{"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/poisson-flow-generative-models","title":"Poisson Flow Generative Models","arxiv_id":"2209.11178","date":"2022-09-22","proceeding":null,"authors":["Yilun Xu","Ziming Liu","Max Tegmark","Tommi Jaakkola"],"abstract":"We propose a new \"Poisson flow\" generative model (PFGM) that maps a uniform distribution on a high-dimensional hemisphere into any data distribution. We interpret the data points as electrical charges on the $z=0$ hyperplane in a space augmented with an additional dimension $z$, generating a high-dimensional electric field (the gradient of the solution to Poisson equation). We prove that if these charges flow upward along electric field lines, their initial distribution in the $z=0$ plane transforms into a distribution on the hemisphere of radius $r$ that becomes uniform in the $r \\to\\infty$ limit. To learn the bijective transformation, we estimate the normalized field in the augmented space. For sampling, we devise a backward ODE that is anchored by the physically meaningful additional dimension: the samples hit the unaugmented data manifold when the $z$ reaches zero. Experimentally, PFGM achieves current state-of-the-art performance among the normalizing flow models on CIFAR-10, with an Inception score of $9.68$ and a FID score of $2.35$. It also performs on par with the state-of-the-art SDE approaches while offering $10\\times $ to $20 \\times$ acceleration on image generation tasks. Additionally, PFGM appears more tolerant of estimation errors on a weaker network architecture and robust to the step size in the Euler method. The code is available at https://github.com/Newbeeer/poisson_flow .","url_abs":"https://arxiv.org/abs/2209.11178v4","url_pdf":"https://arxiv.org/pdf/2209.11178v4.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":"poisson-flow-generative-models","repo_url":"https://github.com/newbeeer/poisson_flow","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"jax","reach":{"status":"ok","spdx":"Apache-2.0"}}],"tasks":[{"task_slug":"image-generation","task_name":"Image Generation"}],"methods":[{"method_slug":"pfgm","method_name":"PFGM"}],"datasets_introduced":[],"methods_introduced":[{"slug":"pfgm","name":"PFGM","full_name":"Poisson Flow Generative Models"}],"results":[{"leaderboard":"/sota/image-generation-on-cifar-10","task":"Image Generation","dataset":"CIFAR-10","model":"PFGM","rank_in_archive_order":22,"of":78,"metrics":{"FID":"2.48"},"uses_additional_data":false}],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2209.11178","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2209.11178"}},"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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