  Using powerful posterior distributions is a popular approach to achieving
better variational inference. However, recent works showed that the aggregated
posterior may fail to match unit Gaussian prior, thus learning the prior
becomes an alternative way to improve the lower-bound. In this paper, for the
first time in the literature, we prove the necessity and effectiveness of
learning the prior when aggregated posterior does not match unit Gaussian
prior, analyze why this situation may happen, and propose a hypothesis that
learning the prior may improve reconstruction loss, all of which are supported
by our extensive experiment results. We show that using learned Real NVP prior
and just one latent variable in VAE, we can achieve test NLL comparable to very
deep state-of-the-art hierarchical VAE, outperforming many previous works with
complex hierarchical VAE architectures.
