The ability of likelihood-based probabilistic models to generalize to unseen data is central to many machine learning applications such as lossless compression. In this work, we study the generalizations of a popular class of probabilistic models - the Variational Auto-Encoder (VAE). We point out the two generalization gaps that can affect the generalization ability of VAEs and show that the over-fitting phenomenon is usually dominated by the amortized inference network. Based on this observatio…