{"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/reflected-diffusion-models","title":"Reflected Diffusion Models","arxiv_id":"2304.04740","date":"2023-04-10","proceeding":null,"authors":["Aaron Lou","Stefano Ermon"],"abstract":"Score-based diffusion models learn to reverse a stochastic differential equation that maps data to noise. However, for complex tasks, numerical error can compound and result in highly unnatural samples. Previous work mitigates this drift with thresholding, which projects to the natural data domain (such as pixel space for images) after each diffusion step, but this leads to a mismatch between the training and generative processes. To incorporate data constraints in a principled manner, we present Reflected Diffusion Models, which instead reverse a reflected stochastic differential equation evolving on the support of the data. Our approach learns the perturbed score function through a generalized score matching loss and extends key components of standard diffusion models including diffusion guidance, likelihood-based training, and ODE sampling. We also bridge the theoretical gap with thresholding: such schemes are just discretizations of reflected SDEs. On standard image benchmarks, our method is competitive with or surpasses the state of the art without architectural modifications and, for classifier-free guidance, our approach enables fast exact sampling with ODEs and produces more faithful samples under high guidance weight.","url_abs":"https://arxiv.org/abs/2304.04740v3","url_pdf":"https://arxiv.org/pdf/2304.04740v3.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":"reflected-diffusion-models","repo_url":"https://github.com/louaaron/Reflected-Diffusion","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"image-generation","task_name":"Image Generation"}],"methods":[{"method_slug":"denoising-score-matching","method_name":"Denoising Score Matching"},{"method_slug":"diffusion","method_name":"Diffusion"}],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/image-generation-on-imagenet-32x32","task":"Image Generation","dataset":"ImageNet 32x32","model":"Reflected Diffusion","rank_in_archive_order":19,"of":35,"metrics":{"bpd":"3.74"},"uses_additional_data":false}],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2304.04740","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2304.04740"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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