EXHIBIT 31.1

DIFFUSION PHARMACEUTICALS INC.CERTIFICATION OF CEO PURSUANT TO SECTION 302 OFTHE SARBANES-OXLEY ACT OF 2002

CERTIFICATION

I, David G. Kalergis, certify that:

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|1. | I have reviewed this Amendment No. 1 to this annual report on Form 10-K of Diffusion Pharmaceuticals Inc.;                                                                                                                                                                                                                          
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|2. | Based on my knowledge, this report does not contain any untrue statement of a material fact or omit to state a material fact necessary to make the statements made, in light of the circumstances under which such statements were made, not misleading with respect to the period covered by this report;                          
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|3. | Based on my knowledge, the financial statements, and other financial information included in this report, fairly present in all material respects the financial condition, results of operations and cash flows of the registrant as of, and for, the periods presented in this report;                                             
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|4. | The registrant’s other certifying officer and I are responsible for establishing and maintaining disclosure controls and procedures (as defined in Exchange Act Rules 13a-15(e) and 15d-15(e)) and internal control over financial reporting (as defined in Exchange Act Rules 13a-15(f) and 15d-15(f)) for the registrant and have:
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|5. | The registrant’s other certifying officer and I have disclosed, based on our most recent evaluation of internal control over financial reporting, to the registrant’s auditors and the audit committee of the registrant’s board of directors (or persons performing the equivalent functions):                                     
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|Date: April 28, 2017 | /s/ David G. Kalergis                                              | 
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|                     | David G. Kalergis                                                  | 
|                     | Chairman and Chief Executive Officer
(Principal Executive Officer) |