{"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/image-restoration-with-mean-reverting","title":"Image Restoration with Mean-Reverting Stochastic Differential Equations","arxiv_id":"2301.11699","date":"2023-01-27","proceeding":null,"authors":["Ziwei Luo","Fredrik K. Gustafsson","Zheng Zhao","Jens Sjölund","Thomas B. Schön"],"abstract":"This paper presents a stochastic differential equation (SDE) approach for general-purpose image restoration. The key construction consists in a mean-reverting SDE that transforms a high-quality image into a degraded counterpart as a mean state with fixed Gaussian noise. Then, by simulating the corresponding reverse-time SDE, we are able to restore the origin of the low-quality image without relying on any task-specific prior knowledge. Crucially, the proposed mean-reverting SDE has a closed-form solution, allowing us to compute the ground truth time-dependent score and learn it with a neural network. Moreover, we propose a maximum likelihood objective to learn an optimal reverse trajectory that stabilizes the training and improves the restoration results. The experiments show that our proposed method achieves highly competitive performance in quantitative comparisons on image deraining, deblurring, and denoising, setting a new state-of-the-art on two deraining datasets. Finally, the general applicability of our approach is further demonstrated via qualitative results on image super-resolution, inpainting, and dehazing. Code is available at https://github.com/Algolzw/image-restoration-sde.","url_abs":"https://arxiv.org/abs/2301.11699v3","url_pdf":"https://arxiv.org/pdf/2301.11699v3.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":"image-restoration-with-mean-reverting","repo_url":"https://github.com/algolzw/image-restoration-sde","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"deblurring","task_name":"Deblurring"},{"task_slug":"denoising","task_name":"Denoising"},{"task_slug":"image-deblurring","task_name":"Image Deblurring"},{"task_slug":"image-denoising","task_name":"Image Denoising"},{"task_slug":"image-generation","task_name":"Image Generation"},{"task_slug":"image-inpainting","task_name":"Image Inpainting"},{"task_slug":"image-restoration","task_name":"Image Restoration"},{"task_slug":"image-super-resolution","task_name":"Image Super-Resolution"},{"task_slug":"rain-removal","task_name":"Rain Removal"},{"task_slug":"single-image-dehazing","task_name":"Single Image Dehazing"},{"task_slug":"single-image-deraining","task_name":"Single Image Deraining"},{"task_slug":"super-resolution","task_name":"Super-Resolution"}],"methods":[{"method_slug":"diffusion","method_name":"Diffusion"}],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/image-deblurring-on-gopro","task":"Image Deblurring","dataset":"GoPro","model":"IR-SDE","rank_in_archive_order":46,"of":55,"metrics":{"FID":"6.32","LPIPS":"0.064","PSNR":"30.7","SSIM":"0.901"},"uses_additional_data":false},{"leaderboard":"/sota/single-image-deraining-on-rain100h","task":"Single Image Deraining","dataset":"Rain100H","model":"IR-SDE","rank_in_archive_order":5,"of":19,"metrics":{"FID":"18.64","LPIPS":"0.047","PSNR":"31.65","SSIM":"0.9041"},"uses_additional_data":false},{"leaderboard":"/sota/single-image-deraining-on-rain100l","task":"Single Image Deraining","dataset":"Rain100L","model":"IR-SDE","rank_in_archive_order":8,"of":19,"metrics":{"FID":"7.94","LPIPS":"0.014","PSNR":"38.3","SSIM":"0.9805"},"uses_additional_data":false}],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2301.11699","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2301.11699"}},"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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