The flow approach may be unsuited to data that do not populate the full ambient data space they natively reside in, but are restricted to a lower-dimensional manifold [7]. Normalizing flows are by construction not able to represent such a structure exactly, instead they learn a smeared-out version with support offthedata manifold.

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).