Variational Diffusion Autoencoders with Random Walk Sampling

Henry Li, Ofir Lindenbaum, Xiuyuan Cheng, Alexander Cloninger

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

7 Scopus citations


Variational autoencoders (VAEs) and generative adversarial networks (GANs) enjoy an intuitive connection to manifold learning: in training the decoder/generator is optimized to approximate a homeomorphism between the data distribution and the sampling space. This is a construction that strives to define the data manifold. A major obstacle to VAEs and GANs, however, is choosing a suitable prior that matches the data topology. Well-known consequences of poorly picked priors are posterior and mode collapse. To our knowledge, no existing method sidesteps this user choice. Conversely, diffusion maps automatically infer the data topology and enjoy a rigorous connection to manifold learning, but do not scale easily or provide the inverse homeomorphism (i.e. decoder/generator). We propose a method ( that combines these approaches into a generative model that inherits the asymptotic guarantees of diffusion maps while preserving the scalability of deep models. We prove approximation theoretic results for the dimension dependence of our proposed method. Finally, we demonstrate the effectiveness of our method with various real and synthetic datasets.

Original languageEnglish
Title of host publicationComputer Vision – ECCV 2020 - 16th European Conference, Glasgow, 2020, Proceedings
EditorsAndrea Vedaldi, Horst Bischof, Thomas Brox, Jan-Michael Frahm
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages17
ISBN (Print)9783030585914
StatePublished - 2020
Externally publishedYes
Event16th European Conference on Computer Vision, ECCV 2020 - Glasgow, United Kingdom
Duration: 23 Aug 202028 Aug 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12368 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference16th European Conference on Computer Vision, ECCV 2020
Country/TerritoryUnited Kingdom

Bibliographical note

Publisher Copyright:
© 2020, Springer Nature Switzerland AG.


  • Deep learning
  • Generative models
  • Image and video synthesis
  • Manifold learning
  • Unsupervised learning
  • Variational inference


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