b9523d484af624986c2e0c630ac44ecb-Supplemental-Conference.pdf

Lemma B.4. (Lemma 2.1.8 in [4]) For any diffeomorphismf Diffkc Rd and any δ > 0, there exists a finite sequence of(δ,k)-near-identity diffeomorphismsg1,,gs such that f = gs gs 1 g1. Let πi: Rd R denote the projection onto theith coordinate. Supposef: Rd Rd is compactly supported and sufficientlyCk-close to the identity. In this section, we analysis how to make the affine coupling flow with dimension-augmentation invertible. Tohandle this problem, we need to makesure thatRange(F)is tractable for easy sampling.