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

    <schemaVersion>X0407</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2023-06-07</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001020214</issuerCik>
        <issuerName>CERUS CORP</issuerName>
        <issuerTradingSymbol>CERS</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001323113</rptOwnerCik>
            <rptOwnerName>Swisher Daniel N JR</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CERUS CORPORATION</rptOwnerStreet1>
            <rptOwnerStreet2>1220 CONCORD AVE</rptOwnerStreet2>
            <rptOwnerCity>CONCORD</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94520</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>0</aff10b5One>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2023-06-07</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>40000</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>5.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>104545</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Represents the number of shares underlying RSUs. Each RSU represents a contingent right to receive one share of common stock of the Issuer. The RSUs vest on the earlier of the first anniversary of the date of grant or the day prior to the next annual meeting of stockholders, subject to the Reporting Person's continuous service to the Issuer through such vesting date.</footnote>
        <footnote id="F2">Since the date of the reporting person's last ownership report, the number of shares beneficially owned by the reporting person has been reduced by 54,263 shares pursuant to the terms of a domestic relations order. The reporting person no longer reports as beneficially owned any securities owned by his ex-spouse.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Daniel N Swisher JR by Chrystal Jensen, attorney-in-fact</signatureName>
        <signatureDate>2023-06-09</signatureDate>
    </ownerSignature>
</ownershipDocument>
