Reviews: Adaptive Density Estimation for Generative Models

Summary: The authors propose a hybrid method that combines VAEs with adversarial training and flow based models. In particular, they derive an explicit density function p(x) where the likelihood can be evaluated, the corresponding components p(x z) are more flexible than the standard VAE that utilizes diagonal Gaussians, and the generated samples have better quality than a standard VAE. The basic idea of the proposed model is that the VAE is defined between a latent space and an intermediate representation space, and then, the representation space is connected with the data space through an invertible non-linear flow. In general, I think the paper is quite well written, but on the same time I believe that there is a lot of compressed information, and the consequence is that in some parts it is not even clear what the authors want to say (see Clarity comments). The proposed idea of the paper seems quite interesting, but on the same time I have some doubts (see Quality comments).