<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>4</documentType><periodOfReport>2003-08-31</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><derivativeTable><derivativeTransaction><securityTitle><value>Phantom Stock Units</value><footnoteId id="F1" /></securityTitle><conversionOrExercisePrice><value>0</value><footnoteId id="F2" /></conversionOrExercisePrice><transactionDate><value>2003-08-31</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>P</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>5150.685</value></transactionShares><transactionPricePerShare><value>3.65</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><exerciseDate><value>1988-08-08</value></exerciseDate><expirationDate><value>1988-08-08</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>5150.685</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>386390.741</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeTransaction></derivativeTable><footnotes><footnote id="F1">The phantom stock units were accrued under the VIT directors' deferred compensation plan and are to be settled 100% in cash, in generally equal annual installments over a period of five (5) years beginning on the date of the Director's retirement or disability, except that the Board of Directors, in its sole discretion, may accelerate or extend the distribution.</footnote><footnote id="F2">1 for 1</footnote></footnotes><remarks></remarks><ownerSignature><signatureName>/s/ Rod Dammeyer</signatureName><signatureDate>2003-09-02</signatureDate></ownerSignature></ownershipDocument>

