Riemannian Flow Matching

Riemannian Flow Matching (RFM) is a generative modeling framework that addresses the challenge of learning and generating data residing on complex, non-Euclidean manifolds. Current research focuses on developing efficient algorithms, such as those leveraging pullback geometry and neural ordinary differential equations (NODEs), to improve the training and inference of RFM models across diverse data types, including those with inherent symmetries like crystalline structures or discrete variables. This approach shows promise in various fields, enabling the generation of novel materials with desired properties, improved robot motion planning, and more accurate modeling of complex systems like protein dynamics and articulated poses. The ability to handle high-dimensional, non-Euclidean data makes RFM a powerful tool for scientific discovery and technological advancement.