Exhibit 5.1

1095 Avenue of the Americas New York, NY 10036-6797 +1  212  698  3500  Main +1  212  698  3599  Fax www.dechert.com

January 16, 2018

Re:      Registration Statement on Form S-1

Ladies and Gentlemen:

We have acted as counsel to Diffusion Pharmaceuticals Inc., a Delaware corporation (the “Company”), in connection with the sale by the Company of (i) up to $14,950,000 of shares (the “Shares”) of its common stock, par value $0.001 per share (“Common Stock”), (ii) warrants to purchase up to $14,950,000 of shares of Common Stock (the “Investor Warrants”), (iii) underwriters’ warrants to purchase up to $934,375 of shares of Common Stock (the “Underwriter Warrants” and collectively with the  Investor Warrants, the “Warrants”), and (iv) up to $15,884,375 of shares of the Company’s Common Stock issuable upon exercise of the Warrants (the “Warrant Shares” and collectively with the Common Stock and the Warrants, the “Securities”), pursuant to the Registration Statement on Form S-1 as amended by Amendment No. 1 thereto on January 16, 2018 (File No. 333-222203) (the “Registration Statement”) filed by the Company with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), and the related Prospectus filed with the Commission. All of the Securities are to be sold by the Company as described in the Registration Statement and the related Prospectus. The term “Securities” shall include any additional Securities registered by the Company pursuant to Rule 462(b) under the Act in connection with the offering contemplated by the Registration Statement.

In connection with this opinion (this “Opinion”), we have examined originals or copies (in each case signed, certified or otherwise proven to our satisfaction to be genuine) of: (i) the Registration Statement and the related Prospectus; (ii) the Company’s Certificate of Incorporation (as amended to date); (iii) the Company’s Bylaws as currently in effect; (iv) the form of Warrant; (vi) minutes evidencing corporate action of the Company authorizing the issuance and sale of the Securities; and (vii) a certificate of an officer of the Company as to matters of fact material to this Opinion. We have also examined the Form of Underwriting Agreement, by and between the Company and H.C. Wainwright & Co., LLC.

In our examination, we have assumed the genuineness of all signatures, the authenticity of all documents submitted to us as original documents, and the conformity to original documents of all documents submitted to us as copies, the legal capacity of natural persons who are signatories to the documents examined by us and the legal power and authority of all persons signing on behalf of parties (other than the Company) to all documents.

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We have further assumed that the Securities will be issued and sold in the manner stated in the Registration Statement and the related Prospectus, and in compliance with the applicable provisions of the Act and the rules and regulations of the Commission thereunder and the securities or blue sky laws of various states and the terms and conditions of the Underwriting Agreement.  

Our opinions set forth herein are based solely upon the laws of the State of New York and the General Corporation Law of the State of Delaware as in effect on the date hereof, and we express no opinion with respect to any other laws, rules or regulations (including, without limitation, the application of the securities or “Blue Sky” laws of any state to the offer and/or sale of the Securities).

Based upon and subject to the foregoing, we are of the opinion that, as of the date hereof, (i) the Shares have been duly authorized for issuance by the Company and, when the Shares have been duly registered on the books of the transfer agent and registrar in the name and on behalf of the purchasers thereof and have been issued by the Company and delivered against payment therefor in accordance with the terms of the Underwriting Agreement, the Shares will be validly issued, fully paid and non-assessable, (ii) the Warrants have been duly authorized by the Company and, when the Warrants have been duly registered on the books of the warrant agent and registrar in the name and on behalf of the purchasers thereof and have been issued by the Company and delivered against payment therefor in accordance with the terms of the Underwriting Agreement, the Warrants will be legally valid and binding obligations of the Company and (iii) Warrant Shares have been duly authorized for issuance by the Company and, when the Warrant Shares have been duly registered on the books of the transfer agent and registrar in the name and on behalf of the holders and have been issued by the Company and delivered against payment therefor in accordance with the terms of the Warrants, the Warrant Shares will be validly issued, fully paid and non-assessable.

We hereby consent to the filing of this Opinion as an exhibit to the Company’s Amendment No. 1 to the Registration Statement, filed with the Commission on January 16, 2018 and as an exhibit to any application under the securities or other laws of any state of the United States which relate to the offer and sale of the Shares. We further consent to the use of our name under the heading “Legal Matters” in the Prospectus related to the Registration Statement and to the incorporation by reference of this letter and consent into any registration statement filed pursuant to Rule 462(b) with respect to the Securities. In giving such consent, we do not admit hereby that we come within the category of persons whose consent is required under Section 7 of the Act, or the rules and regulations of the Commission thereunder.

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This Opinion is furnished to you in connection with the offer and sale of the Securities and is not to be used, circulated, quoted or otherwise relied upon for any other purpose, except as expressly provided in the preceding paragraph. This Opinion is furnished as of the date hereof and we disclaim any undertaking to update this Opinion after the date hereof or to advise you of any subsequent changes of the facts stated or assumed herein or of any subsequent changes in applicable law.