Organization of the supplementary

The supplementary is organized as follows. First, in Appendix S2, we give details on why the generated distribution in each aforementioned generative model is a push-forward of a standard Gaussian distribution. In Appendix S5, we give details on the experiments. S3.1 Proof of Theorem 1 We start by recalling the Gaussian isoperimetric inequality Sudakov and Tsirelson ( 1978). We are now ready to turn to the proof of Theorem 1 . S3.5 Proof of Corollary 5 To prove Corollary 5, we will need the following lemma: Lemma S10.