Simultaneous Neural Optimal Transport

2026-09-29

AI Summary

This study addresses the challenge of mapping multiple source distributions to a single target, where naive pooling often leads to misalignment of individual distributions. To overcome this, we propose a Simultaneous Optimal Transport (Simultaneous OT) framework that learns a shared transport map to minimize the average cost while aligning each source with the target. By formulating a max-min optimization objective, the method achieves aggregate alignment while preserving the independent alignment of each source distribution. This problem is efficiently solved by integrating neural networks with game-theoretic algorithms. We demonstrate the effectiveness of our approach on image restoration tasks, where a single model can uniformly handle diverse degradation types, yielding substantial improvements in recovery quality.

Abstract

Optimal Transport (OT) provides a principled framework for learning transformations between probability distributions from unpaired samples. In many applications, however, a single transformation must map several source distributions to a common target distribution. For example, image restoration might require handling different types of degradation without knowing the degradation of each input at inference time. Simple approaches of pooling the source distributions only encourage alignment with the target at the aggregate level and may leave individual sources misaligned. In our paper, we consider the simultaneous OT problem which formalizes the task of learning a shared transport map that minimizes the average transport cost while aligning each source distribution with a prescribed target. We propose a neural method for solving the simultaneous OT problem by learning a shared transport map that minimizes the average transport cost while aligning each source distribution with a prescribed target. We derive a max-min formulation for learning this map. We illustrate its application to image restoration, where a single model handles multiple degradation types using a common collection of clean target images.

Problem

• Simultaneous Optimal Transport
• Optimal Transport
• Image Restoration
• Unpaired Samples
• Shared Transport Map

Innovation

• Simultaneous Optimal Transport
• Neural Optimal Transport
• Max-Min Formulation
• Shared Transport Map
• Image Restoration