Title: Shallow VAEs with RealNVP Prior Can Perform as Well as Deep Hierarchical VAEs. Abstract: Using powerful posterior distributions is a popular technique in variational inference.  However, recent works showed that the aggregated posterior may fail to match unit Gaussian prior, even with expressive posteriors, thus learning the prior becomes an alternative way to improve the variational lower-bound.  We show that using learned RealNVP 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.  We hypothesize that, when coupled with Gaussian posteriors, the learned prior can encourage appropriate posterior overlapping, which is likely to improve reconstruction loss and lower-bound, supported by our experimental results.  We demonstrate that, with learned RealNVP prior, ß-VAE can have better rate-distortion curve than using fixed Gaussian prior.