Disentanglement with Hyperspherical Latent Spaces using Diffusion Variational Autoencoders

A disentangled representation of a data set should be capable of recovering the underlying factors that generated it. One question that arises is whether using Euclidean space for latent variable models can produce a disentangled representation when the underlying generating factors have a certain geometrical structure. Take for example the images of a car seen from different angles. The angle has a periodic structure but a 1-dimensional representation would fail to capture this topology. How can we address this problem? The submissions presented for the first stage of the NeurIPS2019 Disentanglement Challenge consist of a Diffusion Variational Autoencoder ($\Delta$VAE) with a hyperspherical latent space which can, for example, recover periodic true factors. The training of the $\Delta$VAE is enhanced by incorporating a modified version of the Evidence Lower Bound (ELBO) for tailoring the encoding capacity of the posterior approximate.