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A disentangled representation of a data set should be capable of recoveringthe underlying factors that generated it. One question that arises is whetherusing Euclidean space for latent variable models can produce a disentangledrepresentation when the underlying generating factors have a certaingeometrical structure. Take for example the images of a car seen from differentangles. The angle has a periodic structure but a 1-dimensional representationwould fail to capture this topology. How can we address this problem? Thesubmissions presented for the first stage of the NeurIPS2019 DisentanglementChallenge consist of a Diffusion Variational Autoencoder ($\Delta$VAE) with ahyperspherical latent space which can, for example, recover periodic truefactors. The training of the $\Delta$VAE is enhanced by incorporating amodified version of the Evidence Lower Bound (ELBO) for tailoring the encodingcapacity of the posterior approximate.

Disentanglement with Hyperspherical Latent Spaces using Diffusion Variational Autoencoders