{"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/tractable-density-estimation-on-learned-1","title":"Tractable Density Estimation on Learned Manifolds with Conformal Embedding Flows","arxiv_id":null,"date":"2021-12-01","proceeding":"NeurIPS 2021 12","authors":["Brendan Ross","Jesse Cresswell"],"abstract":"Normalizing flows are generative models that provide tractable density estimation via an invertible transformation from a simple base distribution to a complex target distribution. However, this technique cannot directly model data supported on an unknown low-dimensional manifold, a common occurrence in real-world domains such as image data. Recent attempts to remedy this limitation have introduced geometric complications that defeat a central benefit of normalizing flows: exact density estimation. We recover this benefit with Conformal Embedding Flows, a framework for designing flows that learn manifolds with tractable densities. We argue that composing a standard flow with a trainable conformal embedding is the most natural way to model manifold-supported data. To this end, we present a series of conformal building blocks and apply them in experiments with synthetic and real-world data to demonstrate that flows can model manifold-supported distributions without sacrificing tractable likelihoods.","url_abs":"http://proceedings.neurips.cc/paper/2021/hash/dfd786998e082758be12670d856df755-Abstract.html","url_pdf":"http://proceedings.neurips.cc/paper/2021/file/dfd786998e082758be12670d856df755-Paper.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":"tractable-density-estimation-on-learned-1","repo_url":"https://github.com/layer6ai-labs/CEF","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"density-estimation","task_name":"Density Estimation"}],"methods":[{"method_slug":"base","method_name":"BASE"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}