<?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>0001201880</rptOwnerCik>
            <rptOwnerName>MANEY JOHN C</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O PIMCO, 650 NEWPORT CENTER DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEWPORT BEACH</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>92660</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </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>5831</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>12833</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>BY DCP</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 0.818509.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Kevin Van Gorder, Attorney-in-Fact for John C. Maney</signatureName>
        <signatureDate>2021-12-14</signatureDate>
    </ownerSignature>
</ownershipDocument>
