<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2021-12-10</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001510599</issuerCik>
        <issuerName>PIMCO Dynamic Income Fund</issuerName>
        <issuerTradingSymbol>PDI</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001694396</rptOwnerCik>
            <rptOwnerName>STRACKE THIBAULT CHRISTIAN</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O PIMCO</rptOwnerStreet1>
            <rptOwnerStreet2>650 NEWPORT CENTER DRIVE</rptOwnerStreet2>
            <rptOwnerCity>NEWPORT BEACH</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>92660</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>SEE REMARKS</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>COMMON SHARES</value>
            </securityTitle>
            <transactionDate>
                <value>2021-12-10</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>34577</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>34577</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The shares of the Issuer were acquired in exchange for shares of PIMCO Income Opportunity Fund (&quot;PKO&quot;) in connection with the reorganization of PKO with and into the Issuer based on PKO and the Issuer's respective net asset value per share at the time of the closing of such reorganization, which resulted in an exchange ratio of 0.949037.</footnote>
    </footnotes>

    <remarks>Pacific Investment Management Company LLC (&quot;PIMCO&quot;) is the investment adviser of the Issuer. The Reporting Person is a member of PIMCO's Executive Committee and a Managing Director of the Issuer at PIMCO.</remarks>

    <ownerSignature>
        <signatureName>/s/ Kevin Van Gorder, Attorney-in-Fact for Thibault Christian Stracke</signatureName>
        <signatureDate>2021-12-14</signatureDate>
    </ownerSignature>
</ownershipDocument>
