Review for NeurIPS paper: Flows for simultaneous manifold learning and density estimation

All reviewers agree that the presented technique for simultaneous manifold and density estimation is interesting and novel. However, they also agree that the paper leaves important questions open. While one of the reviewers would like to see a stronger statistical analysis before acceptance, the others believe that the paper is above acceptance threshold and that the community would benefit from its communication. To address the concerns of the reviewers, the camera-ready paper needed to include at least the following results: 1. Include results that investigate if the invertible nature of the normalising flow in the decoder is useful by e.g considering a version of the Me-flow where g is not constrained to be invertible. In the same vein, a comparison with a simple VAE baseline should be included. Investigate how the results on CelebA depend on the latent dimension n.