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.

翻译：流动正常化是一种灵活的深层基因化模型,可以很容易地进行计算。尽管这些模型取得了经验成功,但它们的表达性在理论上却鲜为人知。在这项工作中,我们研究的是由利普西茨残余区块组成的一类流动正常化流。我们证明,剩余流动是通用的近似物,其平均差异最大。我们提供了剩余区块数量上限,以便在不同的假设下达到近似值。