<?xml version="1.0"?><?xml-stylesheet type="text/xsl" href="../4_X02.xsl"?><ownershipDocument>    <schemaVersion>X0303</schemaVersion>    <documentType>4</documentType>    <periodOfReport>2010-09-03</periodOfReport>    <notSubjectToSection16>0</notSubjectToSection16>    <issuer>        <issuerCik>0000910638</issuerCik>        <issuerName>3D SYSTEMS CORP</issuerName>        <issuerTradingSymbol>TDSC</issuerTradingSymbol>    </issuer>    <reportingOwner>        <reportingOwnerId>            <rptOwnerCik>0001105969</rptOwnerCik>            <rptOwnerName>MOORE KEVIN S</rptOwnerName>        </reportingOwnerId>        <reportingOwnerAddress>            <rptOwnerStreet1>333 THREE D SYSTEMS CIRCLE</rptOwnerStreet1>            <rptOwnerStreet2></rptOwnerStreet2>            <rptOwnerCity>ROCK HILL</rptOwnerCity>            <rptOwnerState>SC</rptOwnerState>            <rptOwnerZipCode>29730</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>2010-09-03</value>            </transactionDate>            <deemedExecutionDate></deemedExecutionDate>            <transactionCoding>                <transactionFormType>4</transactionFormType>                <transactionCode>P</transactionCode>                <equitySwapInvolved>0</equitySwapInvolved>            </transactionCoding>            <transactionTimeliness>                <value></value>            </transactionTimeliness>            <transactionAmounts>                <transactionShares>                    <value>400</value>                </transactionShares>                <transactionPricePerShare>                    <value>13.19</value>                </transactionPricePerShare>                <transactionAcquiredDisposedCode>                    <value>A</value>                </transactionAcquiredDisposedCode>            </transactionAmounts>            <postTransactionAmounts>                <sharesOwnedFollowingTransaction>                    <value>2228257</value>                </sharesOwnedFollowingTransaction>            </postTransactionAmounts>            <ownershipNature>                <directOrIndirectOwnership>                    <value>I</value>                </directOrIndirectOwnership>                <natureOfOwnership>                    <value>See Footnotes</value>                    <footnoteId id="F1"/>                    <footnoteId id="F2"/>                </natureOfOwnership>            </ownershipNature>        </nonDerivativeTransaction>        <nonDerivativeHolding>            <securityTitle>                <value>Common Stock</value>            </securityTitle>            <postTransactionAmounts>                <sharesOwnedFollowingTransaction>                    <value>25150</value>                </sharesOwnedFollowingTransaction>            </postTransactionAmounts>            <ownershipNature>                <directOrIndirectOwnership>                    <value>D</value>                </directOrIndirectOwnership>            </ownershipNature>        </nonDerivativeHolding>    </nonDerivativeTable>    <footnotes>        <footnote id="F1">These securities are beneficially owned through The Clark Estates, Inc., a New York corporation, of which the Reporting Person is President and a director.</footnote>        <footnote id="F2">The Reporting Person disclaims beneficial ownership of these securities except to the extent of any pecuniary interest therein.</footnote>    </footnotes>    <remarks></remarks>    <ownerSignature>        <signatureName>/s/Robert M. Grace, Jr., Attorney-in-Fact</signatureName>        <signatureDate>2010-09-07</signatureDate>    </ownerSignature></ownershipDocument>
