Optimal Transport Flow

Optimal transport (OT) flow leverages the mathematical framework of optimal transport to learn and manipulate probability distributions, primarily for generative modeling tasks. Current research focuses on developing efficient neural network architectures, such as flow-based models and neural ordinary differential equations, to approximate OT maps and generate high-quality samples, often improving upon traditional diffusion models in speed and flexibility. This approach enables applications like image-to-image translation, density estimation, and even trajectory inference from sparse data, offering significant advancements in both theoretical understanding and practical capabilities of generative modeling.