  Normalizing flows are a class of flexible deep generative models that offer
easy likelihood computation. Despite their empirical success, there is little
theoretical understanding of their expressiveness. In this work, we study
residual flows, a class of normalizing flows composed of Lipschitz residual
blocks. We prove residual flows are universal approximators in maximum mean
discrepancy. We provide upper bounds on the number of residual blocks to
achieve approximation under different assumptions.
