  We introduce Riemannian Flow Matching Policies (RFMP), a novel model for
learning and synthesizing robot visuomotor policies. RFMP leverages the
efficient training and inference capabilities of flow matching methods. By
design, RFMP inherits the strengths of flow matching: the ability to encode
high-dimensional multimodal distributions, commonly encountered in robotic
tasks, and a very simple and fast inference process. We demonstrate the
applicability of RFMP to both state-based and vision-conditioned robot motion
policies. Notably, as the robot state resides on a Riemannian manifold, RFMP
inherently incorporates geometric awareness, which is crucial for realistic
robotic tasks. To evaluate RFMP, we conduct two proof-of-concept experiments,
comparing its performance against Diffusion Policies. Although both approaches
successfully learn the considered tasks, our results show that RFMP provides
smoother action trajectories with significantly lower inference times.
