We thank the reviewers for their insightful feedback! Our goal is not to reduce the dimensionality further below n . What are the convergence properties of the proposed training method (R4)? Is the sequential or alternating training scheme better (R4)? It would be nice to have a different metric to compare the models (R1).

Inferring a probability distribution from example data is a common problem that is increasingly tackled with deep generative models.

We thank the reviewers for their insightful feedback! Our goal is not to reduce the dimensionality further below n . What are the convergence properties of the proposed training method (R4)? Is the sequential or alternating training scheme better (R4)? It would be nice to have a different metric to compare the models (R1).