Riemannian MeanFlow for One-Step Generation on Manifolds
Researchers have introduced Riemannian MeanFlow (RMF), a novel method for generative models operating on Riemannian manifolds. Unlike previous approaches that require extensive simulation for sampling, RMF enables one-step generation by defining an average-velocity field through parallel transport. This method is practical in a log-map tangent representation, reducing computational costs and avoiding trajectory simulation. Experiments on various manifolds, including spheres, tori, SO(3), and SE(3), show that RMF achieves competitive sampling quality with improved efficiency and lower costs, and also supports conditional generation. AI
IMPACT Introduces a more efficient method for generative models on complex data structures, potentially speeding up training and sampling.