  Many methods that build powerful variational distributions based on
unadjusted Langevin transitions exist. Most of these were developed using a
wide range of different approaches and techniques. Unfortunately, the lack of a
unified analysis and derivation makes developing new methods and reasoning
about existing ones a challenging task. We address this giving a single
analysis that unifies and generalizes these existing techniques. The main idea
is to augment the target and variational by numerically simulating the
underdamped Langevin diffusion process and its time reversal. The benefits of
this approach are twofold: it provides a unified formulation for many existing
methods, and it simplifies the development of new ones. In fact, using our
formulation we propose a new method that combines the strengths of previously
existing algorithms; it uses underdamped Langevin transitions and powerful
augmentations parameterized by a score network. Our empirical evaluation shows
that our proposed method consistently outperforms relevant baselines in a wide
range of tasks.
