Resampling Base Distributions of Normalizing Flows
This addresses a problem for researchers and practitioners in machine learning by enabling normalizing flows to handle complex topological structures without sacrificing key properties, though it is incremental as it builds on existing flow methods.
The paper tackles the limitation of normalizing flows in modeling complex distributions like Boltzmann distributions by introducing a base distribution based on learned rejection sampling, which maintains invertibility and tractability. In experiments on 2D densities, tabular data, image generation, and Boltzmann distributions, the method is competitive with or outperforms baselines.
Normalizing flows are a popular class of models for approximating probability distributions. However, their invertible nature limits their ability to model target distributions whose support have a complex topological structure, such as Boltzmann distributions. Several procedures have been proposed to solve this problem but many of them sacrifice invertibility and, thereby, tractability of the log-likelihood as well as other desirable properties. To address these limitations, we introduce a base distribution for normalizing flows based on learned rejection sampling, allowing the resulting normalizing flow to model complicated distributions without giving up bijectivity. Furthermore, we develop suitable learning algorithms using both maximizing the log-likelihood and the optimization of the Kullback-Leibler divergence, and apply them to various sample problems, i.e. approximating 2D densities, density estimation of tabular data, image generation, and modeling Boltzmann distributions. In these experiments our method is competitive with or outperforms the baselines.