{"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/flows-for-simultaneous-manifold-learning-and","title":"Flows for simultaneous manifold learning and density estimation","arxiv_id":"2003.13913","date":"2020-03-31","proceeding":"NeurIPS 2020 12","authors":["Johann Brehmer","Kyle Cranmer"],"abstract":"We introduce manifold-learning flows (M-flows), a new class of generative models that simultaneously learn the data manifold as well as a tractable probability density on that manifold. Combining aspects of normalizing flows, GANs, autoencoders, and energy-based models, they have the potential to represent datasets with a manifold structure more faithfully and provide handles on dimensionality reduction, denoising, and out-of-distribution detection. We argue why such models should not be trained by maximum likelihood alone and present a new training algorithm that separates manifold and density updates. In a range of experiments we demonstrate how M-flows learn the data manifold and allow for better inference than standard flows in the ambient data space.","url_abs":"https://arxiv.org/abs/2003.13913v3","url_pdf":"https://arxiv.org/pdf/2003.13913v3.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":"flows-for-simultaneous-manifold-learning-and","repo_url":"https://github.com/johannbrehmer/manifold-flow","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"flows-for-simultaneous-manifold-learning-and","repo_url":"https://github.com/layer6ai-labs/rectangular-flows","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"denoising","task_name":"Denoising"},{"task_slug":"density-estimation","task_name":"Density Estimation"},{"task_slug":"dimensionality-reduction","task_name":"Dimensionality Reduction"},{"task_slug":"out-of-distribution-detection","task_name":"Out-of-Distribution Detection"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2003.13913","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}