{"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/pseudo-numerical-methods-for-diffusion-models-1","title":"Pseudo Numerical Methods for Diffusion Models on Manifolds","arxiv_id":"2202.09778","date":"2022-02-20","proceeding":"ICLR 2022 4","authors":["Luping Liu","Yi Ren","Zhijie Lin","Zhou Zhao"],"abstract":"Denoising Diffusion Probabilistic Models (DDPMs) can generate high-quality samples such as image and audio samples. However, DDPMs require hundreds to thousands of iterations to produce final samples. Several prior works have successfully accelerated DDPMs through adjusting the variance schedule (e.g., Improved Denoising Diffusion Probabilistic Models) or the denoising equation (e.g., Denoising Diffusion Implicit Models (DDIMs)). However, these acceleration methods cannot maintain the quality of samples and even introduce new noise at a high speedup rate, which limit their practicability. To accelerate the inference process while keeping the sample quality, we provide a fresh perspective that DDPMs should be treated as solving differential equations on manifolds. Under such a perspective, we propose pseudo numerical methods for diffusion models (PNDMs). Specifically, we figure out how to solve differential equations on manifolds and show that DDIMs are simple cases of pseudo numerical methods. We change several classical numerical methods to corresponding pseudo numerical methods and find that the pseudo linear multi-step method is the best in most situations. According to our experiments, by directly using pre-trained models on Cifar10, CelebA and LSUN, PNDMs can generate higher quality synthetic images with only 50 steps compared with 1000-step DDIMs (20x speedup), significantly outperform DDIMs with 250 steps (by around 0.4 in FID) and have good generalization on different variance schedules. Our implementation is available at https://github.com/luping-liu/PNDM.","url_abs":"https://arxiv.org/abs/2202.09778v2","url_pdf":"https://arxiv.org/pdf/2202.09778v2.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":"pseudo-numerical-methods-for-diffusion-models-1","repo_url":"https://github.com/luping-liu/PNDM","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null},{"paper_slug":"pseudo-numerical-methods-for-diffusion-models-1","repo_url":"https://github.com/HE-diffusion/HE-diffusion","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"pseudo-numerical-methods-for-diffusion-models-1","repo_url":"https://github.com/MoonInTheRiver/DiffSinger","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"pseudo-numerical-methods-for-diffusion-models-1","repo_url":"https://github.com/beresandras/clear-diffusion-keras","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":null},{"paper_slug":"pseudo-numerical-methods-for-diffusion-models-1","repo_url":"https://github.com/compvis/latent-diffusion","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"pseudo-numerical-methods-for-diffusion-models-1","repo_url":"https://github.com/hankpipi/diffusers-hetu","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"jax","reach":{"status":"ok","spdx":"Apache-2.0"}},{"paper_slug":"pseudo-numerical-methods-for-diffusion-models-1","repo_url":"https://github.com/sanster/lama-cleaner","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"pseudo-numerical-methods-for-diffusion-models-1","repo_url":"https://github.com/voletiv/mcvd-pytorch","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"pseudo-numerical-methods-for-diffusion-models-1","repo_url":"https://github.com/MaximeVandegar/Papers-in-100-Lines-of-Code/tree/main/Pseudo_Numerical_Methods_for_Diffusion_Models_on_Manifolds","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"denoising","task_name":"Denoising"},{"task_slug":"image-generation","task_name":"Image Generation"}],"methods":[{"method_slug":"diffusion","method_name":"Diffusion"}],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/image-generation-on-celeba-64x64","task":"Image Generation","dataset":"CelebA 64x64","model":"PNDM","rank_in_archive_order":16,"of":39,"metrics":{"FID":"2.71"},"uses_additional_data":false},{"leaderboard":"/sota/image-generation-on-lsun-bedroom-256-x-256","task":"Image Generation","dataset":"LSUN Bedroom 256 x 256","model":"PNDM","rank_in_archive_order":13,"of":32,"metrics":{"FID":"5.68"},"uses_additional_data":false},{"leaderboard":"/sota/image-generation-on-lsun-churches-256-x-256","task":"Image Generation","dataset":"LSUN Churches 256 x 256","model":"PNDM","rank_in_archive_order":23,"of":27,"metrics":{"FID":"8.69"},"uses_additional_data":false}],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2202.09778","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2202.09778"}},"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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