A generative flow model for conditional sampling via optimal transport

Jason Alfonso, Ricardo Baptista, Anupam Bhakta, Noam Gal, Alfin Hou, Vasilisa Lyubimova, Daniel Pocklington, Josef Sajonz, Giulio Trigila, Ryan Tsai

Keywords: Conditional sampling, Bayesian inference, Flow-based generative model, Optimal transport, Block-triangular transport map

Abstract: Sampling conditional distributions is a fundamental task for Bayesian inference and density estimation. Generative models characterize conditionals by learning a transport map that pushes forward a reference (e.g., a standard Gaussian) to the target distribution. While these approaches can successfully describe many non-Gaussian problems, their performance is often limited by parametric bias and the reliability of gradient-based (adversarial) optimizers to learn the map. This work proposes a non-parametric generative model that adaptively maps reference samples to the target. The model uses block-triangular transport maps, whose components characterize conditionals of the target distribution. These maps arise from solving an optimal transport problem with a weighted $L^2$ cost function, thereby extending the data-driven approach in [Trigila and Tabak, 2016] for conditional sampling. The proposed approach is demonstrated on a low-dimensional example and a parameter inference problem involving nonlinear ODEs.

Submission Number: 76