Riemannian Motion Generation: A Unified Framework for Human Motion Representation and Generation via Riemannian Flow Matching

TL;DR

This paper introduces Riemannian Motion Generation (RMG), a novel framework that models human motion on product manifolds using Riemannian flow matching, achieving state-of-the-art results in motion generation benchmarks.

Contribution

RMG is the first unified Riemannian framework for human motion generation that factorizes motion into manifold components and employs Riemannian flow matching for training and sampling.

Findings

Achieves state-of-the-art FID scores on HumanML3D and MotionStreamer datasets.

Outperforms strong baselines on MotionMillion with high R@1 accuracy.

Demonstrates the effectiveness of geometry-aware $ ext{T}+ ext{R}$ representation.

Abstract

Human motion generation is often learned in Euclidean spaces, although valid motions follow structured non-Euclidean geometry. We present Riemannian Motion Generation (RMG), a unified framework that represents motion on a product manifold and learns dynamics via Riemannian flow matching. RMG factorizes motion into several manifold factors, yielding a scale-free representation with intrinsic normalization, and uses geodesic interpolation, tangent-space supervision, and manifold-preserving ODE integration for training and sampling. On HumanML3D, RMG achieves state-of-the-art FID in the HumanML3D format (0.043) and ranks first on all reported metrics under the MotionStreamer format. On MotionMillion, it also surpasses strong baselines (FID 5.6, R@1 0.86). Ablations show that the compact $\mathscr{T}+\mathscr{R}$ (translation + rotations) representation is the most stable and effective, highlighting geometry-aware modeling as a practical and scalable route to high-fidelity motion generation.