Learning Deep-Latent Hierarchies by Stacking Wasserstein Autoencoders

Benoit Gaujac, Ilya Feige, David Barber

Keywords: Generative modelling, Optimal Transport

TL;DR: We train a deep-hierarchical-latent-variable model based on Optimal Transport.

Abstract: Probabilistic models with hierarchical-latent-variable structures provide state-of-the-art results amongst non-autoregressive, unsupervised density-based models. However, the most common approach to training such models based on Variational Autoencoders often fails to leverage deep-latent hierarchies; successful approaches require complex inference and optimisation schemes. Optimal Transport is an alternative, non-likelihood-based framework for training generative models with appealing theoretical properties, in principle allowing easier training convergence between distributions. In this work we propose a novel approach to training models with deep-latent hierarchies based on Optimal Transport, without the need for highly bespoke models and inference networks. We show that our method enables the generative model to fully leverage its deep-latent hierarchy, and that in-so-doing, it is more effective than the original Wasserstein Autoencoder with Maximum Mean Discrepancy divergence.