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<ownershipDocument>

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    <documentType>4</documentType>

    <periodOfReport>2018-01-17</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001358403</issuerCik>
        <issuerName>BELLICUM PHARMACEUTICALS, INC</issuerName>
        <issuerTradingSymbol>BLCM</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001263508</rptOwnerCik>
            <rptOwnerName>BAKER BROS. ADVISORS LP</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>860 WASHINGTON STREET</rptOwnerStreet1>
            <rptOwnerStreet2>3RD FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10014</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
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            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001580575</rptOwnerCik>
            <rptOwnerName>Baker Bros. Advisors (GP) LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>860 WASHINGTON STREET</rptOwnerStreet1>
            <rptOwnerStreet2>3RD FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10014</rptOwnerZipCode>
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    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001087940</rptOwnerCik>
            <rptOwnerName>BAKER FELIX</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>860 WASHINGTON STREET</rptOwnerStreet1>
            <rptOwnerStreet2>3RD FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10014</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
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    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001087939</rptOwnerCik>
            <rptOwnerName>BAKER JULIAN</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>860 WASHINGTON STREET, 3RD FLOOR</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10014</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
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    </reportingOwner>

    <nonDerivativeTable>
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                <value>Common Stock</value>
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            <transactionDate>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>22514</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>8.6259</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
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                    <value>412246</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F7"/>
                    <footnoteId id="F8"/>
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                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionTimeliness>
                <value></value>
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            <transactionAmounts>
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                    <value>234437</value>
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                <transactionPricePerShare>
                    <value>8.6259</value>
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                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
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                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
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                    <footnoteId id="F7"/>
                    <footnoteId id="F8"/>
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            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
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                <value>Common Stock</value>
            </securityTitle>
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                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>3649</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>8.6259</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>66815</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F4"/>
                    <footnoteId id="F7"/>
                    <footnoteId id="F8"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2018-01-18</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>28058</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>8.1157</value>
                    <footnoteId id="F5"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>384188</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F7"/>
                    <footnoteId id="F8"/>
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            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2018-01-18</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>292168</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>8.1157</value>
                    <footnoteId id="F5"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
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                <sharesOwnedFollowingTransaction>
                    <value>4000484</value>
                </sharesOwnedFollowingTransaction>
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                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F7"/>
                    <footnoteId id="F8"/>
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        </nonDerivativeTransaction>
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            <transactionDate>
                <value>2018-01-18</value>
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                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>4548</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>8.1157</value>
                    <footnoteId id="F5"/>
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                <transactionAcquiredDisposedCode>
                    <value>D</value>
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                <sharesOwnedFollowingTransaction>
                    <value>62267</value>
                </sharesOwnedFollowingTransaction>
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                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F4"/>
                    <footnoteId id="F7"/>
                    <footnoteId id="F8"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2018-01-19</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionTimeliness>
                <value></value>
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            <transactionAmounts>
                <transactionShares>
                    <value>25517</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>7.9097</value>
                    <footnoteId id="F6"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
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                <sharesOwnedFollowingTransaction>
                    <value>358671</value>
                </sharesOwnedFollowingTransaction>
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                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
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                    <footnoteId id="F7"/>
                    <footnoteId id="F8"/>
                </natureOfOwnership>
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        </nonDerivativeTransaction>
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                <value>Common Stock</value>
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            <transactionDate>
                <value>2018-01-19</value>
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                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionTimeliness>
                <value></value>
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            <transactionAmounts>
                <transactionShares>
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                <transactionPricePerShare>
                    <value>7.9097</value>
                    <footnoteId id="F6"/>
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                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
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                    <footnoteId id="F7"/>
                    <footnoteId id="F8"/>
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                <value>Common Stock</value>
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            <transactionDate>
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                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
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            <transactionTimeliness>
                <value></value>
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            <transactionAmounts>
                <transactionShares>
                    <value>4136</value>
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                <transactionPricePerShare>
                    <value>7.9097</value>
                    <footnoteId id="F6"/>
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                <transactionAcquiredDisposedCode>
                    <value>D</value>
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            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F4"/>
                    <footnoteId id="F7"/>
                    <footnoteId id="F8"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The price in Column 4 is a weighted average price. These shares were traded in multiple transactions at prices ranging from $8.46 to $9.20, inclusive. The reporting persons undertake to provide to Bellicum Pharmaceuticals, Inc. (the &quot;Issuer&quot;), any security holder of the Issuer, or the staff of the Securities and Exchange Commission (&quot;SEC&quot;), upon request, full information regarding the number of shares traded at each separate price within the range set forth in this footnote.</footnote>
        <footnote id="F2">After giving effect to the transactions reported herein and as a result of Felix J. Baker's and Julian C. Baker's ownership interest in Baker Biotech Capital (GP), LLC, Felix J. Baker and Julian C. Baker may be deemed to have an indirect pecuniary interest in the Issuer's shares of Common Stock reported in column 5 of Table I directly held by 667, L.P. (&quot;667&quot;), a limited partnership of which the sole general partner is Baker Biotech Capital, L.P., a limited partnership of which the sole general partner is Baker Biotech Capital (GP),LLC, due to Baker Biotech Capital, L.P.'s right to receive an allocation of a portion of the profits from 667.</footnote>
        <footnote id="F3">After giving effect to the transactions reported herein and as a result of Felix J. Baker's and Julian C. Baker's ownership interest in Baker Brothers Life Sciences Capital (GP), LLC, Felix J. Baker and Julian C. Baker may be deemed to have an indirect pecuniary interest in the Issuer's shares of Common Stock reported in column 5 of Table I directly held by Baker Brothers Life Sciences, L.P. (&quot;Life Sciences&quot;), a limited partnership of which the sole general partner is Baker Brothers Life Sciences Capital, L.P., a limited partnership of which the sole general partner is Baker Brothers Life Sciences Capital (GP), LLC, due to Baker Brothers Life Sciences Capital, L.P.'s right to receive an allocation of a portion of the profits from Life Sciences.</footnote>
        <footnote id="F4">As a result of Felix J. Baker's and Julian C. Baker's ownership interest in 14159 Capital (GP), LLC, Felix J. Baker and Julian C. Baker may be deemed to have an indirect pecuniary interest in in the Issuer's shares of Common Stock reported in column 5 of Table I directly held by 14159, L.P. (&quot;14159&quot; and together with Life Sciences and 667, the &quot;Funds&quot;), a limited partnership of which the sole general partner is 14159 Capital, L.P., a limited partnership of which the sole general partner is 14159 Capital (GP), LLC, due to 14159 Capital, L.P.'s right to receive an allocation of a portion of the profits from 14159.</footnote>
        <footnote id="F5">The price in Column 4 is a weighted average price. These shares were traded in multiple transactions at prices ranging from $8.01 to $8.22, inclusive. The reporting persons undertake to provide to the Issuer, any security holder of the Issuer, or the staff of the SEC, upon request, full information regarding the number of shares traded at each separate price within the range set forth in this footnote.</footnote>
        <footnote id="F6">The price in Column 4 is a weighted average price. These shares were traded in multiple transactions at prices ranging from $7.70 to $8.14, inclusive. The reporting persons undertake to provide to the Issuer, any security holder of the Issuer, or the staff of the SEC, upon request, full information regarding the number of shares traded at each separate price within the range set forth in this footnote.</footnote>
        <footnote id="F7">Baker Bros. Advisors LP (the &quot;Adviser&quot;) serves as the Investment Adviser to the Funds. In connection with the services provided by the Adviser, the Adviser receives an asset-based management fee that does not confer any pecuniary interest in the securities held by the Funds. Baker Bros. Advisors (GP) LLC (the &quot;Adviser GP&quot;) is the Adviser's sole general partner. Julian C. Baker and Felix J. Baker are principals of the Adviser GP. The Adviser has complete and unlimited discretion and authority with respect to the investment and voting power of the securities held by the Funds. The general partners of the Funds relinquished to the Adviser all discretion and authority with respect to the investment and voting power of the securities held by the Funds.</footnote>
        <footnote id="F8">Julian C. Baker, Felix J. Baker, the Adviser GP and the Adviser disclaim beneficial ownership of the securities held directly by the Funds except to the extent of their pecuniary interest therein, and this report shall not be deemed an admission that any of Julian C. Baker, Felix J. Baker, the Adviser GP or the Adviser is a beneficial owner of such securities for purposes of Section 16 or any other purpose.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>By: Baker Bros. Advisors LP, Name: Scott L. Lessing, Title: President /s/ Scott L. Lessing</signatureName>
        <signatureDate>2018-01-19</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>By: Baker Bros. Advisors (GP) LLC, Name: Scott L. Lessing, Title: President /s/ Scott L. Lessing</signatureName>
        <signatureDate>2018-01-19</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Felix J. Baker</signatureName>
        <signatureDate>2018-01-19</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Julian C. Baker</signatureName>
        <signatureDate>2018-01-19</signatureDate>
    </ownerSignature>
</ownershipDocument>
