_en-US" xlink:label="lab_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccounts" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Uncollectable premium receivables</link:label>
    <link:label id="lab_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccounts_label_en-US" xlink:label="lab_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccounts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Premium Receivable, Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccounts" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PremiumsReceivableAllowanceForDoubtfulAccounts"/>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossFinancialLiabilityFairValueOptionUnrealizedGainLossArisingDuringPeriodTax_825b42e0-4003-45dc-966c-2abd0e14e89c_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossFinancialLiabilityFairValueOptionUnrealizedGainLossArisingDuringPeriodTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Financial Liability, Fair Value Option, Unrealized Gain (Loss) Arising During Period, Tax</link:label>
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    <link:label id="lab_us-gaap_PrivateEquityFundsMember_31e4ffff-eba8-4937-b673-f7fa4376ccab_terseLabel_en-US" xlink:label="lab_us-gaap_PrivateEquityFundsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Private Equity Funds [Member]</link:label>
    <link:label id="lab_us-gaap_PrivateEquityFundsMember_label_en-US" xlink:label="lab_us-gaap_PrivateEquityFundsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Private Equity Funds [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrivateEquityFundsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PrivateEquityFundsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PrivateEquityFundsMember" xlink:to="lab_us-gaap_PrivateEquityFundsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnDerivativeInstrumentsMember_e3fd0d6a-9b9a-4851-b757-07b3c87d0028_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnDerivativeInstrumentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Derivative Instruments [Member]</link:label>
    <link:label id="lab_us-gaap_GainLossOnDerivativeInstrumentsMember_label_en-US" xlink:label="lab_us-gaap_GainLossOnDerivativeInstrumentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Derivative Instruments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnDerivativeInstrumentsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_GainLossOnDerivativeInstrumentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnDerivativeInstrumentsMember" xlink:to="lab_us-gaap_GainLossOnDerivativeInstrumentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableInterestEntityActivityBetweenVIEAndEntityOperatingIncomeOrLoss_403c0ba7-d402-4ba0-bd1b-dece2e394a3f_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityActivityBetweenVIEAndEntityOperatingIncomeOrLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income (loss) on variable interest entities</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityActivityBetweenVIEAndEntityOperatingIncomeOrLoss_1baeb45b-581d-409c-9655-687e51334d71_negatedLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityActivityBetweenVIEAndEntityOperatingIncomeOrLoss" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Variable interest entity activities</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityActivityBetweenVIEAndEntityOperatingIncomeOrLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_VariableInterestEntityActivityBetweenVIEAndEntityOperatingIncomeOrLoss"/>
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    <link:label id="lab_us-gaap_AvailableforsaleSecuritiesMember_a912e438-d61c-4b38-91cf-6e7e7f3533ab_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableforsaleSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fixed Income Investments [Member]</link:label>
    <link:label id="lab_us-gaap_AvailableforsaleSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_AvailableforsaleSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Available-for-Sale Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableforsaleSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AvailableforsaleSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableforsaleSecuritiesMember" xlink:to="lab_us-gaap_AvailableforsaleSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssumedPremiumsWritten_4b35f7fa-bfc1-4a23-9c0d-acbcff765343_terseLabel_en-US" xlink:label="lab_us-gaap_AssumedPremiumsWritten" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assumed Reinsurance Premiums Written</link:label>
    <link:label id="lab_us-gaap_AssumedPremiumsWritten_label_en-US" xlink:label="lab_us-gaap_AssumedPremiumsWritten" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assumed Premiums Written</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssumedPremiumsWritten" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssumedPremiumsWritten"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssumedPremiumsWritten" xlink:to="lab_us-gaap_AssumedPremiumsWritten" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxesPaid_2a456d54-1c4b-48a4-bcbb-ab5583b0a59f_verboseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaid" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Income Taxes Paid</link:label>
    <link:label id="lab_us-gaap_IncomeTaxesPaid_label_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Taxes Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxesPaid" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncomeTaxesPaid"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxesPaid" xlink:to="lab_us-gaap_IncomeTaxesPaid" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_13b52b72-75e2-4369-95e7-c8dbc77fda27_terseLabel_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidation, Policy</link:label>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation, Policy [Policy Text Block]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:to="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentTransitionReport_e7beee37-f3cc-4cf0-866d-4f5b02d940db_terseLabel_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Ex Transition Period</link:label>
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    <link:label id="lab_us-gaap_InterestExpenseMember_b65bef34-97e8-4df3-bea3-2353f0dbc818_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseMember_label_en-US" xlink:label="lab_us-gaap_InterestExpenseMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InterestExpenseMember"/>
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    <link:label id="lab_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccountsPeriodIncreaseDecrease_273939e8-23bb-4996-b814-856869ec6145_terseLabel_en-US" xlink:label="lab_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccountsPeriodIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Uncollectable premiums</link:label>
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    <link:label id="lab_us-gaap_OtherThanTemporaryImpairmentCreditLossesRecognizedInEarningsCategoriesOfInvestmentsDomain_3c3c31ff-f314-4794-a027-0869fd10b043_terseLabel_en-US" xlink:label="lab_us-gaap_OtherThanTemporaryImpairmentCreditLossesRecognizedInEarningsCategoriesOfInvestmentsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Security Category [Domain]</link:label>
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    <link:label id="lab_us-gaap_InvestmentIncomeTextBlock_e2902f29-d782-4537-b336-9f455f0ddc07_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Net Investment Income</link:label>
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    <link:label id="lab_ambc_SurveillanceCategoryFourMember_541b66c1-6618-4ab1-b92f-e0bef3bf99d8_terseLabel_en-US" xlink:label="lab_ambc_SurveillanceCategoryFourMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">IV [Member]</link:label>
    <link:label id="lab_ambc_SurveillanceCategoryFourMember_label_en-US" xlink:label="lab_ambc_SurveillanceCategoryFourMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Surveillance Category Four [Member]</link:label>
    <link:label id="lab_ambc_SurveillanceCategoryFourMember_documentation_en-US" xlink:label="lab_ambc_SurveillanceCategoryFourMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Surveillance category four.</link:label>
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    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_592313c2-6ea7-469c-a236-14e9d1bca6b0_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instrument [Axis]</link:label>
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    <link:label id="lab_us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments_53e87aad-67e6-4f44-baee-3fb2e04f1f9c_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverable for Unpaid Claims and Claims Adjustments</link:label>
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    <link:label id="lab_us-gaap_FairValueByLiabilityClassAxis_fb9f0e05-8e32-4232-b72b-2b1d94f7d1c5_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByLiabilityClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liability Class [Axis]</link:label>
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    <link:label id="lab_ecd_AllTradingArrangementsMember_terseLabel_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Trading Arrangements</link:label>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost_779a9a75-86f5-44a4-9707-097642885cc8_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortized Cost, Due in one year or less</link:label>
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    <link:label id="lab_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccountsWriteOffsAgainstAllowance_71a5a284-94be-4bf2-ac3d-df28320cf79f_terseLabel_en-US" xlink:label="lab_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccountsWriteOffsAgainstAllowance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Premium Receivable, Allowance for Credit Loss, Writeoff</link:label>
    <link:label id="lab_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccountsWriteOffsAgainstAllowance_label_en-US" xlink:label="lab_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccountsWriteOffsAgainstAllowance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Premium Receivable, Allowance for Credit Loss, Writeoff</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccountsWriteOffsAgainstAllowance" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PremiumsReceivableAllowanceForDoubtfulAccountsWriteOffsAgainstAllowance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccountsWriteOffsAgainstAllowance" xlink:to="lab_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccountsWriteOffsAgainstAllowance" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssets_20b1600c-ba56-4790-9dd5-687659826221_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative assets</link:label>
    <link:label id="lab_us-gaap_DerivativeAssets_9cbaa109-a84a-470f-826b-362aa62a1bea_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net Amounts of Assets Presented in the Consolidated Balance Sheet, Derivative Assets</link:label>
    <link:label id="lab_us-gaap_DerivativeAssets_label_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssets" xlink:to="lab_us-gaap_DerivativeAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredIncomeTaxExpenseBenefit_a4703794-272d-4c83-b7e4-43f22883035c_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred Income Tax Expense (Benefit)</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DeferredIncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventTypeAxis_7b2cfb6a-78c2-4664-a48c-dd88b6e41466_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Catastrophic Event [Axis]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTypeAxis_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SubsequentEventTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTypeAxis" xlink:to="lab_us-gaap_SubsequentEventTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PremiumsWrittenGross_284d66df-bce8-466b-b7e9-4fcf20ffb78a_terseLabel_en-US" xlink:label="lab_us-gaap_PremiumsWrittenGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Premiums Written, Gross</link:label>
    <link:label id="lab_us-gaap_PremiumsWrittenGross_label_en-US" xlink:label="lab_us-gaap_PremiumsWrittenGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Premiums Written, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumsWrittenGross" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PremiumsWrittenGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PremiumsWrittenGross" xlink:to="lab_us-gaap_PremiumsWrittenGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan20AndWithin25YearsFromBalanceSheetDate_d46971d1-a752-4687-ad7d-36aa7e200a5f_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan20AndWithin25YearsFromBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Future premiums expected to be collected, December 31, 2045</link:label>
    <link:label id="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan20AndWithin25YearsFromBalanceSheetDate_label_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan20AndWithin25YearsFromBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Guarantee Insurance Contract, Premium Receivable, to be Collected, after Year 20 Through 25</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan20AndWithin25YearsFromBalanceSheetDate" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan20AndWithin25YearsFromBalanceSheetDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan20AndWithin25YearsFromBalanceSheetDate" xlink:to="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan20AndWithin25YearsFromBalanceSheetDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock_2cbf2f01-e208-4815-b590-0789c9c49b34_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Gross Fair Values of Individual Derivative Instruments</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Derivatives Instruments Statements of Financial Performance and Financial Position, Location [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_PWICMember_eb5bd574-2eeb-49f0-9936-c8f8e664c005_terseLabel_en-US" xlink:label="lab_ambc_PWICMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PWIC</link:label>
    <link:label id="lab_ambc_PWICMember_label_en-US" xlink:label="lab_ambc_PWICMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PWIC [Member]</link:label>
    <link:label id="lab_ambc_PWICMember_documentation_en-US" xlink:label="lab_ambc_PWICMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">PWIC</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_PWICMember" xlink:href="ambc-20240630.xsd#ambc_PWICMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_PWICMember" xlink:to="lab_ambc_PWICMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThan15AndWithin20YearsFromBalanceSheetDate_03d0e1d4-63d4-429c-ad58-c1c571ba7a5d_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThan15AndWithin20YearsFromBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Future expected premiums to be earned, net of reinsurance, December 31, 2040</link:label>
    <link:label id="lab_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThan15AndWithin20YearsFromBalanceSheetDate_label_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThan15AndWithin20YearsFromBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Guarantee Insurance Contract, Premium Revenue to be Recognized, after Year 15 Through 20</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThan15AndWithin20YearsFromBalanceSheetDate" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThan15AndWithin20YearsFromBalanceSheetDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThan15AndWithin20YearsFromBalanceSheetDate" xlink:to="lab_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThan15AndWithin20YearsFromBalanceSheetDate" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_NumberOfConsolidatedVariableInterestEntities_5e2b91c0-21a1-4766-b0ad-1e49d94be2ee_terseLabel_en-US" xlink:label="lab_ambc_NumberOfConsolidatedVariableInterestEntities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number Of Consolidated Variable Interest Entities</link:label>
    <link:label id="lab_ambc_NumberOfConsolidatedVariableInterestEntities_label_en-US" xlink:label="lab_ambc_NumberOfConsolidatedVariableInterestEntities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number Of Consolidated Variable Interest Entities</link:label>
    <link:label id="lab_ambc_NumberOfConsolidatedVariableInterestEntities_documentation_en-US" xlink:label="lab_ambc_NumberOfConsolidatedVariableInterestEntities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number of consolidated variable interest entities.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_NumberOfConsolidatedVariableInterestEntities" xlink:href="ambc-20240630.xsd#ambc_NumberOfConsolidatedVariableInterestEntities"/>
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    <link:label id="lab_us-gaap_OtherAssets_0bd0ba8a-09af-4d04-8de4-9505a312fde8_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_us-gaap_OtherAssets_label_en-US" xlink:label="lab_us-gaap_OtherAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssets" xlink:to="lab_us-gaap_OtherAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_FairValueInputsCouponRate_9fe17cf8-ce0a-47e8-a91c-99d569d0f8eb_verboseLabel_en-US" xlink:label="lab_ambc_FairValueInputsCouponRate" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Coupon rate</link:label>
    <link:label id="lab_ambc_FairValueInputsCouponRate_2b1d608d-5450-4e3d-b503-e6d15bc6920e_terseLabel_en-US" xlink:label="lab_ambc_FairValueInputsCouponRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Inputs Coupon Rate</link:label>
    <link:label id="lab_ambc_FairValueInputsCouponRate_label_en-US" xlink:label="lab_ambc_FairValueInputsCouponRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Inputs Coupon Rate</link:label>
    <link:label id="lab_ambc_FairValueInputsCouponRate_documentation_en-US" xlink:label="lab_ambc_FairValueInputsCouponRate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair value inputs coupon rate.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_FairValueInputsCouponRate" xlink:href="ambc-20240630.xsd#ambc_FairValueInputsCouponRate"/>
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    <link:label id="lab_ambc_LongTermDebtUnpaidPrincipalBalance_a74550f0-636d-4d00-b168-90de55c09e42_terseLabel_en-US" xlink:label="lab_ambc_LongTermDebtUnpaidPrincipalBalance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long Term Debt Unpaid Principal Balance</link:label>
    <link:label id="lab_ambc_LongTermDebtUnpaidPrincipalBalance_label_en-US" xlink:label="lab_ambc_LongTermDebtUnpaidPrincipalBalance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long Term Debt Unpaid Principal Balance</link:label>
    <link:label id="lab_ambc_LongTermDebtUnpaidPrincipalBalance_documentation_en-US" xlink:label="lab_ambc_LongTermDebtUnpaidPrincipalBalance" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">This represents the amount of principal outstanding on long-term debt that is presented on the balance sheet at fair value, whether such presentation is as a separate caption or parenthetical disclosure.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_LongTermDebtUnpaidPrincipalBalance" xlink:href="ambc-20240630.xsd#ambc_LongTermDebtUnpaidPrincipalBalance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_LongTermDebtUnpaidPrincipalBalance" xlink:to="lab_ambc_LongTermDebtUnpaidPrincipalBalance" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_StandardPoorsAPlusRatingMember_ec4a3e8b-8917-4cc4-9d15-2bded08a8bca_terseLabel_en-US" xlink:label="lab_srt_StandardPoorsAPlusRatingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Standard &amp; Poor's, A+ Rating</link:label>
    <link:label id="lab_srt_StandardPoorsAPlusRatingMember_label_en-US" xlink:label="lab_srt_StandardPoorsAPlusRatingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Standard &amp; Poor's, A+ Rating [Member]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_StandardPoorsAPlusRatingMember" xlink:to="lab_srt_StandardPoorsAPlusRatingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_BusinessCombinationVolumeWeightedAveragePrice_30e0425d-d498-4b2d-9978-af01bc245424_terseLabel_en-US" xlink:label="lab_ambc_BusinessCombinationVolumeWeightedAveragePrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Volume Weighted Average Price</link:label>
    <link:label id="lab_ambc_BusinessCombinationVolumeWeightedAveragePrice_label_en-US" xlink:label="lab_ambc_BusinessCombinationVolumeWeightedAveragePrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Volume Weighted Average Price</link:label>
    <link:label id="lab_ambc_BusinessCombinationVolumeWeightedAveragePrice_documentation_en-US" xlink:label="lab_ambc_BusinessCombinationVolumeWeightedAveragePrice" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Volume Weighted Average Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_BusinessCombinationVolumeWeightedAveragePrice" xlink:href="ambc-20240630.xsd#ambc_BusinessCombinationVolumeWeightedAveragePrice"/>
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    <link:label id="lab_ambc_GlobalStructuredFinanceMember_caf4ac77-ad18-4548-aeab-5df39c235e51_terseLabel_en-US" xlink:label="lab_ambc_GlobalStructuredFinanceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Global Structured Finance [Member]</link:label>
    <link:label id="lab_ambc_GlobalStructuredFinanceMember_label_en-US" xlink:label="lab_ambc_GlobalStructuredFinanceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Global Structured Finance [Member]</link:label>
    <link:label id="lab_ambc_GlobalStructuredFinanceMember_documentation_en-US" xlink:label="lab_ambc_GlobalStructuredFinanceMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Global structured finance.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_GlobalStructuredFinanceMember" xlink:href="ambc-20240630.xsd#ambc_GlobalStructuredFinanceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_GlobalStructuredFinanceMember" xlink:to="lab_ambc_GlobalStructuredFinanceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentPeriodEndDate_bd00090b-015e-4817-be00-08b08f0f1d4b_terseLabel_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Period End Date</link:label>
    <link:label id="lab_dei_DocumentPeriodEndDate_label_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Period End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentPeriodEndDate" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_DocumentPeriodEndDate"/>
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    <link:label id="lab_ambc_ScheduleofIncomeBeforeIncomeTaxDomesticandForeignTable_f321f1f2-4c70-4ea3-8c1d-549ab000c11e_terseLabel_en-US" xlink:label="lab_ambc_ScheduleofIncomeBeforeIncomeTaxDomesticandForeignTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Income Before Income Tax, Domestic and Foreign [Table]</link:label>
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    <link:label id="lab_ecd_TrdArrAdoptionDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrAdoptionDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adoption Date</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrAdoptionDate" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_TrdArrAdoptionDate"/>
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    <link:label id="lab_ambc_LossReservesCededToReinsurers_1b9f59da-1693-44b6-b5ab-fc1abc54e979_verboseLabel_en-US" xlink:label="lab_ambc_LossReservesCededToReinsurers" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Losses and loss expense reserves ceded to reinsurers</link:label>
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    <link:label id="lab_ambc_LossReservesCededToReinsurers_label_en-US" xlink:label="lab_ambc_LossReservesCededToReinsurers" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Reserves Ceded To Reinsurers</link:label>
    <link:label id="lab_ambc_LossReservesCededToReinsurers_documentation_en-US" xlink:label="lab_ambc_LossReservesCededToReinsurers" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The known and estimated amount recoverable as of the balance sheet date from reinsurers for claims expected to be paid or incurred by the ceding insurer.</link:label>
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    <link:label id="lab_ambc_BusinessCombinationConsiderationPaidInCash_b2834a4e-4287-4105-8953-a1e18ca68e4c_terseLabel_en-US" xlink:label="lab_ambc_BusinessCombinationConsiderationPaidInCash" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Paid in Cash</link:label>
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    <link:label id="lab_ambc_FairValueofSecuritiesDepositedinConnectionwtihLetterofCredit_bc5be289-8f88-4aab-b19e-f4f4b787553f_terseLabel_en-US" xlink:label="lab_ambc_FairValueofSecuritiesDepositedinConnectionwtihLetterofCredit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value of Securities Deposited in Connection wtih Letter of Credit</link:label>
    <link:label id="lab_ambc_FairValueofSecuritiesDepositedinConnectionwtihLetterofCredit_label_en-US" xlink:label="lab_ambc_FairValueofSecuritiesDepositedinConnectionwtihLetterofCredit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value of Securities Deposited in Connection wtih Letter of Credit</link:label>
    <link:label id="lab_ambc_FairValueofSecuritiesDepositedinConnectionwtihLetterofCredit_documentation_en-US" xlink:label="lab_ambc_FairValueofSecuritiesDepositedinConnectionwtihLetterofCredit" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value of Securities Deposited in Connection wtih Letter of Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_FairValueofSecuritiesDepositedinConnectionwtihLetterofCredit" xlink:href="ambc-20240630.xsd#ambc_FairValueofSecuritiesDepositedinConnectionwtihLetterofCredit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_FairValueofSecuritiesDepositedinConnectionwtihLetterofCredit" xlink:to="lab_ambc_FairValueofSecuritiesDepositedinConnectionwtihLetterofCredit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DirectPremiumsWritten_46d25bf4-2aaf-492c-9dc1-d2a5e22db871_terseLabel_en-US" xlink:label="lab_us-gaap_DirectPremiumsWritten" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Direct Premiums Written</link:label>
    <link:label id="lab_us-gaap_DirectPremiumsWritten_label_en-US" xlink:label="lab_us-gaap_DirectPremiumsWritten" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Direct Premiums Written</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DirectPremiumsWritten" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DirectPremiumsWritten"/>
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    <link:label id="lab_us-gaap_TreasuryStockCommonMember_8838b44b-c85e-4317-9474-0a6236b6bda1_terseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Treasury Stock, Common</link:label>
    <link:label id="lab_us-gaap_TreasuryStockCommonMember_label_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Common [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockCommonMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TreasuryStockCommonMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockCommonMember" xlink:to="lab_us-gaap_TreasuryStockCommonMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeMember_5ef9e939-a004-4d58-885b-1c73fab7d8d3_terseLabel_en-US" xlink:label="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reclassification out of Accumulated Other Comprehensive Income [Member]</link:label>
    <link:label id="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeMember_label_en-US" xlink:label="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reclassification out of Accumulated Other Comprehensive Income [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeMember"/>
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    <link:label id="lab_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationStatementOfFinancialPositionReinsuranceRecoverable_0e4e2e68-a710-4131-97e3-d584e1c04279_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationStatementOfFinancialPositionReinsuranceRecoverable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance recoverable reported on Balance Sheet</link:label>
    <link:label id="lab_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationStatementOfFinancialPositionReinsuranceRecoverable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationStatementOfFinancialPositionReinsuranceRecoverable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Insured Financial Obligations with Credit Deterioration, Statement of Financial Position, Reinsurance Recoverable</link:label>
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    <link:label id="lab_ambc_Tier2NotesMember_fc397a38-fedf-46e4-baf9-a08be2993588_terseLabel_en-US" xlink:label="lab_ambc_Tier2NotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tier 2 Notes</link:label>
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    <link:label id="lab_ambc_Tier2NotesMember_documentation_en-US" xlink:label="lab_ambc_Tier2NotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Tier 2 Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_Tier2NotesMember" xlink:href="ambc-20240630.xsd#ambc_Tier2NotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_Tier2NotesMember" xlink:to="lab_ambc_Tier2NotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_BusinessDisposalWarrantStrikePriceInConnectionWithDisposal_c7509fd8-1cae-4275-bd95-7268762c5c1e_terseLabel_en-US" xlink:label="lab_ambc_BusinessDisposalWarrantStrikePriceInConnectionWithDisposal" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Disposal, Warrant Strike Price in Connection with Disposal</link:label>
    <link:label id="lab_ambc_BusinessDisposalWarrantStrikePriceInConnectionWithDisposal_label_en-US" xlink:label="lab_ambc_BusinessDisposalWarrantStrikePriceInConnectionWithDisposal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Disposal, Warrant Strike Price in Connection with Disposal</link:label>
    <link:label id="lab_ambc_BusinessDisposalWarrantStrikePriceInConnectionWithDisposal_documentation_en-US" xlink:label="lab_ambc_BusinessDisposalWarrantStrikePriceInConnectionWithDisposal" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Disposal, Warrant Strike Price in Connection with Disposal</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_BusinessDisposalWarrantStrikePriceInConnectionWithDisposal" xlink:href="ambc-20240630.xsd#ambc_BusinessDisposalWarrantStrikePriceInConnectionWithDisposal"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_BusinessDisposalWarrantStrikePriceInConnectionWithDisposal" xlink:to="lab_ambc_BusinessDisposalWarrantStrikePriceInConnectionWithDisposal" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationInsuredContractualPaymentsOutstandingPrincipal_b9228d36-77c6-46ac-b752-387ee893ee6e_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationInsuredContractualPaymentsOutstandingPrincipal" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Principal</link:label>
    <link:label id="lab_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationInsuredContractualPaymentsOutstandingPrincipal_label_en-US" xlink:label="lab_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationInsuredContractualPaymentsOutstandingPrincipal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Insured Financial Obligations with Credit Deterioration, Insured Contractual Payments Outstanding, Principal</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationInsuredContractualPaymentsOutstandingPrincipal" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationInsuredContractualPaymentsOutstandingPrincipal"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationInsuredContractualPaymentsOutstandingPrincipal" xlink:to="lab_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationInsuredContractualPaymentsOutstandingPrincipal" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LossContingenciesByNatureOfContingencyAxis_1cae71b0-59fa-423d-a094-327e7941d5cc_terseLabel_en-US" xlink:label="lab_us-gaap_LossContingenciesByNatureOfContingencyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss Contingency Nature [Axis]</link:label>
    <link:label id="lab_us-gaap_LossContingenciesByNatureOfContingencyAxis_label_en-US" xlink:label="lab_us-gaap_LossContingenciesByNatureOfContingencyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingency Nature [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingenciesByNatureOfContingencyAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LossContingenciesByNatureOfContingencyAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LossContingenciesByNatureOfContingencyAxis" xlink:to="lab_us-gaap_LossContingenciesByNatureOfContingencyAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_cbf2450f-1646-43e6-a3b4-7fec51b40364_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Provision for income taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_292687ee-d51f-40ac-86af-8f4828feff77_verboseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Expense (Benefit)</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_9ab6f731-159f-4009-9afa-feae7ac09c87_negatedLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Income tax expense (benefit)</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncomeTaxExpenseBenefit"/>
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    <link:label id="lab_us-gaap_InterestIncomeDebtSecuritiesAvailableForSaleOperating_fd5bca92-4bfe-4047-9e5d-43d8807d682a_terseLabel_en-US" xlink:label="lab_us-gaap_InterestIncomeDebtSecuritiesAvailableForSaleOperating" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Income, Debt Securities, Available-for-Sale, Operating</link:label>
    <link:label id="lab_us-gaap_InterestIncomeDebtSecuritiesAvailableForSaleOperating_label_en-US" xlink:label="lab_us-gaap_InterestIncomeDebtSecuritiesAvailableForSaleOperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Income, Debt Securities, Available-for-Sale, Operating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestIncomeDebtSecuritiesAvailableForSaleOperating" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InterestIncomeDebtSecuritiesAvailableForSaleOperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestIncomeDebtSecuritiesAvailableForSaleOperating" xlink:to="lab_us-gaap_InterestIncomeDebtSecuritiesAvailableForSaleOperating" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_InsuranceLineItems_0e03ff08-82ff-4ef8-a460-d969714af8e8_terseLabel_en-US" xlink:label="lab_ambc_InsuranceLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insurance [Line Items]</link:label>
    <link:label id="lab_ambc_InsuranceLineItems_label_en-US" xlink:label="lab_ambc_InsuranceLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insurance [Line Items]</link:label>
    <link:label id="lab_ambc_InsuranceLineItems_documentation_en-US" xlink:label="lab_ambc_InsuranceLineItems" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Insurance [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_InsuranceLineItems" xlink:href="ambc-20240630.xsd#ambc_InsuranceLineItems"/>
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    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_f40c10a5-c9ae-4094-aec9-75d1d2d93151_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurements</link:label>
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    <link:label id="lab_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThanFiveAndWithin10YearsFromBalanceSheetDate_4235a330-9904-403d-9dce-6c2d15087005_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThanFiveAndWithin10YearsFromBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Future expected premiums to be earned, net of reinsurance, December 31, 2030</link:label>
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    <link:label id="lab_us-gaap_EquityAbstract_a32bbf61-37f9-48b9-935b-f35af106d7e3_terseLabel_en-US" xlink:label="lab_us-gaap_EquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity [Abstract]</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationGrossClaimLiability_4e899107-0699-425d-a213-61731c694137_totalLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationGrossClaimLiability" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Gross claim liability before all subrogation and before reinsurance</link:label>
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    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_377f5103-dbbc-4aa2-a251-d6eb02e90809_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents, at Carrying Value</link:label>
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    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_62c0ea0f-1476-41e1-a5da-ea21f59868af_totalLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total comprehensive income (loss), net of income tax</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossPensionAndOtherPostretirementBenefitPlansPlanAmendmentsTaxEffect" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossPensionAndOtherPostretirementBenefitPlansPlanAmendmentsTaxEffect" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_ComponentsofLossandLossExpenseReservesandSubrogationRecoverableTable_2be8804c-82c9-4885-8142-7ba482d36ada_terseLabel_en-US" xlink:label="lab_ambc_ComponentsofLossandLossExpenseReservesandSubrogationRecoverableTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Components of Loss and Loss Expense Reserves and Subrogation Recoverable [Table]</link:label>
    <link:label id="lab_ambc_ComponentsofLossandLossExpenseReservesandSubrogationRecoverableTable_label_en-US" xlink:label="lab_ambc_ComponentsofLossandLossExpenseReservesandSubrogationRecoverableTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Components of Loss and Loss Expense Reserves and Subrogation Recoverable [Table]</link:label>
    <link:label id="lab_ambc_ComponentsofLossandLossExpenseReservesandSubrogationRecoverableTable_documentation_en-US" xlink:label="lab_ambc_ComponentsofLossandLossExpenseReservesandSubrogationRecoverableTable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Components of Loss and Loss Expense Reserves and Subrogation Recoverable [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_ComponentsofLossandLossExpenseReservesandSubrogationRecoverableTable" xlink:href="ambc-20240630.xsd#ambc_ComponentsofLossandLossExpenseReservesandSubrogationRecoverableTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_ComponentsofLossandLossExpenseReservesandSubrogationRecoverableTable" xlink:to="lab_ambc_ComponentsofLossandLossExpenseReservesandSubrogationRecoverableTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral_dd3cbce1-a5fd-4cd4-8140-2bcf211edfa4_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Asset, Fair Value, Amount Offset Against Collateral</link:label>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral_label_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Including Not Subject to Master Netting Arrangement, after Offset and Deduction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral" xlink:to="lab_us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_CompActuallyPaidVsOtherMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ExternalCreditRatingInvestmentGradeMember_a3423c2c-fec1-476d-97fa-c34d7d65cfbc_terseLabel_en-US" xlink:label="lab_us-gaap_ExternalCreditRatingInvestmentGradeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">External Credit Rating, Investment Grade</link:label>
    <link:label id="lab_us-gaap_ExternalCreditRatingInvestmentGradeMember_label_en-US" xlink:label="lab_us-gaap_ExternalCreditRatingInvestmentGradeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">External Credit Rating, Investment Grade [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ExternalCreditRatingInvestmentGradeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ExternalCreditRatingInvestmentGradeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ExternalCreditRatingInvestmentGradeMember" xlink:to="lab_us-gaap_ExternalCreditRatingInvestmentGradeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestRateContractMember_96e156f7-3715-474e-bda5-2fca984a24b2_terseLabel_en-US" xlink:label="lab_us-gaap_InterestRateContractMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Rate Contract [Member]</link:label>
    <link:label id="lab_us-gaap_InterestRateContractMember_label_en-US" xlink:label="lab_us-gaap_InterestRateContractMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Contract [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestRateContractMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InterestRateContractMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestRateContractMember" xlink:to="lab_us-gaap_InterestRateContractMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationReductionsOfGrossClaimLiabilityOtherSubrogation_11557f94-1978-45b9-accd-897431cee8cc_negatedTotalLabel_en-US" xlink:label="lab_ambc_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationReductionsOfGrossClaimLiabilityOtherSubrogation" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xml:lang="en-US">Discounted other subrogation, before reinsurance</link:label>
    <link:label id="lab_ambc_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationReductionsOfGrossClaimLiabilityOtherSubrogation_label_en-US" xlink:label="lab_ambc_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationReductionsOfGrossClaimLiabilityOtherSubrogation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule Of Insured Financial Obligations With Credit Deterioration Reductions Of Gross Claim Liability Other Subrogation</link:label>
    <link:label id="lab_ambc_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationReductionsOfGrossClaimLiabilityOtherSubrogation_documentation_en-US" xlink:label="lab_ambc_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationReductionsOfGrossClaimLiabilityOtherSubrogation" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">This element represents the reduction to gross claim liability for subrogation on insured financial obligations with credit deterioration, excluding the reduction to gross claim liability for subrogation on insured RMBS financial obligations with credit deterioration.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationReductionsOfGrossClaimLiabilityOtherSubrogation" xlink:href="ambc-20240630.xsd#ambc_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationReductionsOfGrossClaimLiabilityOtherSubrogation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationReductionsOfGrossClaimLiabilityOtherSubrogation" xlink:to="lab_ambc_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationReductionsOfGrossClaimLiabilityOtherSubrogation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock_b1acda2b-d395-4b68-8fae-242660f57efd_terseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contract with Customer, Contract Asset, Contract Liability, and Receivable</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract with Customer, Contract Asset, Contract Liability, and Receivable [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock" xlink:to="lab_us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyAndCasualtyCommercialInsuranceProductLineMember_22d79ab3-e880-46fd-981a-023bae880809_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyAndCasualtyCommercialInsuranceProductLineMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property and Casualty, Commercial Insurance</link:label>
    <link:label id="lab_us-gaap_PropertyAndCasualtyCommercialInsuranceProductLineMember_label_en-US" xlink:label="lab_us-gaap_PropertyAndCasualtyCommercialInsuranceProductLineMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property and Casualty, Commercial Insurance [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyAndCasualtyCommercialInsuranceProductLineMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PropertyAndCasualtyCommercialInsuranceProductLineMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyAndCasualtyCommercialInsuranceProductLineMember" xlink:to="lab_us-gaap_PropertyAndCasualtyCommercialInsuranceProductLineMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerTextBlock_80dba0e6-4ade-491a-af90-92388a297944_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerTextBlock_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RevenueFromContractWithCustomerTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:to="lab_us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_5f193bc0-a3fa-47ab-8e7f-546b323654ce_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional Paid-in Capital [Member]</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid-in Capital [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AdditionalPaidInCapitalMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:to="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustmentAbstract_3ad2a8d1-d2aa-4627-84a5-eb207b6c49fe_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustmentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effect of potential dilutive shares:</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustmentAbstract_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustmentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Diluted, Adjustment [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustmentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustmentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustmentAbstract" xlink:to="lab_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustmentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_PresentValueofExpectedNetCashFlowsRecoveriesMember_b2c8790c-768c-438c-9832-d9aa249d29c0_terseLabel_en-US" xlink:label="lab_ambc_PresentValueofExpectedNetCashFlowsRecoveriesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Present Value of Expected Net Cash Flows-Recoveries [Member]</link:label>
    <link:label id="lab_ambc_PresentValueofExpectedNetCashFlowsRecoveriesMember_label_en-US" xlink:label="lab_ambc_PresentValueofExpectedNetCashFlowsRecoveriesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Present Value of Expected Net Cash Flows-Recoveries [Member]</link:label>
    <link:label id="lab_ambc_PresentValueofExpectedNetCashFlowsRecoveriesMember_documentation_en-US" xlink:label="lab_ambc_PresentValueofExpectedNetCashFlowsRecoveriesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Recoveries [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_PresentValueofExpectedNetCashFlowsRecoveriesMember" xlink:href="ambc-20240630.xsd#ambc_PresentValueofExpectedNetCashFlowsRecoveriesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_PresentValueofExpectedNetCashFlowsRecoveriesMember" xlink:to="lab_ambc_PresentValueofExpectedNetCashFlowsRecoveriesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BalanceSheetLocationAxis_05e8dc5e-fd8b-4af0-989c-28273df70e11_terseLabel_en-US" xlink:label="lab_us-gaap_BalanceSheetLocationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Balance Sheet Location [Axis]</link:label>
    <link:label id="lab_us-gaap_BalanceSheetLocationAxis_label_en-US" xlink:label="lab_us-gaap_BalanceSheetLocationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Balance Sheet Location [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BalanceSheetLocationAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_BalanceSheetLocationAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BalanceSheetLocationAxis" xlink:to="lab_us-gaap_BalanceSheetLocationAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNiRealizedGainLoss_1297e273-bd89-4308-9ff6-0c541719f3b3_terseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNiRealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Securities, FV-NI, Realized Gain (Loss)</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNiRealizedGainLoss_label_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNiRealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities, FV-NI, Realized Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesFvNiRealizedGainLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EquitySecuritiesFvNiRealizedGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquitySecuritiesFvNiRealizedGainLoss" xlink:to="lab_us-gaap_EquitySecuritiesFvNiRealizedGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RestatementAxis_5a4ce144-165c-4cb5-b0a2-c9f4a5d343a4_terseLabel_en-US" xlink:label="lab_srt_RestatementAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement [Axis]</link:label>
    <link:label id="lab_srt_RestatementAxis_label_en-US" xlink:label="lab_srt_RestatementAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revision of Prior Period [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RestatementAxis" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_RestatementAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RestatementAxis" xlink:to="lab_srt_RestatementAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InsuranceCommissions_7251dfab-4b8a-4a16-a3d5-ec87b4f4fdeb_terseLabel_en-US" xlink:label="lab_us-gaap_InsuranceCommissions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insurance Commissions</link:label>
    <link:label id="lab_us-gaap_InsuranceCommissions_label_en-US" xlink:label="lab_us-gaap_InsuranceCommissions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insurance Commissions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InsuranceCommissions" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InsuranceCommissions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InsuranceCommissions" xlink:to="lab_us-gaap_InsuranceCommissions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DirectPremiumsEarned_514d973c-10cf-4492-9dd7-80006c1feed4_terseLabel_en-US" xlink:label="lab_us-gaap_DirectPremiumsEarned" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Direct Premiums Earned</link:label>
    <link:label id="lab_us-gaap_DirectPremiumsEarned_label_en-US" xlink:label="lab_us-gaap_DirectPremiumsEarned" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Direct Premiums Earned</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DirectPremiumsEarned" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DirectPremiumsEarned"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DirectPremiumsEarned" xlink:to="lab_us-gaap_DirectPremiumsEarned" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_PreferredStockParOrStatedValuePerShare_76c0dc21-daa4-4009-8670-1c060a5e7464_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, par value</link:label>
    <link:label id="lab_us-gaap_PreferredStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Par or Stated Value Per Share</link:label>
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    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Recurring and Nonrecurring [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable"/>
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    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeLiability_bae3dc01-616b-41c7-8506-6578b5a4b6b7_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative liabilities</link:label>
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    <link:label id="lab_us-gaap_ForeignCurrencyAbstract_40fc3156-546b-4bf6-be4e-027de93dcc06_terseLabel_en-US" xlink:label="lab_us-gaap_ForeignCurrencyAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign Currency [Abstract]</link:label>
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    <link:label id="lab_us-gaap_ReinsurancePayable_8b74cc0d-8d20-40db-9462-9bfa0e5b5ac1_verboseLabel_en-US" xlink:label="lab_us-gaap_ReinsurancePayable" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Ceded premiums payable</link:label>
    <link:label id="lab_us-gaap_ReinsurancePayable_7d09144d-94e0-4aa7-9144-ca8936b6298f_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsurancePayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance Payable</link:label>
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    <link:label id="lab_ambc_DiscountedOtherSubrogationBeforeReinsuranceAbstract_943c1dc3-dd4f-447f-8771-ad9046627a7e_terseLabel_en-US" xlink:label="lab_ambc_DiscountedOtherSubrogationBeforeReinsuranceAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less:</link:label>
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    <link:label id="lab_ambc_InternationalFinanceMember_6a2a6ab3-b073-4dd2-8c59-1158bd8bc879_terseLabel_en-US" xlink:label="lab_ambc_InternationalFinanceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">International Finance [Member]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ambc_InternationalFinanceMember" xlink:href="ambc-20240630.xsd#ambc_InternationalFinanceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_InternationalFinanceMember" xlink:to="lab_ambc_InternationalFinanceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest_165e0460-c703-4688-a5db-6f887b453f33_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Excluding Accrued Interest</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Excluding Accrued Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost_cdbda0c2-cca0-4b77-b278-bdca3c2efbc1_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortized Cost, Due after five years through ten years</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost, Maturity, Allocated and Single Maturity Date, after Year 5 Through 10</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_NonPeoNeoAvgCompActuallyPaidAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:to="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedDuringThirdQuarterFollowingBalanceSheetDate_1ad12fe0-d6aa-4909-8137-e1b5feba4e8b_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedDuringThirdQuarterFollowingBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Future premiums expected to be collected, September 30, 2021</link:label>
    <link:label id="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedDuringThirdQuarterFollowingBalanceSheetDate_label_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedDuringThirdQuarterFollowingBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Guarantee Insurance Contract, Premium Receivable, to be Collected, Third Quarter</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedDuringThirdQuarterFollowingBalanceSheetDate" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedDuringThirdQuarterFollowingBalanceSheetDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedDuringThirdQuarterFollowingBalanceSheetDate" xlink:to="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedDuringThirdQuarterFollowingBalanceSheetDate" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_HighYieldFundMember_04e6f70a-7ae4-4023-aade-e5329b96790a_terseLabel_en-US" xlink:label="lab_ambc_HighYieldFundMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">High Yield Fund</link:label>
    <link:label id="lab_ambc_HighYieldFundMember_label_en-US" xlink:label="lab_ambc_HighYieldFundMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">High Yield Fund [Member]</link:label>
    <link:label id="lab_ambc_HighYieldFundMember_documentation_en-US" xlink:label="lab_ambc_HighYieldFundMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">High Yield Fund</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_HighYieldFundMember" xlink:href="ambc-20240630.xsd#ambc_HighYieldFundMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_HighYieldFundMember" xlink:to="lab_ambc_HighYieldFundMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtFairValue_f962922b-9bd2-4cbe-aaec-3cd9a9e3b80b_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term debt</link:label>
    <link:label id="lab_us-gaap_LongTermDebtFairValue_49d07c52-79b5-4202-92a5-409e579af83c_verboseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtFairValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Long-term debt, Estimated fair value</link:label>
    <link:label id="lab_us-gaap_LongTermDebtFairValue_label_en-US" xlink:label="lab_us-gaap_LongTermDebtFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LongTermDebtFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtFairValue" xlink:to="lab_us-gaap_LongTermDebtFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLoss_496d3d6a-e9f4-48d4-b064-a78ccc0129d5_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net income (loss) attributable to common stockholders</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_8fbab648-f23c-4e00-97f7-7efda1916c59_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income attributable to common shareholders</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_label_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLoss" xlink:to="lab_us-gaap_NetIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_LossandLossReservesAxis_33d81ce6-65c8-4d7f-8060-50261a401ff1_terseLabel_en-US" xlink:label="lab_ambc_LossandLossReservesAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss and Loss Reserves [Axis]</link:label>
    <link:label id="lab_ambc_LossandLossReservesAxis_label_en-US" xlink:label="lab_ambc_LossandLossReservesAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss and Loss Reserves [Axis]</link:label>
    <link:label id="lab_ambc_LossandLossReservesAxis_documentation_en-US" xlink:label="lab_ambc_LossandLossReservesAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loss and Loss Reserves [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_LossandLossReservesAxis" xlink:href="ambc-20240630.xsd#ambc_LossandLossReservesAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_LossandLossReservesAxis" xlink:to="lab_ambc_LossandLossReservesAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_BusinessCombinationTotalConsideration_7b0758df-0b9c-4538-b3db-7d53d154d60b_terseLabel_en-US" xlink:label="lab_ambc_BusinessCombinationTotalConsideration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Total Consideration</link:label>
    <link:label id="lab_ambc_BusinessCombinationTotalConsideration_label_en-US" xlink:label="lab_ambc_BusinessCombinationTotalConsideration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Total Consideration</link:label>
    <link:label id="lab_ambc_BusinessCombinationTotalConsideration_documentation_en-US" xlink:label="lab_ambc_BusinessCombinationTotalConsideration" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Total Consideration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_BusinessCombinationTotalConsideration" xlink:href="ambc-20240630.xsd#ambc_BusinessCombinationTotalConsideration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_BusinessCombinationTotalConsideration" xlink:to="lab_ambc_BusinessCombinationTotalConsideration" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeContractTypeDomain_f6c27301-435e-43d1-a1c9-a13adda7e82e_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeContractTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Contract [Domain]</link:label>
    <link:label id="lab_us-gaap_DerivativeContractTypeDomain_label_en-US" xlink:label="lab_us-gaap_DerivativeContractTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Contract [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeContractTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeContractTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeContractTypeDomain" xlink:to="lab_us-gaap_DerivativeContractTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfNotionalAmountsOfOutstandingDerivativePositionsTableTextBlock_8b8ee029-320b-4b75-b762-c306a3993055_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfNotionalAmountsOfOutstandingDerivativePositionsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Notional Amounts of AFS's Trading Derivative Products</link:label>
    <link:label id="lab_us-gaap_ScheduleOfNotionalAmountsOfOutstandingDerivativePositionsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfNotionalAmountsOfOutstandingDerivativePositionsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Notional Amounts of Outstanding Derivative Positions [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfNotionalAmountsOfOutstandingDerivativePositionsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfNotionalAmountsOfOutstandingDerivativePositionsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfNotionalAmountsOfOutstandingDerivativePositionsTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfNotionalAmountsOfOutstandingDerivativePositionsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock_6c41938b-10c6-4f8f-9c0c-e08176f48076_terseLabel_en-US" xlink:label="lab_us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign Currency Transactions and Translations Policy [Policy Text Block]</link:label>
    <link:label id="lab_us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Foreign Currency Transactions and Translations Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock" xlink:to="lab_us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChangedPeerGroupFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changed Peer Group, Footnote</link:label>
    <link:label id="lab_ecd_ChangedPeerGroupFnTextBlock_label_en-US" xlink:label="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Changed Peer Group, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChangedPeerGroupFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_ChangedPeerGroupFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChangedPeerGroupFnTextBlock" xlink:to="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureName_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureName_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureName" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_CoSelectedMeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureName" xlink:to="lab_ecd_CoSelectedMeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationGrossUndiscountedClaimLiability_9c294ab4-d849-4728-a34f-ee8e25fdd47c_negatedTerseLabel_en-US" xlink:label="lab_ambc_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationGrossUndiscountedClaimLiability" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Gross undiscounted claim liability</link:label>
    <link:label id="lab_ambc_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationGrossUndiscountedClaimLiability_label_en-US" xlink:label="lab_ambc_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationGrossUndiscountedClaimLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule Of Insured Financial Obligations With Credit Deterioration Gross Undiscounted Claim Liability</link:label>
    <link:label id="lab_ambc_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationGrossUndiscountedClaimLiability_documentation_en-US" xlink:label="lab_ambc_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationGrossUndiscountedClaimLiability" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">This element represents the gross undiscounted claim liability for financial guarantee insurance contracts presented in the context of each surveillance grouping or category used by management to monitor and track potential deterioration in the credit worthiness of the insured party's ability to meet its financial obligations related to the contracts underlying financial guarantee insurance contracts the entity has issued.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationGrossUndiscountedClaimLiability" xlink:href="ambc-20240630.xsd#ambc_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationGrossUndiscountedClaimLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationGrossUndiscountedClaimLiability" xlink:to="lab_ambc_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationGrossUndiscountedClaimLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost_68df7ace-6675-4f60-8292-fa58b23a6e12_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortized Cost, Due after one year through five years</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost, Maturity, Allocated and Single Maturity Date, after Year One Through Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_SecuritiesAcquiredTransferredInTransactionsRelatedToPuertoRicoRestructurings_14a09ca2-9e6a-453b-879e-600950cca1fa_terseLabel_en-US" xlink:label="lab_ambc_SecuritiesAcquiredTransferredInTransactionsRelatedToPuertoRicoRestructurings" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Securities acquired (transferred) in transactions related to Puerto Rico restructurings</link:label>
    <link:label id="lab_ambc_SecuritiesAcquiredTransferredInTransactionsRelatedToPuertoRicoRestructurings_label_en-US" xlink:label="lab_ambc_SecuritiesAcquiredTransferredInTransactionsRelatedToPuertoRicoRestructurings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Securities acquired (transferred) in transactions related to Puerto Rico restructurings</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByAssetClassAxis_2c28c273-cff9-4f6d-9711-4d03836b8737_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByAssetClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Class [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByAssetClassAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByAssetClassAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Class [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByAssetClassAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueByAssetClassAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByAssetClassAxis" xlink:to="lab_us-gaap_FairValueByAssetClassAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumsReceivableAdjustmentOtherAdjustments_18e0e899-1d88-455d-abba-99517a103b91_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumsReceivableAdjustmentOtherAdjustments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other adjustments (including foreign exchange)</link:label>
    <link:label id="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumsReceivableAdjustmentOtherAdjustments_label_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumsReceivableAdjustmentOtherAdjustments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Guarantee Insurance Contracts, Premiums Receivable, Increase (Decrease), Other Adjustments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialGuaranteeInsuranceContractsPremiumsReceivableAdjustmentOtherAdjustments" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancialGuaranteeInsuranceContractsPremiumsReceivableAdjustmentOtherAdjustments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialGuaranteeInsuranceContractsPremiumsReceivableAdjustmentOtherAdjustments" xlink:to="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumsReceivableAdjustmentOtherAdjustments" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_BusinessDisposalCashExpectedToBeReceived_cea1680d-6643-433d-96a4-5186d4a3e883_terseLabel_en-US" xlink:label="lab_ambc_BusinessDisposalCashExpectedToBeReceived" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Disposal, Cash Expected to be Received</link:label>
    <link:label id="lab_ambc_BusinessDisposalCashExpectedToBeReceived_label_en-US" xlink:label="lab_ambc_BusinessDisposalCashExpectedToBeReceived" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Disposal, Cash Expected to be Received</link:label>
    <link:label id="lab_ambc_BusinessDisposalCashExpectedToBeReceived_documentation_en-US" xlink:label="lab_ambc_BusinessDisposalCashExpectedToBeReceived" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Disposal, Cash Expected to be Received</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_BusinessDisposalCashExpectedToBeReceived" xlink:href="ambc-20240630.xsd#ambc_BusinessDisposalCashExpectedToBeReceived"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_BusinessDisposalCashExpectedToBeReceived" xlink:to="lab_ambc_BusinessDisposalCashExpectedToBeReceived" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInPremiumsReceivable_355bbd1e-febb-49d1-8eef-54037e1708de_negatedLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInPremiumsReceivable" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Premium receivables</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInPremiumsReceivable_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInPremiumsReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Premiums Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInPremiumsReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncreaseDecreaseInPremiumsReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInPremiumsReceivable" xlink:to="lab_us-gaap_IncreaseDecreaseInPremiumsReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger_be3e79b9-f3a7-4355-98d3-da2eb266fa9c_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-sale, Continuous Unrealized Loss Position, 12 Months or Longer</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Continuous Unrealized Loss Position, 12 Months or Longer</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_c02ae951-c83f-4ebd-acb1-edeb6b5fd22f_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares issued</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonStockSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesIssued" xlink:to="lab_us-gaap_CommonStockSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationInsuredContractualPaymentsOutstandingAbstract_c03e11c3-87c3-48da-9aff-dbca80aa8f81_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationInsuredContractualPaymentsOutstandingAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross insured contractual payments outstanding:</link:label>
    <link:label id="lab_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationInsuredContractualPaymentsOutstandingAbstract_label_en-US" xlink:label="lab_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationInsuredContractualPaymentsOutstandingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Insured Financial Obligations with Credit Deterioration, Insured Contractual Payments Outstanding [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationInsuredContractualPaymentsOutstandingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationInsuredContractualPaymentsOutstandingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationInsuredContractualPaymentsOutstandingAbstract" xlink:to="lab_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationInsuredContractualPaymentsOutstandingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosure_373874b9-9af1-483d-8f72-cffa859c8690_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total financial assets</link:label>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssetsFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsFairValueDisclosure" xlink:to="lab_us-gaap_AssetsFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebt_88da409e-3faf-4593-a602-6d7e1bbf09bf_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term debt</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_037cf3a1-e720-47bd-a55c-d0e0a2428f4c_verboseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Long-term Debt</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_label_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebt" xlink:to="lab_us-gaap_LongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceRecoverableCreditQualityIndicatorTableTextBlock_34636bc4-0ece-4c8b-9d8e-091671769a41_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverableCreditQualityIndicatorTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverable, Credit Quality Indicator</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRecoverableCreditQualityIndicatorTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverableCreditQualityIndicatorTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverable, Credit Quality Indicator [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverableCreditQualityIndicatorTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ReinsuranceRecoverableCreditQualityIndicatorTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceRecoverableCreditQualityIndicatorTableTextBlock" xlink:to="lab_us-gaap_ReinsuranceRecoverableCreditQualityIndicatorTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThan10AndWithin15YearsFromBalanceSheetDate_0de1550e-ddc0-4308-aae7-918c3b7c542c_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThan10AndWithin15YearsFromBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Future expected premiums to be earned, net of reinsurance, December 31, 2035</link:label>
    <link:label id="lab_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThan10AndWithin15YearsFromBalanceSheetDate_label_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThan10AndWithin15YearsFromBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Guarantee Insurance Contract, Premium Revenue to be Recognized, after Year 10 Through 15</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThan10AndWithin15YearsFromBalanceSheetDate" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThan10AndWithin15YearsFromBalanceSheetDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThan10AndWithin15YearsFromBalanceSheetDate" xlink:to="lab_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThan10AndWithin15YearsFromBalanceSheetDate" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_NetIncomeLossReconciliationLineItems_108ae456-4a6f-440c-bcc2-442773b9c705_terseLabel_en-US" xlink:label="lab_ambc_NetIncomeLossReconciliationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net Income Loss Reconciliation [Line Items]</link:label>
    <link:label id="lab_ambc_NetIncomeLossReconciliationLineItems_label_en-US" xlink:label="lab_ambc_NetIncomeLossReconciliationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income Loss Reconciliation [Line Items]</link:label>
    <link:label id="lab_ambc_NetIncomeLossReconciliationLineItems_documentation_en-US" xlink:label="lab_ambc_NetIncomeLossReconciliationLineItems" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Net Income Loss Reconciliation [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_NetIncomeLossReconciliationLineItems" xlink:href="ambc-20240630.xsd#ambc_NetIncomeLossReconciliationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_NetIncomeLossReconciliationLineItems" xlink:to="lab_ambc_NetIncomeLossReconciliationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_PremiumsReceivablebyRiskClassificationCodeTableTextBlock_4efb2b5d-8f79-43e4-a1dd-87ee8a6ccecc_terseLabel_en-US" xlink:label="lab_ambc_PremiumsReceivablebyRiskClassificationCodeTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Premiums Receivable by Risk Classification Code [Table Text Block]</link:label>
    <link:label id="lab_ambc_PremiumsReceivablebyRiskClassificationCodeTableTextBlock_label_en-US" xlink:label="lab_ambc_PremiumsReceivablebyRiskClassificationCodeTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Premiums Receivable by Risk Classification Code [Table Text Block]</link:label>
    <link:label id="lab_ambc_PremiumsReceivablebyRiskClassificationCodeTableTextBlock_documentation_en-US" xlink:label="lab_ambc_PremiumsReceivablebyRiskClassificationCodeTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Premiums Receivable by Risk Classification Code [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_PremiumsReceivablebyRiskClassificationCodeTableTextBlock" xlink:href="ambc-20240630.xsd#ambc_PremiumsReceivablebyRiskClassificationCodeTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_PremiumsReceivablebyRiskClassificationCodeTableTextBlock" xlink:to="lab_ambc_PremiumsReceivablebyRiskClassificationCodeTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedTranslationAdjustmentMember_bccb2552-aa41-48a1-97a8-24f8f21c5131_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedTranslationAdjustmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Translation Adjustment [Member]</link:label>
    <link:label id="lab_us-gaap_AccumulatedTranslationAdjustmentMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedTranslationAdjustmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Foreign Currency Adjustment Attributable to Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedTranslationAdjustmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccumulatedTranslationAdjustmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedTranslationAdjustmentMember" xlink:to="lab_us-gaap_AccumulatedTranslationAdjustmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterestDisclosureTextBlock_161a0d1f-e7d5-4f1c-9ce9-0be75a77e9ad_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest Disclosure</link:label>
    <link:label id="lab_us-gaap_MinorityInterestDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_MinorityInterestDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_MinorityInterestDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterestDisclosureTextBlock" xlink:to="lab_us-gaap_MinorityInterestDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_OtherConsumerAssetBackedMember_e95d0605-1e7e-43f9-9f51-0123abaee014_terseLabel_en-US" xlink:label="lab_ambc_OtherConsumerAssetBackedMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Consumer Asset-Backed [Member]</link:label>
    <link:label id="lab_ambc_OtherConsumerAssetBackedMember_label_en-US" xlink:label="lab_ambc_OtherConsumerAssetBackedMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Consumer Asset Backed [Member]</link:label>
    <link:label id="lab_ambc_OtherConsumerAssetBackedMember_documentation_en-US" xlink:label="lab_ambc_OtherConsumerAssetBackedMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other consumer asset-backed.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_OtherConsumerAssetBackedMember" xlink:href="ambc-20240630.xsd#ambc_OtherConsumerAssetBackedMember"/>
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    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_1d5e06b4-3a63-45e0-9912-04ccc2e75cd0_totalLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total comprehensive income (loss) attributable to common stockholders</link:label>
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    <link:label id="lab_us-gaap_FinancialInstrumentsFinancialLiabilitiesBalanceSheetGroupingsAbstract_fd38e9a1-417e-4758-b2d7-38a52f10bab8_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentsFinancialLiabilitiesBalanceSheetGroupingsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial liabilities:</link:label>
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    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings (Accumulated Deficit)</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:to="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CollateralDomain_a8737590-84bb-4d5a-a519-c8a5b70f7897_terseLabel_en-US" xlink:label="lab_us-gaap_CollateralDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateral [Domain]</link:label>
    <link:label id="lab_us-gaap_CollateralDomain_label_en-US" xlink:label="lab_us-gaap_CollateralDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collateral Held [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CollateralDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CollateralDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CollateralDomain" xlink:to="lab_us-gaap_CollateralDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersPriorYearClaimsAndClaimsAdjustmentExpense_d434128a-c768-400a-96cc-1da87ec3c6b6_terseLabel_en-US" xlink:label="lab_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersPriorYearClaimsAndClaimsAdjustmentExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prior Year Claims and Claims Adjustment Expense</link:label>
    <link:label id="lab_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersPriorYearClaimsAndClaimsAdjustmentExpense_label_en-US" xlink:label="lab_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersPriorYearClaimsAndClaimsAdjustmentExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prior Year Claims and Claims Adjustment Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersPriorYearClaimsAndClaimsAdjustmentExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersPriorYearClaimsAndClaimsAdjustmentExpense"/>
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    <link:label id="lab_dei_EntityAddressStateOrProvince_eb48d341-43a6-4e9b-979a-e8666e72206b_terseLabel_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:label id="lab_dei_EntityAddressStateOrProvince_label_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressStateOrProvince" xlink:to="lab_dei_EntityAddressStateOrProvince" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Total Shareholder Return</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock"/>
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    <link:label id="lab_ambc_CashCollateralPayable_0ae82087-9f8f-42b5-b97c-fb51c876e900_terseLabel_en-US" xlink:label="lab_ambc_CashCollateralPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash collateral payable</link:label>
    <link:label id="lab_ambc_CashCollateralPayable_label_en-US" xlink:label="lab_ambc_CashCollateralPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash collateral payable</link:label>
    <link:label id="lab_ambc_CashCollateralPayable_documentation_en-US" xlink:label="lab_ambc_CashCollateralPayable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Cash collateral payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_CashCollateralPayable" xlink:href="ambc-20240630.xsd#ambc_CashCollateralPayable"/>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_42d47d19-9edf-4712-9972-01d89f406403_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from operating activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Operating Activities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract"/>
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    <link:label id="lab_us-gaap_ResidentialMortgageBackedSecuritiesMember_fddd5368-1cd2-4729-91c9-5c3c6eefd142_terseLabel_en-US" xlink:label="lab_us-gaap_ResidentialMortgageBackedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Residential Mortgage-Backed Securities [Member]</link:label>
    <link:label id="lab_us-gaap_ResidentialMortgageBackedSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_ResidentialMortgageBackedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Residential Mortgage-Backed Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ResidentialMortgageBackedSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ResidentialMortgageBackedSecuritiesMember"/>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInInterestPayableNet_d3833e2c-102f-45ed-8263-082440d6a0cd_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInInterestPayableNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest payable</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInInterestPayableNet_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInInterestPayableNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Interest Payable, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInInterestPayableNet" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncreaseDecreaseInInterestPayableNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInInterestPayableNet" xlink:to="lab_us-gaap_IncreaseDecreaseInInterestPayableNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromMaturitiesPrepaymentsAndCallsOfAvailableForSaleSecurities_f4823681-fa6e-4713-bd93-afea45cc0ec0_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromMaturitiesPrepaymentsAndCallsOfAvailableForSaleSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from matured bonds</link:label>
    <link:label id="lab_us-gaap_ProceedsFromMaturitiesPrepaymentsAndCallsOfAvailableForSaleSecurities_label_en-US" xlink:label="lab_us-gaap_ProceedsFromMaturitiesPrepaymentsAndCallsOfAvailableForSaleSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Maturities, Prepayments and Calls of Debt Securities, Available-for-Sale</link:label>
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    <link:label id="lab_us-gaap_MinorityInterestChangeInRedemptionValue_4014e277-5776-4e62-9629-393bb77a9b66_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestChangeInRedemptionValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest, Change in Redemption Value</link:label>
    <link:label id="lab_us-gaap_MinorityInterestChangeInRedemptionValue_label_en-US" xlink:label="lab_us-gaap_MinorityInterestChangeInRedemptionValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest, Change in Redemption Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestChangeInRedemptionValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_MinorityInterestChangeInRedemptionValue"/>
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    <link:label id="lab_us-gaap_GainLossOnInvestmentsMember1_c57b55b1-84fb-4cdc-a376-241ffe65ff4d_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnInvestmentsMember1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Investments [Member]</link:label>
    <link:label id="lab_us-gaap_GainLossOnInvestmentsMember1_label_en-US" xlink:label="lab_us-gaap_GainLossOnInvestmentsMember1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Investments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnInvestmentsMember1" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_GainLossOnInvestmentsMember1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnInvestmentsMember1" xlink:to="lab_us-gaap_GainLossOnInvestmentsMember1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest_cad1384c-f1e6-49f5-b394-5d53592e3351_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income (Loss) from Continuing Operations, Net of Tax, Including Portion Attributable to Noncontrolling Interest</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest_e52fe86a-f6fc-4b2c-89a7-f72981a564f8_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total before tax</link:label>
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    <link:label id="lab_srt_StandardPoorsAARatingMember_ee641c06-a0b5-45be-b970-7cd12fdae450_terseLabel_en-US" xlink:label="lab_srt_StandardPoorsAARatingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Standard &amp; Poor's, AA Rating</link:label>
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    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems_95910036-0295-4137-9e58-d2c893372da1_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Line Items]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems"/>
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    <link:label id="lab_ambc_BusinessDisposalPotentialOutOfPocketExpenseReimbursement_32a1649f-9d0f-4c06-a119-cfc04ebfc6b3_terseLabel_en-US" xlink:label="lab_ambc_BusinessDisposalPotentialOutOfPocketExpenseReimbursement" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Disposal, Potential Out Of Pocket Expense Reimbursement</link:label>
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    <link:label id="lab_ambc_BusinessDisposalPotentialOutOfPocketExpenseReimbursement_documentation_en-US" xlink:label="lab_ambc_BusinessDisposalPotentialOutOfPocketExpenseReimbursement" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Disposal, Potential Out Of Pocket Expense Reimbursement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_BusinessDisposalPotentialOutOfPocketExpenseReimbursement" xlink:href="ambc-20240630.xsd#ambc_BusinessDisposalPotentialOutOfPocketExpenseReimbursement"/>
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    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain_5d9b8d0d-5c91-4eda-b432-194a0bc59f91_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Class [Domain]</link:label>
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    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeAsset_b48e9461-d1e3-4d63-ae8e-5ce5ca1442a8_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative assets</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeFairValueOfDerivativeAsset"/>
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    <link:label id="lab_ambc_EquitySecuritiesExcludedFromFairValue_f8056673-85d1-4456-9e27-ab4a35c42e5f_terseLabel_en-US" xlink:label="lab_ambc_EquitySecuritiesExcludedFromFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Securities Excluded From Fair Value Table</link:label>
    <link:label id="lab_ambc_EquitySecuritiesExcludedFromFairValue_label_en-US" xlink:label="lab_ambc_EquitySecuritiesExcludedFromFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities Excluded From Fair Value</link:label>
    <link:label id="lab_ambc_EquitySecuritiesExcludedFromFairValue_documentation_en-US" xlink:label="lab_ambc_EquitySecuritiesExcludedFromFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Equity Securities Excluded From Fair Value</link:label>
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    <link:label id="lab_us-gaap_ClassOfStockDomain_916a3666-ce18-40f3-85d7-f569e881e214_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_ClassOfStockDomain_label_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfStockDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfStockDomain" xlink:to="lab_us-gaap_ClassOfStockDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_527e8f6f-83e1-4e65-a2e2-ca60001b11ac_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net of tax and noncontrolling interest</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_d7ed397a-aa6c-423f-82f4-122a1b92db55_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Basic</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic"/>
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    <link:label id="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock_0067d4d7-faa0-4e98-8201-e1e5784a6cad_terseLabel_en-US" xlink:label="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Amounts Reclassed Out of Each Component of Accumulated Other Comprehensive Income</link:label>
    <link:label id="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reclassification out of Accumulated Other Comprehensive Income [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock"/>
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    <link:label id="lab_srt_CreditRatingMoodysAxis_fde7a57d-9cfe-478e-936b-07a56f445150_terseLabel_en-US" xlink:label="lab_srt_CreditRatingMoodysAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Rating, Moody's [Axis]</link:label>
    <link:label id="lab_srt_CreditRatingMoodysAxis_label_en-US" xlink:label="lab_srt_CreditRatingMoodysAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Rating, Moody's [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_CreditRatingMoodysAxis" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_CreditRatingMoodysAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_CreditRatingMoodysAxis" xlink:to="lab_srt_CreditRatingMoodysAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_ComponentsofLossandLossExpenseReservesandSubrogationRecoverableLineItems_0838b6c7-05ac-4b65-be67-280f23ac0e76_terseLabel_en-US" xlink:label="lab_ambc_ComponentsofLossandLossExpenseReservesandSubrogationRecoverableLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Components of Loss and Loss Expense Reserves and Subrogation Recoverable [Line Items]</link:label>
    <link:label id="lab_ambc_ComponentsofLossandLossExpenseReservesandSubrogationRecoverableLineItems_label_en-US" xlink:label="lab_ambc_ComponentsofLossandLossExpenseReservesandSubrogationRecoverableLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Components of Loss and Loss Expense Reserves and Subrogation Recoverable [Line Items]</link:label>
    <link:label id="lab_ambc_ComponentsofLossandLossExpenseReservesandSubrogationRecoverableLineItems_documentation_en-US" xlink:label="lab_ambc_ComponentsofLossandLossExpenseReservesandSubrogationRecoverableLineItems" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">[Line Items] for Components of Loss and Loss Expense Reserves and Subrogation Recoverable [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_ComponentsofLossandLossExpenseReservesandSubrogationRecoverableLineItems" xlink:href="ambc-20240630.xsd#ambc_ComponentsofLossandLossExpenseReservesandSubrogationRecoverableLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_ComponentsofLossandLossExpenseReservesandSubrogationRecoverableLineItems" xlink:to="lab_ambc_ComponentsofLossandLossExpenseReservesandSubrogationRecoverableLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentOwnedAtFairValue_ca005160-0c7d-45d2-8ac8-aa8b811f959c_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentOwnedAtFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Owned, at Fair Value</link:label>
    <link:label id="lab_us-gaap_InvestmentOwnedAtFairValue_d82fe059-334f-4aaf-908c-bc041f4c4b46_verboseLabel_en-US" xlink:label="lab_us-gaap_InvestmentOwnedAtFairValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Fair value of securities that include benefit of guarantees provided by financial guarantors</link:label>
    <link:label id="lab_us-gaap_InvestmentOwnedAtFairValue_label_en-US" xlink:label="lab_us-gaap_InvestmentOwnedAtFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Owned, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentOwnedAtFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InvestmentOwnedAtFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentOwnedAtFairValue" xlink:to="lab_us-gaap_InvestmentOwnedAtFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock_6ccef4c6-779a-470b-97a0-0e61b83cacce_terseLabel_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements Disclosure</link:label>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock"/>
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    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_TotalShareholderRtnVsPeerGroupTextBlock"/>
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    <link:label id="lab_ambc_UnsecuredReinsuranceRecoverableAllOther_15343f83-a754-42b4-b634-9d64fc8bfac3_terseLabel_en-US" xlink:label="lab_ambc_UnsecuredReinsuranceRecoverableAllOther" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unsecured Reinsurance Recoverable, All Other</link:label>
    <link:label id="lab_ambc_UnsecuredReinsuranceRecoverableAllOther_label_en-US" xlink:label="lab_ambc_UnsecuredReinsuranceRecoverableAllOther" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unsecured Reinsurance Recoverable, All Other</link:label>
    <link:label id="lab_ambc_UnsecuredReinsuranceRecoverableAllOther_documentation_en-US" xlink:label="lab_ambc_UnsecuredReinsuranceRecoverableAllOther" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Unsecured Reinsurance Recoverable, All Other</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_UnsecuredReinsuranceRecoverableAllOther" xlink:href="ambc-20240630.xsd#ambc_UnsecuredReinsuranceRecoverableAllOther"/>
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    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_257fecc7-2455-4d03-98c5-9b1d99b789af_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AOCI Attributable to Parent [Member]</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_4b8b0145-aed4-4e07-bd38-31e027f81ba6_verboseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Retained Earnings [Member]</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI Attributable to Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeMember"/>
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    <link:label id="lab_ecd_AggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_AggtErrCompAmt"/>
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    <link:label id="lab_ambc_ReinsuranceRecoverableCreditExposure_c2c92ddd-9cae-4d41-b43f-6aedc029b090_terseLabel_en-US" xlink:label="lab_ambc_ReinsuranceRecoverableCreditExposure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverable Credit Exposure</link:label>
    <link:label id="lab_ambc_ReinsuranceRecoverableCreditExposure_label_en-US" xlink:label="lab_ambc_ReinsuranceRecoverableCreditExposure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverable Credit Exposure</link:label>
    <link:label id="lab_ambc_ReinsuranceRecoverableCreditExposure_documentation_en-US" xlink:label="lab_ambc_ReinsuranceRecoverableCreditExposure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverable Credit Exposure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_ReinsuranceRecoverableCreditExposure" xlink:href="ambc-20240630.xsd#ambc_ReinsuranceRecoverableCreditExposure"/>
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    <link:label id="lab_us-gaap_TypeAndTierIdentifierDomain_307e3584-e1d3-4c8b-a8e5-c16bd91ddee7_terseLabel_en-US" xlink:label="lab_us-gaap_TypeAndTierIdentifierDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Type and Tier Identifier [Domain]</link:label>
    <link:label id="lab_us-gaap_TypeAndTierIdentifierDomain_label_en-US" xlink:label="lab_us-gaap_TypeAndTierIdentifierDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Type and Tier Identifier [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TypeAndTierIdentifierDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TypeAndTierIdentifierDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TypeAndTierIdentifierDomain" xlink:to="lab_us-gaap_TypeAndTierIdentifierDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_terseLabel_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Executive Categories</link:label>
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    <link:label id="lab_ambc_AmbacInsuredSecuritiesMember_31ffd362-4df5-4a60-8783-dd019b8dbb5d_terseLabel_en-US" xlink:label="lab_ambc_AmbacInsuredSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ambac Insured Securities</link:label>
    <link:label id="lab_ambc_AmbacInsuredSecuritiesMember_label_en-US" xlink:label="lab_ambc_AmbacInsuredSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ambac Insured Securities [Member]</link:label>
    <link:label id="lab_ambc_AmbacInsuredSecuritiesMember_documentation_en-US" xlink:label="lab_ambc_AmbacInsuredSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Ambac Insured Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_AmbacInsuredSecuritiesMember" xlink:href="ambc-20240630.xsd#ambc_AmbacInsuredSecuritiesMember"/>
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    <link:label id="lab_us-gaap_CommitmentsMember_bdc3ffec-8387-4b6f-8a25-ece178399057_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments [Member]</link:label>
    <link:label id="lab_us-gaap_CommitmentsMember_label_en-US" xlink:label="lab_us-gaap_CommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments [Member]</link:label>
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    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterestAbstract_f7da4bf9-29a6-468c-a87e-c9bf9b14a478_terseLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterestAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less: comprehensive (gain) loss attributable to the noncontrolling interest</link:label>
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    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable_f84aea4d-3b38-454d-8032-e046f456ed64_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Table]</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossTable"/>
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    <link:label id="lab_us-gaap_FinancialGuaranteeMember_a19429c8-6a6a-452d-a140-7c5047cfb41e_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Guarantee</link:label>
    <link:label id="lab_us-gaap_FinancialGuaranteeMember_label_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Guarantee [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialGuaranteeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancialGuaranteeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialGuaranteeMember" xlink:to="lab_us-gaap_FinancialGuaranteeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetOrLiabilitySettlements_0861b2e0-bac4-458e-adf5-02452f1a0dec_negatedTerseLabel_en-US" xlink:label="lab_ambc_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetOrLiabilitySettlements" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurement With Unobservable Inputs Reconciliation Recurring Basis Asset Or Liability Settlements</link:label>
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    <link:label id="lab_ambc_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetOrLiabilitySettlements_documentation_en-US" xlink:label="lab_ambc_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetOrLiabilitySettlements" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Amount of settlements related to financial instruments measured on a recurring basis using unobservable inputs.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetOrLiabilitySettlements" xlink:href="ambc-20240630.xsd#ambc_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetOrLiabilitySettlements"/>
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    <link:label id="lab_us-gaap_PremiumsReceivableGross_092e0082-ed51-4508-a40e-0b6d4112243d_terseLabel_en-US" xlink:label="lab_us-gaap_PremiumsReceivableGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Premiums Receivable, Gross</link:label>
    <link:label id="lab_us-gaap_PremiumsReceivableGross_label_en-US" xlink:label="lab_us-gaap_PremiumsReceivableGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Premiums Receivable, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumsReceivableGross" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PremiumsReceivableGross"/>
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    <link:label id="lab_srt_StandardPoorsBRatingMember_cd156bf5-9b32-4d67-b12e-1095592e0d27_terseLabel_en-US" xlink:label="lab_srt_StandardPoorsBRatingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Standard &amp; Poor's, B Rating [Member]</link:label>
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    <link:label id="lab_us-gaap_DebtDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureAbstract" xlink:to="lab_us-gaap_DebtDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PremiumReceivableCreditLossExpenseReversal_871e475e-a501-4199-8a2a-f4a5d64b9114_terseLabel_en-US" xlink:label="lab_us-gaap_PremiumReceivableCreditLossExpenseReversal" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Premium Receivable, Credit Loss Expense (Reversal)</link:label>
    <link:label id="lab_us-gaap_PremiumReceivableCreditLossExpenseReversal_label_en-US" xlink:label="lab_us-gaap_PremiumReceivableCreditLossExpenseReversal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Premium Receivable, Credit Loss Expense (Reversal)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumReceivableCreditLossExpenseReversal" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PremiumReceivableCreditLossExpenseReversal"/>
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    <link:label id="lab_us-gaap_NumberOfReportableSegments_852ea80a-efb3-4086-8641-e889451477e8_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of Reportable Segments</link:label>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_label_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Reportable Segments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfReportableSegments" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NumberOfReportableSegments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfReportableSegments" xlink:to="lab_us-gaap_NumberOfReportableSegments" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_PercentageOfInvestmentPortfolioValuedUsingDealerQuotes_1077aab8-2119-428c-ba66-86c4bd75173c_terseLabel_en-US" xlink:label="lab_ambc_PercentageOfInvestmentPortfolioValuedUsingDealerQuotes" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percentage of investment portfolio valued using dealer quotes</link:label>
    <link:label id="lab_ambc_PercentageOfInvestmentPortfolioValuedUsingDealerQuotes_label_en-US" xlink:label="lab_ambc_PercentageOfInvestmentPortfolioValuedUsingDealerQuotes" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Percentage Of Investment Portfolio Valued Using Dealer Quotes</link:label>
    <link:label id="lab_ambc_PercentageOfInvestmentPortfolioValuedUsingDealerQuotes_documentation_en-US" xlink:label="lab_ambc_PercentageOfInvestmentPortfolioValuedUsingDealerQuotes" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment portfolio valued using dealer quotes.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_PercentageOfInvestmentPortfolioValuedUsingDealerQuotes" xlink:href="ambc-20240630.xsd#ambc_PercentageOfInvestmentPortfolioValuedUsingDealerQuotes"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_PercentageOfInvestmentPortfolioValuedUsingDealerQuotes" xlink:to="lab_ambc_PercentageOfInvestmentPortfolioValuedUsingDealerQuotes" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_d5dbf94e-494e-4349-823d-c3347e08493c_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Abstract]</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Abstract]</link:label>
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    <link:label id="lab_us-gaap_CommonStockValue_8ba45123-df5b-4061-a0b7-248e2ec1a0dc_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Stock, Value, Issued</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockValue" xlink:to="lab_us-gaap_CommonStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_InsuranceTable_45a85b01-3217-4958-8243-8a02ddf797ec_terseLabel_en-US" xlink:label="lab_ambc_InsuranceTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insurance [Table]</link:label>
    <link:label id="lab_ambc_InsuranceTable_label_en-US" xlink:label="lab_ambc_InsuranceTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insurance [Table]</link:label>
    <link:label id="lab_ambc_InsuranceTable_documentation_en-US" xlink:label="lab_ambc_InsuranceTable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Insurance [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_InsuranceTable" xlink:href="ambc-20240630.xsd#ambc_InsuranceTable"/>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue_ab6526d7-4be5-4c43-a409-99d5725629ab_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Estimated Fair Value, Due after one year through five years</link:label>
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    <link:label id="lab_us-gaap_FairValueMeasuredAtNetAssetValuePerShareMember_a178076e-1c2f-4587-ae67-f24a703cc15e_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasuredAtNetAssetValuePerShareMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measured at Net Asset Value Per Share [Member]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasuredAtNetAssetValuePerShareMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueMeasuredAtNetAssetValuePerShareMember"/>
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    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_c1d881ba-2278-4543-941b-8a07a6211895_terseLabel_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract"/>
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    <link:label id="lab_ambc_VariableInterestEntityNonconsolidatedCarryingAmountInsuranceLiabilities_2be4dc70-82fc-4255-a93e-44bbd13d15ab_terseLabel_en-US" xlink:label="lab_ambc_VariableInterestEntityNonconsolidatedCarryingAmountInsuranceLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insurance Liabilities</link:label>
    <link:label id="lab_ambc_VariableInterestEntityNonconsolidatedCarryingAmountInsuranceLiabilities_label_en-US" xlink:label="lab_ambc_VariableInterestEntityNonconsolidatedCarryingAmountInsuranceLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity Nonconsolidated Carrying Amount Insurance Liabilities</link:label>
    <link:label id="lab_ambc_VariableInterestEntityNonconsolidatedCarryingAmountInsuranceLiabilities_documentation_en-US" xlink:label="lab_ambc_VariableInterestEntityNonconsolidatedCarryingAmountInsuranceLiabilities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The carrying amount of insurance liabilities in the reporting entity's statement of financial position that relate to the entity's variable interests in Variable Interest Entities (VIEs) where the VIEs are not consolidated.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_VariableInterestEntityNonconsolidatedCarryingAmountInsuranceLiabilities" xlink:href="ambc-20240630.xsd#ambc_VariableInterestEntityNonconsolidatedCarryingAmountInsuranceLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_VariableInterestEntityNonconsolidatedCarryingAmountInsuranceLiabilities" xlink:to="lab_ambc_VariableInterestEntityNonconsolidatedCarryingAmountInsuranceLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CollateralAlreadyPostedAggregateFairValue_9b729bf1-7d63-43c1-b3f9-1ac06316877d_terseLabel_en-US" xlink:label="lab_us-gaap_CollateralAlreadyPostedAggregateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value of posted assets as collateral</link:label>
    <link:label id="lab_us-gaap_CollateralAlreadyPostedAggregateFairValue_label_en-US" xlink:label="lab_us-gaap_CollateralAlreadyPostedAggregateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collateral Already Posted, Aggregate Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CollateralAlreadyPostedAggregateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CollateralAlreadyPostedAggregateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CollateralAlreadyPostedAggregateFairValue" xlink:to="lab_us-gaap_CollateralAlreadyPostedAggregateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_IncomeLossOnVariableInterestEntitiesMember_b2644d79-ab01-4c77-9844-a8df9e49463c_terseLabel_en-US" xlink:label="lab_ambc_IncomeLossOnVariableInterestEntitiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Loss On Variable Interest Entities [Member]</link:label>
    <link:label id="lab_ambc_IncomeLossOnVariableInterestEntitiesMember_label_en-US" xlink:label="lab_ambc_IncomeLossOnVariableInterestEntitiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Loss On Variable Interest Entities [Member]</link:label>
    <link:label id="lab_ambc_IncomeLossOnVariableInterestEntitiesMember_documentation_en-US" xlink:label="lab_ambc_IncomeLossOnVariableInterestEntitiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Income (loss) on variable interest entities.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_IncomeLossOnVariableInterestEntitiesMember" xlink:href="ambc-20240630.xsd#ambc_IncomeLossOnVariableInterestEntitiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_IncomeLossOnVariableInterestEntitiesMember" xlink:to="lab_ambc_IncomeLossOnVariableInterestEntitiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestPayableCurrentAndNoncurrent_7577e8ed-484c-495b-a632-1e862ecc0e07_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest payable</link:label>
    <link:label id="lab_us-gaap_InterestPayableCurrentAndNoncurrent_df14ae6b-b311-48fb-920e-f9a8dd5aa87c_verboseLabel_en-US" xlink:label="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Interest Payable</link:label>
    <link:label id="lab_us-gaap_InterestPayableCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InterestPayableCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:to="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_StandardPoorsARatingMember_bcfc7400-9719-444d-96ac-26811c10287e_terseLabel_en-US" xlink:label="lab_srt_StandardPoorsARatingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Standard &amp; Poor's, A Rating</link:label>
    <link:label id="lab_srt_StandardPoorsARatingMember_label_en-US" xlink:label="lab_srt_StandardPoorsARatingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Standard &amp; Poor's, A Rating [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StandardPoorsARatingMember" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_StandardPoorsARatingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_StandardPoorsARatingMember" xlink:to="lab_srt_StandardPoorsARatingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedCash_e25edd0b-e5ba-470f-8866-12622a0fda82_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedCash" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted Cash</link:label>
    <link:label id="lab_us-gaap_RestrictedCash_label_en-US" xlink:label="lab_us-gaap_RestrictedCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Cash</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedCash" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RestrictedCash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedCash" xlink:to="lab_us-gaap_RestrictedCash" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllIndividualsMember_terseLabel_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Individuals</link:label>
    <link:label id="lab_ecd_AllIndividualsMember_label_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Individuals [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllIndividualsMember" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_AllIndividualsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllIndividualsMember" xlink:to="lab_ecd_AllIndividualsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate_6e10d471-e16f-4741-8c83-f4fe0bf064eb_totalLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Estimated Fair Value due, Total</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Maturity, Allocated and Single Maturity Date, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityFundsMember_db40c426-0902-4faa-b1b3-b61dff2c91ba_terseLabel_en-US" xlink:label="lab_us-gaap_EquityFundsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Funds</link:label>
    <link:label id="lab_us-gaap_EquityFundsMember_label_en-US" xlink:label="lab_us-gaap_EquityFundsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Funds [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityFundsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EquityFundsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityFundsMember" xlink:to="lab_us-gaap_EquityFundsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFilerCategory_7256be1f-fe70-429c-bebf-02cf75644f83_terseLabel_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:label id="lab_dei_EntityFilerCategory_label_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFilerCategory" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityFilerCategory"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityFilerCategory" xlink:to="lab_dei_EntityFilerCategory" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_a2b0e15e-d81f-446d-a5e3-2525f0b30a0a_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Equity Method Investments [Line Items]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Equity Method Investments [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfEquityMethodInvestmentsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:to="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_NonPeoNeoAvgTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:to="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementTable_d7d5fab6-56e6-469a-823b-7c49c5f6c8f8_terseLabel_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:label id="lab_us-gaap_StatementTable_label_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementTable" xlink:to="lab_us-gaap_StatementTable" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_c4d53ac0-848b-44fb-bbf9-700402b0d97b_terseLabel_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_label_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CurrentFiscalYearEndDate" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_CurrentFiscalYearEndDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CurrentFiscalYearEndDate" xlink:to="lab_dei_CurrentFiscalYearEndDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseLongTermDebt_630db2ab-2dff-41b0-b5a3-867960e6fd9b_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Expense, Long-term Debt</link:label>
    <link:label id="lab_us-gaap_InterestExpenseLongTermDebt_label_en-US" xlink:label="lab_us-gaap_InterestExpenseLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseLongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InterestExpenseLongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseLongTermDebt" xlink:to="lab_us-gaap_InterestExpenseLongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxAuthorityAxis_5b8d556b-a8ae-40c1-9478-2d184a156b4b_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Authority [Axis]</link:label>
    <link:label id="lab_us-gaap_IncomeTaxAuthorityAxis_label_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Authority [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxAuthorityAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncomeTaxAuthorityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxAuthorityAxis" xlink:to="lab_us-gaap_IncomeTaxAuthorityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoName_terseLabel_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:label id="lab_ecd_PeoName_label_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoName" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_PeoName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoName" xlink:to="lab_ecd_PeoName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherSundryLiabilitiesCurrent_d3459b34-0be4-4348-a77a-2e2714908e74_terseLabel_en-US" xlink:label="lab_us-gaap_OtherSundryLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Sundry Liabilities, Current</link:label>
    <link:label id="lab_us-gaap_OtherSundryLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_OtherSundryLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Sundry Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherSundryLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherSundryLiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherSundryLiabilitiesCurrent" xlink:to="lab_us-gaap_OtherSundryLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationNumberOfContractsIssuedAndOutstanding_fcc0a420-7fbc-4a84-8ff4-138b649d3e30_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationNumberOfContractsIssuedAndOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of policies</link:label>
    <link:label id="lab_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationNumberOfContractsIssuedAndOutstanding_label_en-US" xlink:label="lab_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationNumberOfContractsIssuedAndOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Insured Financial Obligations with Credit Deterioration, Number of Contracts Issued and Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationNumberOfContractsIssuedAndOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationNumberOfContractsIssuedAndOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationNumberOfContractsIssuedAndOutstanding" xlink:to="lab_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationNumberOfContractsIssuedAndOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesAuthorized_1e94125b-79e1-4123-9e8a-9b3ebb1690c1_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, shares authorized</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PreferredStockSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesAuthorized" xlink:to="lab_us-gaap_PreferredStockSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_VariableInterestEntityClassificationOfCarryingAmountAssetsAbstract_cf28a95a-41a1-49c5-8489-c29dfc7b00fa_terseLabel_en-US" xlink:label="lab_ambc_VariableInterestEntityClassificationOfCarryingAmountAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable interest entity assets:</link:label>
    <link:label id="lab_ambc_VariableInterestEntityClassificationOfCarryingAmountAssetsAbstract_label_en-US" xlink:label="lab_ambc_VariableInterestEntityClassificationOfCarryingAmountAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity Classification Of Carrying Amount Assets [Abstract]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ambc_VariableInterestEntityClassificationOfCarryingAmountAssetsAbstract" xlink:href="ambc-20240630.xsd#ambc_VariableInterestEntityClassificationOfCarryingAmountAssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_VariableInterestEntityClassificationOfCarryingAmountAssetsAbstract" xlink:to="lab_ambc_VariableInterestEntityClassificationOfCarryingAmountAssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_ScheduleOfLoansAndAllowanceForLoanByClassIndividuallyAndCollectivelyEvaluatedForImpairmentLineItems_d9f57188-ccec-44bf-8376-fa33fab59725_terseLabel_en-US" xlink:label="lab_ambc_ScheduleOfLoansAndAllowanceForLoanByClassIndividuallyAndCollectivelyEvaluatedForImpairmentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule Of Loans And Allowance For Loan By Class Individually And Collectively Evaluated For Impairment [Line Items]</link:label>
    <link:label id="lab_ambc_ScheduleOfLoansAndAllowanceForLoanByClassIndividuallyAndCollectivelyEvaluatedForImpairmentLineItems_label_en-US" xlink:label="lab_ambc_ScheduleOfLoansAndAllowanceForLoanByClassIndividuallyAndCollectivelyEvaluatedForImpairmentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule Of Loans And Allowance For Loan By Class Individually And Collectively Evaluated For Impairment [Line Items]</link:label>
    <link:label id="lab_ambc_ScheduleOfLoansAndAllowanceForLoanByClassIndividuallyAndCollectivelyEvaluatedForImpairmentLineItems_documentation_en-US" xlink:label="lab_ambc_ScheduleOfLoansAndAllowanceForLoanByClassIndividuallyAndCollectivelyEvaluatedForImpairmentLineItems" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule Of Loans And Allowance For Loan By Class Individually And Collectively Evaluated For Impairment [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_ScheduleOfLoansAndAllowanceForLoanByClassIndividuallyAndCollectivelyEvaluatedForImpairmentLineItems" xlink:href="ambc-20240630.xsd#ambc_ScheduleOfLoansAndAllowanceForLoanByClassIndividuallyAndCollectivelyEvaluatedForImpairmentLineItems"/>
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    <link:label id="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems_3b2b0ba2-64e0-4cdf-ba6e-5b180face6c7_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Net Derivative Asset (Liability) Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Net Derivative Asset (Liability) Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems"/>
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    <link:label id="lab_ambc_BusinessCombinationNumberOfSharesIssuedForBeatAcquisition_ec5e11f8-afb3-4422-a121-84603d002028_terseLabel_en-US" xlink:label="lab_ambc_BusinessCombinationNumberOfSharesIssuedForBeatAcquisition" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Number of Shares Issued for Beat Acquisition</link:label>
    <link:label id="lab_ambc_BusinessCombinationNumberOfSharesIssuedForBeatAcquisition_label_en-US" xlink:label="lab_ambc_BusinessCombinationNumberOfSharesIssuedForBeatAcquisition" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Number of Shares Issued for Beat Acquisition</link:label>
    <link:label id="lab_ambc_BusinessCombinationNumberOfSharesIssuedForBeatAcquisition_documentation_en-US" xlink:label="lab_ambc_BusinessCombinationNumberOfSharesIssuedForBeatAcquisition" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Number of Shares Issued for Beat Acquisition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_BusinessCombinationNumberOfSharesIssuedForBeatAcquisition" xlink:href="ambc-20240630.xsd#ambc_BusinessCombinationNumberOfSharesIssuedForBeatAcquisition"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_BusinessCombinationNumberOfSharesIssuedForBeatAcquisition" xlink:to="lab_ambc_BusinessCombinationNumberOfSharesIssuedForBeatAcquisition" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfGoodwillTextBlock_e1d771fb-326d-4699-b60d-772bc4ddcf48_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfGoodwillTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Goodwill</link:label>
    <link:label id="lab_us-gaap_ScheduleOfGoodwillTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfGoodwillTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Goodwill [Table Text Block]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfGoodwillTextBlock" xlink:to="lab_us-gaap_ScheduleOfGoodwillTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_IlliquidInvestmentsMember_a08ff643-f399-4d71-b5e1-98a190a9c33c_terseLabel_en-US" xlink:label="lab_ambc_IlliquidInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Illiquid Investments [Member]</link:label>
    <link:label id="lab_ambc_IlliquidInvestmentsMember_label_en-US" xlink:label="lab_ambc_IlliquidInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Illiquid Investments [Member]</link:label>
    <link:label id="lab_ambc_IlliquidInvestmentsMember_documentation_en-US" xlink:label="lab_ambc_IlliquidInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Illiquid Investments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_IlliquidInvestmentsMember" xlink:href="ambc-20240630.xsd#ambc_IlliquidInvestmentsMember"/>
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    <link:label id="lab_us-gaap_PrepaidReinsurancePremiums_c25a137b-2e18-475c-803d-0e471eae3309_terseLabel_en-US" xlink:label="lab_us-gaap_PrepaidReinsurancePremiums" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred ceded premium</link:label>
    <link:label id="lab_us-gaap_PrepaidReinsurancePremiums_label_en-US" xlink:label="lab_us-gaap_PrepaidReinsurancePremiums" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prepaid Reinsurance Premiums</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrepaidReinsurancePremiums" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PrepaidReinsurancePremiums"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PrepaidReinsurancePremiums" xlink:to="lab_us-gaap_PrepaidReinsurancePremiums" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherIncomeMember_f0a3f1b0-7b3f-4a27-9d07-79830b3cf29b_terseLabel_en-US" xlink:label="lab_us-gaap_OtherIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Income or (Loss) [Member]</link:label>
    <link:label id="lab_us-gaap_OtherIncomeMember_bf7ecf71-20a3-4741-8237-c61fad34c920_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherIncomeMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other Income [Member]</link:label>
    <link:label id="lab_us-gaap_OtherIncomeMember_label_en-US" xlink:label="lab_us-gaap_OtherIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Income [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherIncomeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherIncomeMember" xlink:to="lab_us-gaap_OtherIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtSecuritiesCurrent_a80f5d54-c5d5-451b-bf0e-f7a3f3f5116b_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtSecuritiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Current</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtSecuritiesCurrent_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtSecuritiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtSecuritiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AvailableForSaleSecuritiesDebtSecuritiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtSecuritiesCurrent" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtSecuritiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireOtherInvestments_bab2db79-3a8c-4b5c-9033-94397bcb3a46_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireOtherInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Purchases of other invested assets</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireOtherInvestments_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireOtherInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Other Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireOtherInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PaymentsToAcquireOtherInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireOtherInvestments" xlink:to="lab_us-gaap_PaymentsToAcquireOtherInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PremiumsWrittenNet_0dd47b99-df0f-4e52-881e-2dcb0ab49f41_terseLabel_en-US" xlink:label="lab_us-gaap_PremiumsWrittenNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Premiums Written, Net</link:label>
    <link:label id="lab_us-gaap_PremiumsWrittenNet_5f10a40d-0fca-4623-8586-b56e972ba209_negatedTotalLabel_en-US" xlink:label="lab_us-gaap_PremiumsWrittenNet" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xml:lang="en-US">Premiums written, net of reinsurance</link:label>
    <link:label id="lab_us-gaap_PremiumsWrittenNet_label_en-US" xlink:label="lab_us-gaap_PremiumsWrittenNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Premiums Written, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumsWrittenNet" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PremiumsWrittenNet"/>
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    <link:label id="lab_ambc_InvestmentPortfolioMember_18493ac8-c59d-4e7f-baf9-cca255dd97f6_terseLabel_en-US" xlink:label="lab_ambc_InvestmentPortfolioMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Portfolio [Member]</link:label>
    <link:label id="lab_ambc_InvestmentPortfolioMember_label_en-US" xlink:label="lab_ambc_InvestmentPortfolioMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Portfolio [Member]</link:label>
    <link:label id="lab_ambc_InvestmentPortfolioMember_documentation_en-US" xlink:label="lab_ambc_InvestmentPortfolioMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment portfolio.</link:label>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet_68b5d7f4-13cd-4d70-9182-92d5e4efe7bb_negatedLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Other, net</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Operating Assets and Liabilities, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet"/>
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    <link:label id="lab_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationInsuredContractualPaymentsOutstanding_6c6b51ab-ac53-41e0-b65e-322b7d9930be_totalLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfInsuredFinancialObligationsWithCreditDeteriorationInsuredContractualPaymentsOutstanding" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
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    <link:label id="lab_currency_EUR_948984d3-47b0-4fb8-8ac6-41fb26ee7163_terseLabel_en-US" xlink:label="lab_currency_EUR" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Euro Member Countries, Euro</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_currency_EUR" xlink:href="https://xbrl.sec.gov/currency/2023/currency-2023.xsd#currency_EUR"/>
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    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_20864944-408c-4ab5-b450-1586b50a1a44_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementOfFinancialPositionAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:to="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquity_b8d660a2-ef8d-484a-b807-48c48b703021_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Ambac Financial Group, Inc. stockholders&#8217; equity</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquity" xlink:to="lab_us-gaap_StockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_BusinessCombinationCreditFacilityCashUsedForBeatAcquisition_60573b3e-4284-45df-bdf6-c308594db51a_terseLabel_en-US" xlink:label="lab_ambc_BusinessCombinationCreditFacilityCashUsedForBeatAcquisition" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Credit Facility Cash Used for Beat Acquisition</link:label>
    <link:label id="lab_ambc_BusinessCombinationCreditFacilityCashUsedForBeatAcquisition_label_en-US" xlink:label="lab_ambc_BusinessCombinationCreditFacilityCashUsedForBeatAcquisition" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Credit Facility Cash Used for Beat Acquisition</link:label>
    <link:label id="lab_ambc_BusinessCombinationCreditFacilityCashUsedForBeatAcquisition_documentation_en-US" xlink:label="lab_ambc_BusinessCombinationCreditFacilityCashUsedForBeatAcquisition" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Credit Facility Cash Used for Beat Acquisition</link:label>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_d251f88b-15f5-4868-84c0-cdba8cc34918_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets by Major Class [Axis]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis"/>
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    <link:label id="lab_us-gaap_LiabilitiesFairValueDisclosure_fc547c50-aa51-4e84-bc3f-f60588398e37_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total financial liabilities</link:label>
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    <link:label id="lab_us-gaap_UnderlyingAssetClassAxis_014e8154-aa53-4493-9edf-998e113fee23_terseLabel_en-US" xlink:label="lab_us-gaap_UnderlyingAssetClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underlying Asset Class [Axis]</link:label>
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    <link:label id="lab_us-gaap_ProductAndServiceOtherMember_a500c138-8ecd-4e31-a1f5-5ba08c779f5c_terseLabel_en-US" xlink:label="lab_us-gaap_ProductAndServiceOtherMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product and Service, Other</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:to="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote</link:label>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_label_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_EquityValuationAssumptionDifferenceFnTextBlock"/>
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    <link:label id="lab_us-gaap_CurrentForeignTaxExpenseBenefit_395d2866-a206-4415-bc3a-48ae3eb74cb3_terseLabel_en-US" xlink:label="lab_us-gaap_CurrentForeignTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current Foreign Tax Expense (Benefit)</link:label>
    <link:label id="lab_us-gaap_CurrentForeignTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_CurrentForeignTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Foreign Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CurrentForeignTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CurrentForeignTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CurrentForeignTaxExpenseBenefit" xlink:to="lab_us-gaap_CurrentForeignTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CollateralPledgedMember_83335f4e-db90-4bb7-9050-107fac5e5737_terseLabel_en-US" xlink:label="lab_us-gaap_CollateralPledgedMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateral Pledged [Member]</link:label>
    <link:label id="lab_us-gaap_CollateralPledgedMember_label_en-US" xlink:label="lab_us-gaap_CollateralPledgedMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collateral Pledged [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CollateralPledgedMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CollateralPledgedMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CollateralPledgedMember" xlink:to="lab_us-gaap_CollateralPledgedMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_CurrencyAxis_7470e570-84c7-48c8-b509-2b45d31f7eb3_terseLabel_en-US" xlink:label="lab_srt_CurrencyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Currency [Axis]</link:label>
    <link:label id="lab_srt_CurrencyAxis_label_en-US" xlink:label="lab_srt_CurrencyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Currency [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_CurrencyAxis" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_CurrencyAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_CurrencyAxis" xlink:to="lab_srt_CurrencyAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ImpairmentOfInvestments_b113edd3-22e6-4b0b-8473-b376a8b06eb1_terseLabel_en-US" xlink:label="lab_us-gaap_ImpairmentOfInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other than Temporary Impairment Losses, Investments</link:label>
    <link:label id="lab_us-gaap_ImpairmentOfInvestments_label_en-US" xlink:label="lab_us-gaap_ImpairmentOfInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other than Temporary Impairment Losses, Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ImpairmentOfInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ImpairmentOfInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ImpairmentOfInvestments" xlink:to="lab_us-gaap_ImpairmentOfInvestments" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_SurveillanceCategoryDomain_label_en-US" xlink:label="lab_us-gaap_SurveillanceCategoryDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Surveillance Category [Domain]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SurveillanceCategoryDomain" xlink:to="lab_us-gaap_SurveillanceCategoryDomain" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_InvestmentIncomeInvestmentExpense_6c8ef5e3-56f7-48e0-a00e-e4792da68f17_negatedLabel_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInvestmentExpense" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Investment expense</link:label>
    <link:label id="lab_us-gaap_InvestmentIncomeInvestmentExpense_label_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInvestmentExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Income, Investment Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIncomeInvestmentExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InvestmentIncomeInvestmentExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentIncomeInvestmentExpense" xlink:to="lab_us-gaap_InvestmentIncomeInvestmentExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_FixedIncomeInvestmentsAndOtherInvestmentsMember_7bf47eff-1655-4fa9-9253-d5b901091370_terseLabel_en-US" xlink:label="lab_ambc_FixedIncomeInvestmentsAndOtherInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fixed Income Investments And Other Investments [Member]</link:label>
    <link:label id="lab_ambc_FixedIncomeInvestmentsAndOtherInvestmentsMember_label_en-US" xlink:label="lab_ambc_FixedIncomeInvestmentsAndOtherInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Income Investments And Other Investments [Member]</link:label>
    <link:label id="lab_ambc_FixedIncomeInvestmentsAndOtherInvestmentsMember_documentation_en-US" xlink:label="lab_ambc_FixedIncomeInvestmentsAndOtherInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fixed income investments and other investments Member.</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_FixedIncomeInvestmentsAndOtherInvestmentsMember" xlink:to="lab_ambc_FixedIncomeInvestmentsAndOtherInvestmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressCityOrTown_a4db0039-10a8-45ca-b421-3a84be34690a_terseLabel_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:label id="lab_dei_EntityAddressCityOrTown_label_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressCityOrTown" xlink:to="lab_dei_EntityAddressCityOrTown" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:to="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_ScheduleOfEarningsPerShareTable_4ee29d61-f9ac-495f-bfca-341c63bcc0a0_terseLabel_en-US" xlink:label="lab_ambc_ScheduleOfEarningsPerShareTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule Of Earnings Per Share [Table]</link:label>
    <link:label id="lab_ambc_ScheduleOfEarningsPerShareTable_label_en-US" xlink:label="lab_ambc_ScheduleOfEarningsPerShareTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule Of Earnings Per Share [Table]</link:label>
    <link:label id="lab_ambc_ScheduleOfEarningsPerShareTable_documentation_en-US" xlink:label="lab_ambc_ScheduleOfEarningsPerShareTable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule Of Earnings Per Share [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_ScheduleOfEarningsPerShareTable" xlink:href="ambc-20240630.xsd#ambc_ScheduleOfEarningsPerShareTable"/>
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    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_15664aaa-5f57-445a-a18a-f09be19d6fff_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Segment Reporting Information, by Segment</link:label>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Segment Reporting Information, by Segment [Table Text Block]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:to="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThanOneAndWithinTwoYearsFromBalanceSheetDate_1cc44f04-9b64-474d-866d-ee377985429f_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThanOneAndWithinTwoYearsFromBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Future expected premiums to be earned, net of reinsurance, December 31, 2022</link:label>
    <link:label id="lab_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThanOneAndWithinTwoYearsFromBalanceSheetDate_label_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThanOneAndWithinTwoYearsFromBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Guarantee Insurance Contract, Premium Revenue to be Recognized, Year Two</link:label>
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    <link:label id="lab_ecd_TrdArrTerminationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Termination Date</link:label>
    <link:label id="lab_ecd_TrdArrTerminationDate_label_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Termination Date</link:label>
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    <link:label id="lab_ambc_EstimatedFuturePremiumPaymentsMinimumDiscountedRate_aaae1118-a398-470c-8c83-c3ea7ce633fa_terseLabel_en-US" xlink:label="lab_ambc_EstimatedFuturePremiumPaymentsMinimumDiscountedRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Estimated Future Premium Payments Minimum Discounted Rate</link:label>
    <link:label id="lab_ambc_EstimatedFuturePremiumPaymentsMinimumDiscountedRate_label_en-US" xlink:label="lab_ambc_EstimatedFuturePremiumPaymentsMinimumDiscountedRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Estimated Future Premium Payments Minimum Discounted Rate</link:label>
    <link:label id="lab_ambc_EstimatedFuturePremiumPaymentsMinimumDiscountedRate_documentation_en-US" xlink:label="lab_ambc_EstimatedFuturePremiumPaymentsMinimumDiscountedRate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Estimated Future Premium Payments Minimum Discounted Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_EstimatedFuturePremiumPaymentsMinimumDiscountedRate" xlink:href="ambc-20240630.xsd#ambc_EstimatedFuturePremiumPaymentsMinimumDiscountedRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_EstimatedFuturePremiumPaymentsMinimumDiscountedRate" xlink:to="lab_ambc_EstimatedFuturePremiumPaymentsMinimumDiscountedRate" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetOrLiabilityTransfersIntoOrOutOfLevel3_54968409-9f2f-480f-b831-7ac97282216c_terseLabel_en-US" xlink:label="lab_ambc_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetOrLiabilityTransfersIntoOrOutOfLevel3" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis Asset or Liability, Transfers into or out of Level 3</link:label>
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    <link:label id="lab_us-gaap_ChangeInAccountingPrincipleMember_9fca1ff5-9fc4-472d-aa51-84e8b85215c6_terseLabel_en-US" xlink:label="lab_us-gaap_ChangeInAccountingPrincipleMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustments for Change in Accounting Principle [Domain]</link:label>
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    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_f35d779e-c958-46ac-92a0-9f1c5f1bc713_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares authorized</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AvailableForSaleSecuritiesDebtSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtSecurities" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtSecurities" xlink:type="arc" order="1"/>
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    <link:loc xlink:type="locator" xlink:label="loc_ambc_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetOrLiability" xlink:href="ambc-20240630.xsd#ambc_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetOrLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetOrLiability" xlink:to="lab_ambc_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetOrLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_VariableInterestEntityNotPrimaryBeneficiaryTableTextBlock_4844df84-1e0b-442c-94a9-0c5d26038848_terseLabel_en-US" xlink:label="lab_ambc_VariableInterestEntityNotPrimaryBeneficiaryTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Carrying Amount of Assets, Liabilities and Maximum Exposure to Loss of Ambac's Variable Interests in Non-Consolidated Variable Interest Entities</link:label>
    <link:label id="lab_ambc_VariableInterestEntityNotPrimaryBeneficiaryTableTextBlock_label_en-US" xlink:label="lab_ambc_VariableInterestEntityNotPrimaryBeneficiaryTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity Not Primary Beneficiary Table [Text Block]</link:label>
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    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax_938a771e-6855-40f3-bb93-1677bb6d111e_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-sale, Accumulated Gross Unrealized Gain, before Tax</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Accumulated Gross Unrealized Gain, before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax"/>
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    <link:label id="lab_us-gaap_ShortTermInvestmentsMember_2a3781e1-3006-4256-8b05-df374e2874c1_terseLabel_en-US" xlink:label="lab_us-gaap_ShortTermInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Short-term Investments [Member]</link:label>
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    <link:label id="lab_us-gaap_ShortTermInvestmentsMember_label_en-US" xlink:label="lab_us-gaap_ShortTermInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Term Investments [Member]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShortTermInvestmentsMember" xlink:to="lab_us-gaap_ShortTermInvestmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnderlyingAssetClassDomain_99d9cde1-8f47-4bfd-b434-7f09ad1b9e1f_terseLabel_en-US" xlink:label="lab_us-gaap_UnderlyingAssetClassDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underlying Asset Class [Domain]</link:label>
    <link:label id="lab_us-gaap_UnderlyingAssetClassDomain_label_en-US" xlink:label="lab_us-gaap_UnderlyingAssetClassDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Underlying Asset Class [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnderlyingAssetClassDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_UnderlyingAssetClassDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnderlyingAssetClassDomain" xlink:to="lab_us-gaap_UnderlyingAssetClassDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_4c2cea5b-1ba5-4989-8304-95823e01013e_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustments to reconcile net income to net cash used in operating activities:</link:label>
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    <link:label id="lab_ambc_DerivativeAssetsNetAmount_1eee9d82-c8c3-435a-b674-bc7617250650_terseLabel_en-US" xlink:label="lab_ambc_DerivativeAssetsNetAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net Amount, Derivative Assets</link:label>
    <link:label id="lab_ambc_DerivativeAssetsNetAmount_label_en-US" xlink:label="lab_ambc_DerivativeAssetsNetAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Assets Net Amount</link:label>
    <link:label id="lab_ambc_DerivativeAssetsNetAmount_documentation_en-US" xlink:label="lab_ambc_DerivativeAssetsNetAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Assets Net Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_DerivativeAssetsNetAmount" xlink:href="ambc-20240630.xsd#ambc_DerivativeAssetsNetAmount"/>
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    <link:label id="lab_us-gaap_DerivativeLineItems_4e5784b8-ebb2-4d83-888a-3e7291295dab_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative [Line Items]</link:label>
    <link:label id="lab_us-gaap_DerivativeLineItems_label_en-US" xlink:label="lab_us-gaap_DerivativeLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLineItems" xlink:to="lab_us-gaap_DerivativeLineItems" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_ReinsuranceRetentionPolicyReinsuredRiskPercentage_d336a46f-36f7-4e99-a28c-65fecdaaa59a_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRetentionPolicyReinsuredRiskPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance, Reinsured Risk, Percentage</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRetentionPolicyReinsuredRiskPercentage_label_en-US" xlink:label="lab_us-gaap_ReinsuranceRetentionPolicyReinsuredRiskPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance, Reinsured Risk, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRetentionPolicyReinsuredRiskPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ReinsuranceRetentionPolicyReinsuredRiskPercentage"/>
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    <link:label id="lab_us-gaap_VariableInterestEntityActivityBetweenVIEAndEntityIncomeOrLossBeforeTax_c7c55df6-d947-4905-b59b-039619aa0fb2_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityActivityBetweenVIEAndEntityIncomeOrLossBeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Measure of Activity, Income or Loss before Tax</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityActivityBetweenVIEAndEntityIncomeOrLossBeforeTax_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityActivityBetweenVIEAndEntityIncomeOrLossBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Measure of Activity, Income or Loss before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityActivityBetweenVIEAndEntityIncomeOrLossBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_VariableInterestEntityActivityBetweenVIEAndEntityIncomeOrLossBeforeTax"/>
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    <link:label id="lab_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccountsRecoveries_0f691717-b8e0-4dfe-b96e-0513e66f7bfd_terseLabel_en-US" xlink:label="lab_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccountsRecoveries" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Premium Receivable, Allowance for Credit Loss, Recovery</link:label>
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    <link:label id="lab_us-gaap_OtherCommitmentsAxis_79619225-e2ed-42d4-841e-43126943f34d_terseLabel_en-US" xlink:label="lab_us-gaap_OtherCommitmentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Commitments [Axis]</link:label>
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    <link:label id="lab_us-gaap_AdditionalPaidInCapital_ae2fc929-7fa0-4226-ae7e-e694340fe259_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional paid-in capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapital_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid in Capital</link:label>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Fair Value, Maturity, Allocated and Single Maturity Date, after Year 5 Through 10</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue"/>
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    <link:label id="lab_us-gaap_NetIncomeLossIncludingPortionAttributableToNonredeemableNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossIncludingPortionAttributableToNonredeemableNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss), Including Portion Attributable to Nonredeemable Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossIncludingPortionAttributableToNonredeemableNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetIncomeLossIncludingPortionAttributableToNonredeemableNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossIncludingPortionAttributableToNonredeemableNoncontrollingInterest" xlink:to="lab_us-gaap_NetIncomeLossIncludingPortionAttributableToNonredeemableNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansReceivableFairValueDisclosure_e5770afe-488a-4857-9b75-f3f0489490b1_terseLabel_en-US" xlink:label="lab_us-gaap_LoansReceivableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans</link:label>
    <link:label id="lab_us-gaap_LoansReceivableFairValueDisclosure_1dcb6ec9-a4ca-4349-aff7-ef7d558ca5a7_verboseLabel_en-US" xlink:label="lab_us-gaap_LoansReceivableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Loans, Estimated fair value</link:label>
    <link:label id="lab_us-gaap_LoansReceivableFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_LoansReceivableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans Receivable, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansReceivableFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LoansReceivableFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansReceivableFairValueDisclosure" xlink:to="lab_us-gaap_LoansReceivableFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumsReceivableAdjustmentChangeInPeriodOfContract_eff8b04a-8fd7-4691-972c-d08aa93e0706_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumsReceivableAdjustmentChangeInPeriodOfContract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustments for changes in expected and contractual cash flows</link:label>
    <link:label id="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumsReceivableAdjustmentChangeInPeriodOfContract_label_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumsReceivableAdjustmentChangeInPeriodOfContract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Guarantee Insurance Contracts, Premiums Receivable, Increase (Decrease), Change in Period of Contract</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialGuaranteeInsuranceContractsPremiumsReceivableAdjustmentChangeInPeriodOfContract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancialGuaranteeInsuranceContractsPremiumsReceivableAdjustmentChangeInPeriodOfContract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialGuaranteeInsuranceContractsPremiumsReceivableAdjustmentChangeInPeriodOfContract" xlink:to="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumsReceivableAdjustmentChangeInPeriodOfContract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PledgedStatusDomain_faa8ca33-f0a4-4afd-9ecc-86bc89449d07_terseLabel_en-US" xlink:label="lab_us-gaap_PledgedStatusDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pledged Status [Domain]</link:label>
    <link:label id="lab_us-gaap_PledgedStatusDomain_label_en-US" xlink:label="lab_us-gaap_PledgedStatusDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pledged Status [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PledgedStatusDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PledgedStatusDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PledgedStatusDomain" xlink:to="lab_us-gaap_PledgedStatusDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember_9916b28d-b2fb-4e18-9465-f9c39a5a531e_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Financial Instruments, Liabilities [Member]</link:label>
    <link:label id="lab_us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember_label_en-US" xlink:label="lab_us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Financial Instruments, Liabilities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember" xlink:to="lab_us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetOrLiabilityPurchases_6c6fef11-5eda-477c-875f-ef99a0cf649e_terseLabel_en-US" xlink:label="lab_ambc_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetOrLiabilityPurchases" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurement With Unobservable Inputs Reconciliation Recurring Basis Asset Or Liability Purchases</link:label>
    <link:label id="lab_ambc_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetOrLiabilityPurchases_label_en-US" xlink:label="lab_ambc_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetOrLiabilityPurchases" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement With Unobservable Inputs Reconciliation Recurring Basis Asset Or Liability Purchases</link:label>
    <link:label id="lab_ambc_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetOrLiabilityPurchases_documentation_en-US" xlink:label="lab_ambc_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetOrLiabilityPurchases" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Amount of purchases of financial instruments measured on a recurring basis using unobservable inputs.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetOrLiabilityPurchases" xlink:href="ambc-20240630.xsd#ambc_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetOrLiabilityPurchases"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetOrLiabilityPurchases" xlink:to="lab_ambc_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetOrLiabilityPurchases" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeLiabilityAmountNotOffsetAgainstCollateral_c1303544-c230-4d7f-850e-878308bc840c_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeLiabilityAmountNotOffsetAgainstCollateral" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value of derivative liabilities</link:label>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeLiabilityAmountNotOffsetAgainstCollateral_33474e0e-79c8-4ce5-8c83-332194cbe8ba_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeLiabilityAmountNotOffsetAgainstCollateral" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Derivative Liability, Fair Value, Amount Not Offset Against Collateral</link:label>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeLiabilityAmountNotOffsetAgainstCollateral_label_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeLiabilityAmountNotOffsetAgainstCollateral" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Subject to Master Netting Arrangement, before Offset of Collateral</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeFairValueOfDerivativeLiabilityAmountNotOffsetAgainstCollateral" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeFairValueOfDerivativeLiabilityAmountNotOffsetAgainstCollateral"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeFairValueOfDerivativeLiabilityAmountNotOffsetAgainstCollateral" xlink:to="lab_us-gaap_DerivativeFairValueOfDerivativeLiabilityAmountNotOffsetAgainstCollateral" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan25AndWithin30YearsFromBalanceSheetDate_f62d24f8-d672-48e7-b1e5-c0f90727b00b_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan25AndWithin30YearsFromBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Future premiums expected to be collected, December 31, 2050</link:label>
    <link:label id="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan25AndWithin30YearsFromBalanceSheetDate_label_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan25AndWithin30YearsFromBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Guarantee Insurance Contract, Premium Receivable, to be Collected, after Year 25 Through 30</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan25AndWithin30YearsFromBalanceSheetDate" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan25AndWithin30YearsFromBalanceSheetDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan25AndWithin30YearsFromBalanceSheetDate" xlink:to="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan25AndWithin30YearsFromBalanceSheetDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MunicipalBondsMember_9746a875-6b82-41fc-bbb4-6c02df25628b_terseLabel_en-US" xlink:label="lab_us-gaap_MunicipalBondsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Municipal Bonds [Member]</link:label>
    <link:label id="lab_us-gaap_MunicipalBondsMember_label_en-US" xlink:label="lab_us-gaap_MunicipalBondsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Municipal Bonds [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MunicipalBondsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_MunicipalBondsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MunicipalBondsMember" xlink:to="lab_us-gaap_MunicipalBondsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingArrLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingArrLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Arrangements [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingArrLineItems" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_InsiderTradingArrLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTradingArrLineItems" xlink:to="lab_ecd_InsiderTradingArrLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetOrLiabilityDeconsolidationOfVies_e5b7278e-0cdf-4cb6-885a-b23e0da7e11f_terseLabel_en-US" xlink:label="lab_ambc_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetOrLiabilityDeconsolidationOfVies" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset Value</link:label>
    <link:label id="lab_ambc_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetOrLiabilityDeconsolidationOfVies_label_en-US" xlink:label="lab_ambc_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetOrLiabilityDeconsolidationOfVies" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement With Unobservable Inputs Reconciliation Recurring Basis Asset Or Liability Deconsolidation Of Vies</link:label>
    <link:label id="lab_ambc_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetOrLiabilityDeconsolidationOfVies_documentation_en-US" xlink:label="lab_ambc_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetOrLiabilityDeconsolidationOfVies" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair value of financial instruments measured on a recurring basis using unobservable inputs removed as a result of the deconsolidation of variable interest entities.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetOrLiabilityDeconsolidationOfVies" xlink:href="ambc-20240630.xsd#ambc_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetOrLiabilityDeconsolidationOfVies"/>
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    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_82ff751e-62bd-4d1c-863e-9651d36823ac_verboseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Number of new common stock issued</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Shares Issued, Shares, Share-Based Payment Arrangement, after Forfeiture</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityRegistrantName_984c5115-427e-4448-8295-1622c04d9775_terseLabel_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:label id="lab_dei_EntityRegistrantName_label_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityRegistrantName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityRegistrantName" xlink:to="lab_dei_EntityRegistrantName" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MtrlTermsOfTrdArrTextBlock_terseLabel_en-US" xlink:label="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Material Terms of Trading Arrangement</link:label>
    <link:label id="lab_ecd_MtrlTermsOfTrdArrTextBlock_label_en-US" xlink:label="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Material Terms of Trading Arrangement [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MtrlTermsOfTrdArrTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_MtrlTermsOfTrdArrTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MtrlTermsOfTrdArrTextBlock" xlink:to="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Method</link:label>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_AwardTmgMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMethodTextBlock" xlink:to="lab_ecd_AwardTmgMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation, Amount</link:label>
    <link:label id="lab_ecd_AdjToCompAmt_label_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_AdjToCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAmt" xlink:to="lab_ecd_AdjToCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsNet_575c2932-1f06-4ca3-a595-7aabe117cd69_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments:</link:label>
    <link:label id="lab_us-gaap_AssetsNet_label_en-US" xlink:label="lab_us-gaap_AssetsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssetsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsNet" xlink:to="lab_us-gaap_AssetsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterest_d3910952-e3a5-480b-986d-8ebfbde17c6d_verboseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterest" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Noncontrolling interest</link:label>
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    <link:label id="lab_us-gaap_AllocatedShareBasedCompensationExpense_b213f0ea-1ba7-455c-81fc-5fa9dc3ada01_terseLabel_en-US" xlink:label="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock-based compensation</link:label>
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    <link:label id="lab_ambc_AffinityProductsMember_2339d199-3ff4-4d67-ae9f-f4e918e523e7_terseLabel_en-US" xlink:label="lab_ambc_AffinityProductsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Affinity Products</link:label>
    <link:label id="lab_ambc_AffinityProductsMember_label_en-US" xlink:label="lab_ambc_AffinityProductsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Affinity Products [Member]</link:label>
    <link:label id="lab_ambc_AffinityProductsMember_documentation_en-US" xlink:label="lab_ambc_AffinityProductsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Affinity Products</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_AffinityProductsMember" xlink:href="ambc-20240630.xsd#ambc_AffinityProductsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_AffinityProductsMember" xlink:to="lab_ambc_AffinityProductsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:to="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense_641a8454-0832-49b0-9be7-bb3873bd496d_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred Policy Acquisition Costs, Amortization Expense</link:label>
    <link:label id="lab_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense_label_en-US" xlink:label="lab_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Policy Acquisition Costs, Amortization Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense" xlink:to="lab_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityIncorporationDateOfIncorporation_56e0e7bd-bde2-4bff-9cb4-9494e4a4f7f7_verboseLabel_en-US" xlink:label="lab_dei_EntityIncorporationDateOfIncorporation" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Entity Incorporation, Date of Incorporation</link:label>
    <link:label id="lab_dei_EntityIncorporationDateOfIncorporation_label_en-US" xlink:label="lab_dei_EntityIncorporationDateOfIncorporation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Incorporation, Date of Incorporation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityIncorporationDateOfIncorporation" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityIncorporationDateOfIncorporation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityIncorporationDateOfIncorporation" xlink:to="lab_dei_EntityIncorporationDateOfIncorporation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingExpensesAbstract_7e0f36ca-21c3-487f-9ce9-2702a5d5ca62_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expenses:</link:label>
    <link:label id="lab_us-gaap_OperatingExpensesAbstract_label_en-US" xlink:label="lab_us-gaap_OperatingExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Expenses [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingExpensesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OperatingExpensesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingExpensesAbstract" xlink:to="lab_us-gaap_OperatingExpensesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_NetIncomeLossReconciliationTable_b3a049a2-35ce-4927-b4a2-633330f1ef4c_terseLabel_en-US" xlink:label="lab_ambc_NetIncomeLossReconciliationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net Income Loss Reconciliation [Table]</link:label>
    <link:label id="lab_ambc_NetIncomeLossReconciliationTable_label_en-US" xlink:label="lab_ambc_NetIncomeLossReconciliationTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income Loss Reconciliation [Table]</link:label>
    <link:label id="lab_ambc_NetIncomeLossReconciliationTable_documentation_en-US" xlink:label="lab_ambc_NetIncomeLossReconciliationTable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Net Income Loss Reconciliation [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_NetIncomeLossReconciliationTable" xlink:href="ambc-20240630.xsd#ambc_NetIncomeLossReconciliationTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_NetIncomeLossReconciliationTable" xlink:to="lab_ambc_NetIncomeLossReconciliationTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_FairValueOfCashAndSecuritiesPledgedToDerivativeCounterparties_f05b7655-6bb5-452d-bf6a-1f74c7e22570_terseLabel_en-US" xlink:label="lab_ambc_FairValueOfCashAndSecuritiesPledgedToDerivativeCounterparties" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value of Cash and Securities Pledged to Derivative Counterparties</link:label>
    <link:label id="lab_ambc_FairValueOfCashAndSecuritiesPledgedToDerivativeCounterparties_label_en-US" xlink:label="lab_ambc_FairValueOfCashAndSecuritiesPledgedToDerivativeCounterparties" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Of Cash And Securities Pledged To Derivative Counterparties</link:label>
    <link:label id="lab_ambc_FairValueOfCashAndSecuritiesPledgedToDerivativeCounterparties_documentation_en-US" xlink:label="lab_ambc_FairValueOfCashAndSecuritiesPledgedToDerivativeCounterparties" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair value of cash and securities pledged to derivative counterparties.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_FairValueOfCashAndSecuritiesPledgedToDerivativeCounterparties" xlink:href="ambc-20240630.xsd#ambc_FairValueOfCashAndSecuritiesPledgedToDerivativeCounterparties"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_FairValueOfCashAndSecuritiesPledgedToDerivativeCounterparties" xlink:to="lab_ambc_FairValueOfCashAndSecuritiesPledgedToDerivativeCounterparties" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss_4b9d9255-e777-4141-9134-903e0d5443a1_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-sale, Realized Loss</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss_203b2ec9-0825-480b-a343-86ef0d5cf310_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Available-for-sale Securities, Gross Realized Losses</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Realized Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_CoSelectedMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureAmt" xlink:to="lab_ecd_CoSelectedMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditRiskDerivativesAtFairValueNetAbstract_df14b945-4bf6-44c0-8b50-eade36eac420_terseLabel_en-US" xlink:label="lab_us-gaap_CreditRiskDerivativesAtFairValueNetAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in fair value of credit derivatives:</link:label>
    <link:label id="lab_us-gaap_CreditRiskDerivativesAtFairValueNetAbstract_label_en-US" xlink:label="lab_us-gaap_CreditRiskDerivativesAtFairValueNetAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Risk Derivatives, at Fair Value, Net [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditRiskDerivativesAtFairValueNetAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CreditRiskDerivativesAtFairValueNetAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditRiskDerivativesAtFairValueNetAbstract" xlink:to="lab_us-gaap_CreditRiskDerivativesAtFairValueNetAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_ParsedFixedIncomeSecuritiesMember_45168bac-8409-4144-90c2-940412269f78_terseLabel_en-US" xlink:label="lab_ambc_ParsedFixedIncomeSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Parsed Fixed Income Securities</link:label>
    <link:label id="lab_ambc_ParsedFixedIncomeSecuritiesMember_label_en-US" xlink:label="lab_ambc_ParsedFixedIncomeSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Parsed Fixed Income Securities [Member]</link:label>
    <link:label id="lab_ambc_ParsedFixedIncomeSecuritiesMember_documentation_en-US" xlink:label="lab_ambc_ParsedFixedIncomeSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Parsed Fixed Income Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_ParsedFixedIncomeSecuritiesMember" xlink:href="ambc-20240630.xsd#ambc_ParsedFixedIncomeSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_ParsedFixedIncomeSecuritiesMember" xlink:to="lab_ambc_ParsedFixedIncomeSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Assets_a90b3796-5bf5-4497-9283-3116cd7255bf_terseLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total assets</link:label>
    <link:label id="lab_us-gaap_Assets_label_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Assets" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_Assets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Assets" xlink:to="lab_us-gaap_Assets" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscIndName_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscIndName_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscIndName" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_AwardsCloseToMnpiDiscIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscIndName" xlink:to="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThanFourAndWithinFiveYearsFromBalanceSheetDate_f71bf313-2c00-4a08-be82-20f6714e066a_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThanFourAndWithinFiveYearsFromBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Future expected premiums to be earned, net of reinsurance, December 31, 2025</link:label>
    <link:label id="lab_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThanFourAndWithinFiveYearsFromBalanceSheetDate_label_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThanFourAndWithinFiveYearsFromBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Guarantee Insurance Contract, Premium Revenue to be Recognized, Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThanFourAndWithinFiveYearsFromBalanceSheetDate" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThanFourAndWithinFiveYearsFromBalanceSheetDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThanFourAndWithinFiveYearsFromBalanceSheetDate" xlink:to="lab_us-gaap_FinancialGuaranteeInsuranceContractsFutureExpectedPremiumRevenueToBeRecognizedMoreThanFourAndWithinFiveYearsFromBalanceSheetDate" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_BusinessCombinationPotentialLateClosingPenaltyMaximum_36471638-0524-47ca-b292-b59a838fba6e_terseLabel_en-US" xlink:label="lab_ambc_BusinessCombinationPotentialLateClosingPenaltyMaximum" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Potential Late Closing Penalty Maximum</link:label>
    <link:label id="lab_ambc_BusinessCombinationPotentialLateClosingPenaltyMaximum_label_en-US" xlink:label="lab_ambc_BusinessCombinationPotentialLateClosingPenaltyMaximum" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Potential Late Closing Penalty Maximum</link:label>
    <link:label id="lab_ambc_BusinessCombinationPotentialLateClosingPenaltyMaximum_documentation_en-US" xlink:label="lab_ambc_BusinessCombinationPotentialLateClosingPenaltyMaximum" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Potential Late Closing Penalty Maximum</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_BusinessCombinationPotentialLateClosingPenaltyMaximum" xlink:href="ambc-20240630.xsd#ambc_BusinessCombinationPotentialLateClosingPenaltyMaximum"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_BusinessCombinationPotentialLateClosingPenaltyMaximum" xlink:to="lab_ambc_BusinessCombinationPotentialLateClosingPenaltyMaximum" xlink:type="arc" order="1"/>
    <link:label id="lab_ambc_LossandLossReservesDomain_efdd5b73-6366-4f51-8285-7b4f3fac6821_terseLabel_en-US" xlink:label="lab_ambc_LossandLossReservesDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss and Loss Reserves [Domain]</link:label>
    <link:label id="lab_ambc_LossandLossReservesDomain_label_en-US" xlink:label="lab_ambc_LossandLossReservesDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss and Loss Reserves [Domain]</link:label>
    <link:label id="lab_ambc_LossandLossReservesDomain_documentation_en-US" xlink:label="lab_ambc_LossandLossReservesDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">[Domain] for Loss and Loss Reserves [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ambc_LossandLossReservesDomain" xlink:href="ambc-20240630.xsd#ambc_LossandLossReservesDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ambc_LossandLossReservesDomain" xlink:to="lab_ambc_LossandLossReservesDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan15AndWithin20YearsFromBalanceSheetDate_052c58f1-30f0-498f-94fe-36f1a010d43a_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan15AndWithin20YearsFromBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Future premiums expected to be collected, December 31, 2040</link:label>
    <link:label id="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan15AndWithin20YearsFromBalanceSheetDate_label_en-US" xlink:label="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan15AndWithin20YearsFromBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Guarantee Insurance Contract, Premium Receivable, to be Collected, after Year 15 Through 20</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan15AndWithin20YearsFromBalanceSheetDate" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan15AndWithin20YearsFromBalanceSheetDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan15AndWithin20YearsFromBalanceSheetDate" xlink:to="lab_us-gaap_FinancialGuaranteeInsuranceContractsPremiumExpectedToBeCollectedMoreThan15AndWithin20YearsFromBalanceSheetDate" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityBankruptcyProceedingsReportingCurrent_e8ef5f41-f270-4f96-9271-da6cf67d5bce_terseLabel_en-US" xlink:label="lab_dei_EntityBankruptcyProceedingsReportingCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Bankruptcy Proceedings, Reporting Current</link:label>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_47089978-6b2e-4f5b-9589-cb34d4ee344a_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Financing Activities [Abstract]</link:label>
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