Wasserstein 2

Wasserstein-2 distance, a measure of similarity between probability distributions based on optimal transport, is a key tool in machine learning and related fields. Current research focuses on improving the efficiency and robustness of Wasserstein-2 based methods, particularly for high-dimensional data and heavy-tailed distributions, often employing generative models like GANs and normalizing flows, and variance reduction techniques to enhance optimization. These advancements are enabling more accurate and stable solutions to inverse problems, uncertainty quantification, and generative modeling tasks, with applications ranging from image generation to single-cell genomics analysis. The development of efficient algorithms for computing Wasserstein-2 distances and their conjugates remains a significant area of ongoing investigation.