VAE with a VampPrior

Many different methods to train deep generative models have been introduced in the past. In this paper, we propose to extend the variational auto-encoder (VAE) framework with a new type of prior which we call "Variational Mixture of Posteriors" prior, or VampPrior for short. The VampPrior consists of a mixture distribution (\textit{e.g.}, a mixture of Gaussians) with components given by variational posteriors conditioned on learnable pseudo-inputs. We further extend this prior to a two layer hierarchical model and show that this architecture where prior and posterior are coupled, learns significantly better models. The model also avoids the usual local optima issues that plague VAEs related to useless latent dimensions. We provide empirical studies on three benchmark datasets, namely, MNIST, OMNIGLOT and Caltech 101 Silhouettes, and show that applying the hierarchical VampPrior delivers state-of-the-art results on all three datasets in the unsupervised permutation invariant setting and the best results or comparable to SOTA methods for the approach with convolutional networks.