This prospectus supplement supplements the prospectus dated November8, 2025 (the “Prospectus”), which forms a part of ourregistration statement on FormS-1(No.333-287675).This prospectus supplement is being filed to update and supplement theinformation in the Prospectus with certain information contained in our Annual Report on Form10-K,filed with the Securities andExchange Commission on March31, 2026 (the “Annual Report”). Accordingly, we have attached the Annual Report in relevant part tothis prospectus supplement. The Prospectus and this prospectus supplement relates to the resale by certain of the selling stockholders named in the Prospectus(each a “selling stockholder” and, collectively, the “selling stockholders”) of up to 2,084,117 shares of our common stock, par value$0.001per share(“common stock”)issued to the selling stockholders pursuant to the Agreement and Plan of Merger andReorganization, dated as of December17, 2024 (the “Merger Agreement”), by and among Cara Therapeutics,Inc. (“Cara”), CTConvergence Merger Sub,Inc., a wholly owned subsidiary of Cara, and Tvardi Therapeutics,Inc. Our common stock is listed on The Nasdaq Capital Market (“Nasdaq”) under the symbol “TVRD.” On March31, 2026, the lastquoted sale price for our common stock as reported on Nasdaq was $3.18. This prospectus supplement should be read in conjunction with the Prospectus, including any amendments or supplements thereto,which is to be delivered with this prospectus supplement. This prospectus supplement is qualified by reference to the Prospectus,including any amendments or supplements thereto, except to the extent that the information in this prospectus supplement updates andsupersedes the information contained therein. This prospectus supplement is not complete without, and may not be delivered or utilized except in connection with, the Prospectus,including any amendments or supplements thereto. Investing in our securities involves a high degree of risk. Before buying any securities, you should carefully read thediscussion of the risks of investing in our securities in the section titled “Risk Factors” beginning on page5 of the Prospectusand under similar headings in any amendments or supplements to the Prospectus. Neither the Securities Exchange Commission nor any state securities commission has approved or disapproved of thesesecurities or determined if this prospectus is truthful or complete. Any representation to the contrary is a criminal offense. The date of this prospectus supplement is April 1, 2026. UNITED STATESSECURITIES AND EXCHANGE COMMISSIONWASHINGTON, D.C. 20549 (Mark One) Indicate by check mark if the registrant is a well-known seasoned issuer, as defined in Rule405 of the Securities Act.Yes◻No⌧Indicate by check mark if the registrant is not required to file reports pursuant to Section13 or Section15(d)of the Act.Yes◻No⌧ Indicate by check mark whether the registrant (1)has filed all reports required to be filed by Section13 or 15(d)of the Securities Exchange Act of1934 during the preceding 12months (or for such shorter period that the registrant was required to file such reports), and (2)has been subject to such filingrequirements for the past 90days.Yes⌧No◻ Indicate by check mark whether the registrant has submitted electronically every Interactive Data File required to be submitted pursuant to Rule405of Regulation S-T (§ 232.405 of this chapter) during the preceding 12months (or for such shorter period that the registrant was required to submit suchfiles).Yes⌧No◻ Indicate by check mark whether the registrant is a large accelerated filer, an accelerated filer, a non-accelerated filer, smaller reporting company, or anemerging growth company. See the definitions of “large accelerated filer”, “accelerated filer”, “smaller reporting company” and “emerging growthcompany” in Rule12b-2 of the Exchange Act. Largeacceleratedfiler If an emerging growth company, indicate by check mark if the registrant has elected not to use the extended transition period for complying with anynew or revised financial accounting standards provided pursuant to Section13(a)of the Exchange Act.◻ Indicate by check mark whether the registrant has filed a report on and attestation to its management’s assessment of the effectiveness of its internalcontrol over financial reporting under Section 404(b) of the Sarbanes-Oxley Act (15 U.S.C. 7262(b)) by the registered public accounting firm that preparedor issued its audit report.☐ If securities are registered pursuant to Section 12(b) of the Act, indicate by check mark whether the financial statements of the registrant included inthe filing reflect the correction of an error to previously issued financial statements. Yes☐No⌧ Indicate by check mark whether any of those error corrections are restatements that required a recovery analysis of incentive-based compensationreceived by any of the registrant’s executive officers during the relevant recovery period pursuant to §240.10D




