Flow Matching on Riemannian Symmetric Spaces
A novel framework is designed to train flow matching models within Riemannian symmetric spaces, including spheres, hyperbolic spaces, and Grassmannians. This method redefines the challenge as flow matching within a subspace of the Lie algebra associated with the isometry group, thereby streamlining the management of geodesics. An example of this application is showcased on real Grassmannians SO(n)/SO(k)×SO(n−k).
Key facts
- Framework introduced for flow matching on Riemannian symmetric spaces
- Class of manifolds includes sphere, hyperbolic space, Grassmannians
- Algebraic structure exploited to reformulate as flow matching on Lie algebra subspace
- Simplifies handling of geodesics
- Application shown on real Grassmannians SO(n)/SO(k)×SO(n−k)
Entities
Institutions
- arXiv