Langevin Diffusion Variational Inference
This work addresses a foundational problem in machine learning for researchers and practitioners by unifying and simplifying the development of variational inference methods, though it is incremental in building upon existing techniques.
The paper tackles the lack of unified analysis for variational inference methods based on unadjusted Langevin transitions by providing a single framework that generalizes existing techniques, and it proposes a new method combining underdamped Langevin transitions with score network augmentations that consistently outperforms baselines across tasks.
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.