Residual Flows for Invertible Generative Modeling

Flow-based generative models parameterize probability distributions through an invertible transformation and can be trained by maximum likelihood. Invertible residual networks provide a flexible family of transformations where only Lipschitz conditions rather than strict architectural constraints are needed for enforcing invertibility. However, prior work trained invertible residual networks for density estimation by relying on biased log-density estimates whose bias increased with the network's expressiveness. We give a tractable unbiased estimate of the log density, and reduce the memory required during training by a factor of ten. Furthermore, we improve invertible residual blocks by proposing the use of activation functions that avoid gradient saturation and generalizing the Lipschitz condition to induced mixed norms.