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.

翻译：许多现有方法基于未调整的朗之万转移构建强大的变分分布，但这些方法大多采用截然不同的途径与技术开发而成。遗憾的是，由于缺乏统一的分析与推导框架，开发新方法以及对现有方法进行推理变得极具挑战性。为此，我们提出一种单一分析框架，对现有技术进行统一与泛化。其核心思想是通过数值模拟欠阻尼朗之万扩散过程及其时间反演来增强目标与变分分布。该方法的优势体现在两方面：既为现有多种方法提供了统一公式，又简化了新方法的开发流程。事实上，基于该公式化表述，我们提出了一种融合先前算法优势的新方法——该方法采用欠阻尼朗之万转移，并通过评分网络参数化的强增强技术实现。实验评估表明，我们的方法在各类任务中持续优于相关基线模型。