Variational Diffusion Autoencoders with Random Walk Sampling
This addresses a fundamental bottleneck in generative modeling for machine learning researchers, offering a novel integration to avoid manual prior selection, but it appears incremental as it builds on existing VAEs and diffusion maps.
The paper tackles the problem of choosing suitable priors in variational autoencoders (VAEs) and generative adversarial networks (GANs), which can lead to issues like posterior and mode collapse, by proposing a method that combines VAEs with diffusion maps to automatically infer data topology while maintaining scalability. The result is a generative model that inherits asymptotic guarantees from diffusion maps and is demonstrated effective on real and synthetic datasets, though no concrete numbers are provided.
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, $\textit{diffusion maps}$ 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 $\textit{diffusion maps}$ 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.