Langevin Diffusion Variational Inference

TL;DR

This paper introduces a unified framework for Langevin diffusion-based variational inference, simplifying the development of new algorithms and proposing a novel method that outperforms existing approaches across various tasks.

Contribution

It provides a single analysis unifying and generalizing existing Langevin-based variational methods, and introduces a new, more effective algorithm leveraging underdamped Langevin transitions and score network augmentations.

Findings

Proposed method outperforms relevant baselines in multiple tasks.

Unified analysis simplifies development of Langevin diffusion variational algorithms.

New algorithm combines strengths of existing methods with improved performance.

Abstract

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.