Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

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We consent to the incorporation by reference in the registration statements (Nos. 333-287269 and 333-278442) on Form S-8 and (Nos. 333-293309 and 333-281562) on Form S-3 of our report dated March 30, 2026, with respect to the consolidated financial statements of AEON Biopharma, Inc.

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/s/ KPMG LLP

San Diego, California

March 30, 2026

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