Distribution Matching in Variational Inference

We show that Variational Autoencoders consistently fail to learn marginal distributions in latent and visible space. We ask whether this is a consequence of matching conditional distributions, or a limitation of explicit model and posterior distributions. We explore alternatives provided by marginal distribution matching and implicit distributions through the use of Generative Adversarial Networks in variational inference. We perform a large-scale evaluation of several VAE-GAN hybrids and explore the implications of class probability estimation for learning distributions. We conclude that at present VAE-GAN hybrids have limited applicability: they are harder to scale, evaluate, and use for inference compared to VAEs; and they do not improve over the generation quality of GANs.