  Recent work shows that path gradient estimators for normalizing flows have
lower variance compared to standard estimators for variational inference,
resulting in improved training. However, they are often prohibitively more
expensive from a computational point of view and cannot be applied to maximum
likelihood training in a scalable manner, which severely hinders their
widespread adoption. In this work, we overcome these crucial limitations.
Specifically, we propose a fast path gradient estimator which improves
computational efficiency significantly and works for all normalizing flow
architectures of practical relevance. We then show that this estimator can also
be applied to maximum likelihood training for which it has a regularizing
effect as it can take the form of a given target energy function into account.
We empirically establish its superior performance and reduced variance for
several natural sciences applications.
