<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>4</documentType><periodOfReport>2003-08-04</periodOfReport><notSubjectToSection16>0</notSubjectToSection16><issuer><issuerCik>0000843506</issuerCik><issuerName>VAN KAMPEN HIGH INCOME TRUST</issuerName>        <issuerTradingSymbol>VIT</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001077650</rptOwnerCik><rptOwnerName>DAMMEYER RODNEY F</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>ROD DAMMEYER, CAC, LLC</rptOwnerStreet1><rptOwnerStreet2>4350 LAJOLLA VILLAGE DRIVE, STE 980</rptOwnerStreet2><rptOwnerCity>SAN DIEGO</rptOwnerCity><rptOwnerState>CA</rptOwnerState><rptOwnerZipCode>92122</rptOwnerZipCode><rptOwnerStateDescription></rptOwnerStateDescription></reportingOwnerAddress><reportingOwnerRelationship><isDirector>1</isDirector><isOfficer>0</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther></reportingOwnerRelationship></reportingOwner><nonDerivativeTable><nonDerivativeTransaction><securityTitle><value>common shares</value></securityTitle><transactionDate><value>2003-08-04</value></transactionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>P</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>8000</value></transactionShares><transactionPricePerShare><value>3.53</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>23000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value><footnoteId id="F1" /></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction></nonDerivativeTable><footnotes><footnote id="F1">IRA Account</footnote></footnotes><remarks></remarks><ownerSignature><signatureName>/s/ Rod Dammeyer</signatureName><signatureDate>2003-08-05</signatureDate></ownerSignature></ownershipDocument>

