Computing High-Dimensional Optimal Transport by Flow Neural Networks

GT-MAP Seminar
Friday, April 26, 2024 - 3:00pm for 2 hours
Skiles 005 and
Yao Xie – H. Milton Stewart School of Industrial and Systems Engineering at Georgia Tech – yao.xie@isye.gatech.edu
Wenjing Liao, Haomin Zhou and Molei Tao

Flow-based models are widely used in generative tasks, including normalizing flow, where a neural network transports from a data distribution P to a normal distribution. This work develops a flow-based model that transports from P to an arbitrary Q (which can be pre-determined or induced as the solution to an optimization problem), where both distributions are only accessible via finite samples. We propose to learn the dynamic optimal transport between P and Q by training a flow neural network. The model is trained to optimally find an invertible transport map between P and Q by minimizing the transport cost. The trained optimal transport flow subsequently allows for performing many downstream tasks, including infinitesimal density ratio estimation (DRE) and distribution interpolation in the latent space for generative models. The effectiveness of the proposed model on high-dimensional data is demonstrated by strong empirical performance on high-dimensional DRE, OT baselines, and image-to-image translation.