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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-04-06</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001622229</issuerCik>
        <issuerName>Unum Therapeutics Inc.</issuerName>
        <issuerTradingSymbol>UMRX</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001451612</rptOwnerCik>
            <rptOwnerName>Booth Bruce</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O UNUM THERAPEUTICS INC.</rptOwnerStreet1>
            <rptOwnerStreet2>200 CAMBRIDGE PARK DRIVE, SUITE 3100</rptOwnerStreet2>
            <rptOwnerCity>CAMBRIDGE</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02140</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.3495</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2020-04-06</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>86735</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.2205</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2030-04-06</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>86735</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>86735</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F3"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The option award was issued to the Reporting Person, who elected to take shares in lieu of cash compensation for services as a director, pursuant to the Issuer's non-employee director compensation plan. The number of options granted was determined by dividing the cash compensation otherwise payable with respect to the quarter by the Black-Scholes value of a single option calculated as of the date of the grant.</footnote>
        <footnote id="F2">This option is fully vested at time of grant.</footnote>
        <footnote id="F3">This option was granted to the Reporting Person, a director of the Issuer. The proceeds of any sale of shares of common stock issued to the Reporting Person upon exercise of this option will be transferred to Atlas Venture Advisors, LLC and as such, the Reporting Person disclaims beneficial ownership of the securities reported herein for purposes of Section 16 of the Securities Exchange Act of 1934, as amended, except to the extent of this pecuniary interest therein, if any.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Frank Castellucci, as Attorney-in-Fact</signatureName>
        <signatureDate>2020-04-08</signatureDate>
    </ownerSignature>
</ownershipDocument>
