Computing high-dimensional optimal transport by flow neural networks
This addresses a long-standing problem in machine learning for applications such as domain adaptation and density estimation, though it builds on existing flow-based methods.
The paper tackles the challenge of computing optimal transport for high-dimensional data by proposing a flow neural network that learns dynamic optimal transport between distributions using finite samples, achieving strong empirical performance on tasks like image-to-image translation and density ratio estimation.
Computing optimal transport (OT) for general high-dimensional data has been a long-standing challenge. Despite much progress, most of the efforts including neural network methods have been focused on the static formulation of the OT problem. The current work proposes to compute the dynamic OT between two arbitrary distributions $P$ and $Q$ by optimizing a flow model, where both distributions are only accessible via finite samples. Our method learns the dynamic OT by finding an invertible flow that minimizes the transport cost. The trained optimal transport flow subsequently allows for performing many downstream tasks, including infinitesimal density ratio estimation (DRE) and domain adaptation by interpolating distributions in the latent space. The effectiveness of the proposed model on high-dimensional data is demonstrated by strong empirical performance on OT baselines, image-to-image translation, and high-dimensional DRE.