Diffusion Variational Autoencoders
This addresses a structural limitation in VAEs for researchers in machine learning, particularly in generative modeling, but is incremental as it builds on existing VAE frameworks.
The authors tackled the problem of standard Variational Autoencoders being unable to capture topological properties of datasets by introducing Diffusion Variational Autoencoders with arbitrary manifolds as latent spaces, showing they can capture topological properties in synthetic datasets and train on MNIST across various manifolds like spheres and tori.
A standard Variational Autoencoder, with a Euclidean latent space, is structurally incapable of capturing topological properties of certain datasets. To remove topological obstructions, we introduce Diffusion Variational Autoencoders with arbitrary manifolds as a latent space. A Diffusion Variational Autoencoder uses transition kernels of Brownian motion on the manifold. In particular, it uses properties of the Brownian motion to implement the reparametrization trick and fast approximations to the KL divergence. We show that the Diffusion Variational Autoencoder is capable of capturing topological properties of synthetic datasets. Additionally, we train MNIST on spheres, tori, projective spaces, SO(3), and a torus embedded in R3. Although a natural dataset like MNIST does not have latent variables with a clear-cut topological structure, training it on a manifold can still highlight topological and geometrical properties.