{"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/monge-ampere-flow-for-generative-modeling","title":"Monge-Ampère Flow for Generative Modeling","arxiv_id":"1809.10188","date":"2018-09-26","proceeding":null,"authors":["Linfeng Zhang","Weinan E","Lei Wang"],"abstract":"We present a deep generative model, named Monge-Amp\\`ere flow, which builds\non continuous-time gradient flow arising from the Monge-Amp\\`ere equation in\noptimal transport theory. The generative map from the latent space to the data\nspace follows a dynamical system, where a learnable potential function guides a\ncompressible fluid to flow towards the target density distribution. Training of\nthe model amounts to solving an optimal control problem. The Monge-Amp\\`ere\nflow has tractable likelihoods and supports efficient sampling and inference.\nOne can easily impose symmetry constraints in the generative model by designing\nsuitable scalar potential functions. We apply the approach to unsupervised\ndensity estimation of the MNIST dataset and variational calculation of the\ntwo-dimensional Ising model at the critical point. This approach brings\ninsights and techniques from Monge-Amp\\`ere equation, optimal transport, and\nfluid dynamics into reversible flow-based generative models.","url_abs":"http://arxiv.org/abs/1809.10188v1","url_pdf":"http://arxiv.org/pdf/1809.10188v1.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":"monge-ampere-flow-for-generative-modeling","repo_url":"https://github.com/wangleiphy/MongeAmpereFlow","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"density-estimation","task_name":"Density Estimation"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1809.10188","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}