{"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/from-optimal-transport-to-generative-modeling","title":"From optimal transport to generative modeling: the VEGAN cookbook","arxiv_id":"1705.07642","date":"2017-05-22","proceeding":null,"authors":["Olivier Bousquet","Sylvain Gelly","Ilya Tolstikhin","Carl-Johann Simon-Gabriel","Bernhard Schoelkopf"],"abstract":"We study unsupervised generative modeling in terms of the optimal transport\n(OT) problem between true (but unknown) data distribution $P_X$ and the latent\nvariable model distribution $P_G$. We show that the OT problem can be\nequivalently written in terms of probabilistic encoders, which are constrained\nto match the posterior and prior distributions over the latent space. When\nrelaxed, this constrained optimization problem leads to a penalized optimal\ntransport (POT) objective, which can be efficiently minimized using stochastic\ngradient descent by sampling from $P_X$ and $P_G$. We show that POT for the\n2-Wasserstein distance coincides with the objective heuristically employed in\nadversarial auto-encoders (AAE) (Makhzani et al., 2016), which provides the\nfirst theoretical justification for AAEs known to the authors. We also compare\nPOT to other popular techniques like variational auto-encoders (VAE) (Kingma\nand Welling, 2014). Our theoretical results include (a) a better understanding\nof the commonly observed blurriness of images generated by VAEs, and (b)\nestablishing duality between Wasserstein GAN (Arjovsky and Bottou, 2017) and\nPOT for the 1-Wasserstein distance.","url_abs":"http://arxiv.org/abs/1705.07642v1","url_pdf":"http://arxiv.org/pdf/1705.07642v1.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":"from-optimal-transport-to-generative-modeling","repo_url":"https://github.com/zhenxuan00/graphical-gan","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"unanswered"}}],"tasks":[],"methods":[{"method_slug":"convolution","method_name":"Convolution"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1705.07642","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}