{"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/diffusion-variational-autoencoders","title":"Diffusion Variational Autoencoders","arxiv_id":"1901.08991","date":"2019-01-25","proceeding":null,"authors":["Luis A. Pérez Rey","Vlado Menkovski","Jacobus W. Portegies"],"abstract":"A standard Variational Autoencoder, with a Euclidean latent space, is\nstructurally incapable of capturing topological properties of certain datasets.\nTo remove topological obstructions, we introduce Diffusion Variational\nAutoencoders with arbitrary manifolds as a latent space. A Diffusion\nVariational Autoencoder uses transition kernels of Brownian motion on the\nmanifold. In particular, it uses properties of the Brownian motion to implement\nthe reparametrization trick and fast approximations to the KL divergence. We\nshow that the Diffusion Variational Autoencoder is capable of capturing\ntopological properties of synthetic datasets. Additionally, we train MNIST on\nspheres, tori, projective spaces, SO(3), and a torus embedded in R3. Although a\nnatural dataset like MNIST does not have latent variables with a clear-cut\ntopological structure, training it on a manifold can still highlight\ntopological and geometrical properties.","url_abs":"http://arxiv.org/abs/1901.08991v2","url_pdf":"http://arxiv.org/pdf/1901.08991v2.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":"diffusion-variational-autoencoders","repo_url":"https://github.com/luis-armando-perez-rey/diffusion_vae","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"Apache-2.0"}},{"paper_slug":"diffusion-variational-autoencoders","repo_url":"https://github.com/luis-armando-perez-rey/diffusion_vae_github","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"Apache-2.0"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1901.08991","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1901.08991"}},"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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