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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-07-02</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001420800</issuerCik>
        <issuerName>Colfax CORP</issuerName>
        <issuerTradingSymbol>CFX</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001357529</rptOwnerCik>
            <rptOwnerName>Hix Christopher M</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>420 NATIONAL BUSINESS PARKWAY</rptOwnerStreet1>
            <rptOwnerStreet2>5TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>ANNAPOLIS JUNCTION</rptOwnerCity>
            <rptOwnerState>MD</rptOwnerState>
            <rptOwnerZipCode>20701</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>SVP, Chief Financial Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $.001</value>
            </securityTitle>
            <transactionDate>
                <value>2019-07-02</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>2591</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>27.105</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>29841</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $.001</value>
            </securityTitle>
            <transactionDate>
                <value>2019-07-02</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>2159</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>27.042</value>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>27682</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The sales reported in this Form 4 were effected pursuant to a Rule 10b5-1 trading plan adopted by the reporting person to meet tax obligations relating to the vesting and delivery of certain tranches of restricted stock units and performance-based restricted stock units granted to Mr. Hix upon his hire in July 2016.  For more information on the details of these RSUs and PRSUs, please refer to the &quot;Outstanding Equity Awards&quot; table on page 29 of the Company's Proxy Statement as filed with the SEC on April 5, 2019.</footnote>
        <footnote id="F2">The price reported in this row of Column 4 is a weighted average price. These shares were sold in multiple transactions at prices ranging from $26.83 to $27.32, inclusive. The reporting person undertakes to provide to Colfax Corporation, any security holder of Colfax Corporation, or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of shares sold at each separate price within the ranges set forth in footnote (2) to this Form 4.</footnote>
        <footnote id="F3">The price reported in this row of Column 4 is a weighted average price. These shares were sold in multiple transactions at prices ranging from $26.90 to $27.175, inclusive. The reporting person undertakes to provide to Colfax Corporation, any security holder of Colfax Corporation, or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of shares sold at each separate price within the ranges set forth in footnote (3) to this Form 4.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Bradley Tandy, Attorney-in-Fact</signatureName>
        <signatureDate>2019-07-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
