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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-09-16</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0001328015</issuerCik>
        <issuerName>Imprivata Inc</issuerName>
        <issuerTradingSymbol>IMPR</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001206640</rptOwnerCik>
            <rptOwnerName>BARRETT DAVID E</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O IMPRIVATA, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>10 MAGUIRE ROAD, BUILDING 1, SUITE 125</rptOwnerStreet2>
            <rptOwnerCity>LEXINGTON</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02421</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2016-09-16</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>2797576</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Disposed of pursuant to the Agreement and Plan of Merger between the Issuer, Project Brady Merger Sub, Inc. and Project Brady Holdings, LLC (the &quot;Merger Agreement&quot;) whereby, at the effective time of the merger contemplated therein, all issued and outstanding shares of the Issuer's common stock were converted into the right to receive $19.25 per share in cash and when so converted, automatically cancelled.</footnote>
        <footnote id="F2">2,686,498 of these shares were held directly by Polaris Venture Partners III, L.P., 69,076 of these shares were held directly by Polaris Venture Partners Entrepreneurs' Fund III, L.P. and 42,002 of these shares were held by Polaris Venture Partners Founders' Fund III, L.P. Polaris Venture Management Co. III, L.L.C. is the general partner of each of Polaris Venture Partners III, L.P., Polaris Venture Partners Entrepreneurs' Fund III, L.P. and Polaris Venture Partners Founders' Fund III, L.P. The Reporting Person is a member of Polaris Venture Management Co. III L.L.C., and may be deemed to be an indirect beneficial owner of the reported securities. The Reporting Person disclaims beneficial ownership of such securities, except to the extent of his pecuniary interest therein. This report shall not be deemed to be an admission that the Reporting Person is the beneficial owner of such securities for purposes of Section 16 or any other purpose.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ John Milton, as Attorney-in-Fact for David Barrett</signatureName>
        <signatureDate>2016-09-16</signatureDate>
    </ownerSignature>
</ownershipDocument>
