  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 using a "Russian roulette"
estimator, and reduce the memory required during training by using an
alternative infinite series for the gradient. Furthermore, we improve
invertible residual blocks by proposing the use of activation functions that
avoid derivative saturation and generalizing the Lipschitz condition to induced
mixed norms. The resulting approach, called Residual Flows, achieves
state-of-the-art performance on density estimation amongst flow-based models,
and outperforms networks that use coupling blocks at joint generative and
discriminative modeling.
