  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.
