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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2022-06-03</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001754068</issuerCik>
        <issuerName>Allovir, Inc.</issuerName>
        <issuerTradingSymbol>ALVR</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001457477</rptOwnerCik>
            <rptOwnerName>Hallal David</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O ALLOVIR, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>1100 WINTER STREET</rptOwnerStreet2>
            <rptOwnerCity>WALTHAM</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02451</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2022-06-03</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>65725</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>3.6684</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2077889</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>13420970</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1120965</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>738153</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F5"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">This sale was effected pursuant to a Rule 10b5-1 trading plan adopted on February 7, 2022 to cover tax withholding obligations upon the vesting and settlement of restricted stock units.</footnote>
        <footnote id="F2">The price reported in Column 4 is a weighted average price. The shares were sold in multiple transactions at prices ranging from $3.47 to $3.81. Full information regarding the number of shares sold at each separate price can be furnished to the SEC staff upon request.</footnote>
        <footnote id="F3">Shares held by ElevateBio LLC (&quot;ElevateBio&quot;). The Reporting Person is the Chairman and Chief Executive Officer of ElevateBio, and may be deemed to have shared voting and investment power of the shares held by ElevateBio. The Reporting Person disclaims beneficial ownership of these securities except to the extent of his pecuniary interest therein, and the inclusion of these shares in this report shall not be deemed an admission of beneficial ownership of all of the reported shares for purposes of Section 16 or for any other purpose.</footnote>
        <footnote id="F4">Shares held by The Hallal Family Irrevocable Trust 2012, for which the Reporting Person serves as trustee. The Reporting Person disclaims beneficial ownership of these securities except to the extent of his pecuniary interest therein, and the inclusion of these shares in this report shall not be deemed an admission of beneficial ownership of all of the reported shares for purposes of Section 16 or for any other purpose.</footnote>
        <footnote id="F5">Shares held by Terrie A. Hallal Family Irrevocable Trust 2012, for which the Reporting Person serves as trustee. The Reporting Person disclaims beneficial ownership of these securities except to the extent of his pecuniary interest therein, and the inclusion of these shares in this report shall not be deemed an admission of beneficial ownership of all of the reported shares for purposes of Section 16 or for any other purpose.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Brett Hagen, as Attorney-in-Fact</signatureName>
        <signatureDate>2022-06-06</signatureDate>
    </ownerSignature>
</ownershipDocument>
