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.

翻译：近期研究表明，相较于变分推断中的标准估计器，归一化流的路径梯度估计器具有更低的方差，从而能改进训练效果。然而，从计算角度看，这类估计器通常计算成本过高，且无法以可扩展的方式应用于最大似然训练，这严重阻碍了其广泛采用。在本工作中，我们克服了这些关键限制。具体而言，我们提出了一种快速路径梯度估计器，它在显著提升计算效率的同时，适用于所有实际相关的归一化流架构。我们进一步证明，该估计器同样可应用于最大似然训练，并因其能考虑给定目标能量函数的形式而产生正则化效果。通过多个自然科学领域的应用实例，我们经验性地验证了其优越性能与方差降低特性。