{"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/forward-only-diffusion-probabilistic-models","title":"Forward-only Diffusion Probabilistic Models","arxiv_id":"2505.16733","date":"2025-05-22","proceeding":null,"authors":["Ziwei Luo","Fredrik K. Gustafsson","Jens Sjölund","Thomas B. Schön"],"abstract":"This work presents a forward-only diffusion (FoD) approach for generative modelling. In contrast to traditional diffusion models that rely on a coupled forward-backward diffusion scheme, FoD directly learns data generation through a single forward diffusion process, yielding a simple yet efficient generative framework. The core of FoD is a state-dependent linear stochastic differential equation that involves a mean-reverting term in both the drift and diffusion functions. This mean-reversion property guarantees the convergence to clean data, naturally simulating a stochastic interpolation between source and target distributions. More importantly, FoD is analytically tractable and is trained using a simple stochastic flow matching objective, enabling a few-step non-Markov chain sampling during inference. The proposed FoD model, despite its simplicity, achieves competitive performance on various image-conditioned (e.g., image restoration) and unconditional generation tasks, demonstrating its effectiveness in generative modelling. Our code is available at https://github.com/Algolzw/FoD.","url_abs":"https://arxiv.org/abs/2505.16733v1","url_pdf":"https://arxiv.org/pdf/2505.16733v1.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":"forward-only-diffusion-probabilistic-models","repo_url":"https://github.com/Algolzw/FoD","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"conditional-image-generation","task_name":"Conditional Image Generation"},{"task_slug":"image-dehazing","task_name":"Image Dehazing"},{"task_slug":"image-generation","task_name":"Image Generation"},{"task_slug":"image-restoration","task_name":"Image Restoration"},{"task_slug":"low-light-image-enhancement","task_name":"Low-Light Image Enhancement"},{"task_slug":"single-image-deraining","task_name":"Single Image Deraining"}],"methods":[{"method_slug":"diffusion","method_name":"Diffusion"}],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/image-generation-on-cifar-10","task":"Image Generation","dataset":"CIFAR-10","model":"FoD-ODE","rank_in_archive_order":34,"of":78,"metrics":{"FID":"5.01"},"uses_additional_data":false},{"leaderboard":"/sota/low-light-image-enhancement-on-lol","task":"Low-Light Image Enhancement","dataset":"LOL","model":"FoD","rank_in_archive_order":35,"of":40,"metrics":{"Average PSNR":"21.61","FID":"41.31","LPIPS":"0.105","SSIM":"0.819"},"uses_additional_data":false},{"leaderboard":"/sota/single-image-deraining-on-rain100h","task":"Single Image Deraining","dataset":"Rain100H","model":"Fod w/ NMC","rank_in_archive_order":3,"of":19,"metrics":{"FID":"15.64","LPIPS":"0.041","PSNR":"33.63","SSIM":"0.941"},"uses_additional_data":false},{"leaderboard":"/sota/single-image-deraining-on-rain100h","task":"Single Image Deraining","dataset":"Rain100H","model":"FoD","rank_in_archive_order":4,"of":19,"metrics":{"FID":"14.10","LPIPS":"0.038","PSNR":"32.56","SSIM":"0.925"},"uses_additional_data":false}],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2505.16733","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}