Review for NeurIPS paper: Coupling-based Invertible Neural Networks Are Universal Diffeomorphism Approximators

Additional Feedback: [POST REBUTTAL] --------- I thank the authors for the detailed response. I guess I see how one can parameterize some (Real NVP-style) linear couplings combined with permutation and sign flipping to represent any regular matrices (regular here denotes invertible I suppose?). Perhaps this could be explicitly constructed in the paper to complement the results. Does it also imply the the general linear group in the main result can be replaced with permutation group sign flipping? Furthermore, if someone is only concerned with diffeomorphisms with a jacobian having strictly positive eigenvalues, then can the sign flipping be dropped?