<?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>0001807850</rptOwnerCik>
            <rptOwnerName>Schneider Jerome M</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>2068</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2068</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>BY 401(K)</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The shares of the Issuer were acquired in exchange for shares of PIMCO Dynamic Credit &amp; Mortgage Income Fund (&quot;PCI&quot;) in connection with the reorganization of PCI with and into the Issuer based on PCI 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 0.818509.</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.</remarks>

    <ownerSignature>
        <signatureName>/s/ Kevin Van Gorder, Attorney-in-Fact for [Jerome Schneider</signatureName>
        <signatureDate>2021-12-14</signatureDate>
    </ownerSignature>
</ownershipDocument>
