Optimal Transport Map

Optimal transport (OT) maps aim to find the most efficient way to transform one probability distribution into another, minimizing a specified cost function. Current research focuses on developing stable and efficient algorithms for learning these maps, often employing neural networks (e.g., normalizing flows, generative adversarial networks) to approximate solutions and incorporating prior information through cost function design or regularization techniques like the Monge gap. These advancements are improving the accuracy and scalability of OT map estimation, impacting diverse fields such as Bayesian inference, adversarial robustness in deep learning, and image processing through applications like generative modeling and image-to-image translation.