Conditional Optimal Transport

Conditional Optimal Transport (COT) extends optimal transport theory by incorporating conditional dependencies, aiming to efficiently find mappings between probability distributions while satisfying given constraints. Current research focuses on developing efficient algorithms, including flow-based methods and neural network approaches like PICNNs and neural ODEs, to solve COT problems in high-dimensional spaces and dynamic settings. These advancements are driving progress in diverse applications such as image enhancement, Bayesian inference, and generative modeling, particularly for complex inverse problems where efficient transport of probability measures is crucial. The development of faster and more robust COT algorithms is significantly impacting the scalability and accuracy of various machine learning tasks.