{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/on-the-asymptotic-mean-square-error","title":"On the Asymptotic Mean Square Error Optimality of Diffusion Models","arxiv_id":"2403.02957","date":"2024-03-05","proceeding":null,"authors":["Benedikt Fesl","Benedikt Böck","Florian Strasser","Michael Baur","Michael Joham","Wolfgang Utschick"],"abstract":"Diffusion models (DMs) as generative priors have recently shown great potential for denoising tasks but lack theoretical understanding with respect to their mean square error (MSE) optimality. This paper proposes a novel denoising strategy inspired by the structure of the MSE-optimal conditional mean estimator (CME). The resulting DM-based denoiser can be conveniently employed using a pre-trained DM, being particularly fast by truncating reverse diffusion steps and not requiring stochastic re-sampling. We present a comprehensive (non-)asymptotic optimality analysis of the proposed diffusion-based denoiser, demonstrating polynomial-time convergence to the CME under mild conditions. Our analysis also derives a novel Lipschitz constant that depends solely on the DM's hyperparameters. Further, we offer a new perspective on DMs, showing that they inherently combine an asymptotically optimal denoiser with a powerful generator, modifiable by switching re-sampling in the reverse process on or off. The theoretical findings are thoroughly validated with experiments based on various benchmark datasets.","url_abs":"https://arxiv.org/abs/2403.02957v2","url_pdf":"https://arxiv.org/pdf/2403.02957v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"on-the-asymptotic-mean-square-error","repo_url":"https://github.com/benediktfesl/diffusion_mse","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"denoising","task_name":"Denoising"}],"methods":[{"method_slug":"diffusion","method_name":"Diffusion"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}