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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3/A</documentType>

    <periodOfReport>2015-05-21</periodOfReport>

    <dateOfOriginalSubmission>2015-05-21</dateOfOriginalSubmission>

    <noSecuritiesOwned>1</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001636289</issuerCik>
        <issuerName>AllianzGI Diversified Income &amp; Convertible Fund</issuerName>
        <issuerTradingSymbol>ACV</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001240807</rptOwnerCik>
            <rptOwnerName>YEE MICHAEL</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1633 BROADWAY</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10019</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>Affiliated Person</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <footnotes></footnotes>

    <remarks>Mr. Yee is a portfolio manager of the fund.  Exhibit List: Exhibit 24, Power of Attorney. This amended Form 3 is filed solely for the purpose of correcting Mr. Yee's title originally reported on the Form 3 filed on May 21, 2015.</remarks>

    <ownerSignature>
        <signatureName>/s/ Thomas J. Fuccillo, Attorney-in-Fact for Michael Yee</signatureName>
        <signatureDate>2015-06-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
