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

arXiv: https://arxiv.org/abs/2603.15016 · HTML: https://mlsanity.com/paper/2603.15016/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 37 of its 55 references that are in the map.
- First posted on arXiv 16 Mar 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 30 of 37)

- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Qwen3 Embedding: Advancing Text Embedding and Reranking Through Foundation Models](https://mlsanity.com/paper/2506.05176/) (2025)
- [AMASS: Archive of Motion Capture as Surface Shapes](https://mlsanity.com/paper/1904.03278/) (2019)
- [On the Continuity of Rotation Representations in Neural Networks](https://mlsanity.com/paper/1812.07035/) (2018)
- [Human Motion Diffusion Model](https://mlsanity.com/paper/2209.14916/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [MotionDiffuse: Text-Driven Human Motion Generation with Diffusion Model](https://mlsanity.com/paper/2208.15001/) (2022)
- [T2M-GPT: Generating Human Motion from Textual Descriptions with Discrete Representations](https://mlsanity.com/paper/2301.06052/) (2023)
- [Executing your Commands via Motion Diffusion in Latent Space](https://mlsanity.com/paper/2212.04048/) (2022)
- [MotionGPT: Human Motion as a Foreign Language](https://mlsanity.com/paper/2306.14795/) (2023)
- [Action-Conditioned 3D Human Motion Synthesis with Transformer VAE](https://mlsanity.com/paper/2104.05670/) (2021)
- [TEMOS: Generating diverse human motions from textual descriptions](https://mlsanity.com/paper/2204.14109/) (2022)
- [AI Choreographer: Music Conditioned 3D Dance Generation with AIST++](https://mlsanity.com/paper/2101.08779/) (2021)
- [Action2Motion: Conditioned Generation of 3D Human Motions](https://mlsanity.com/paper/2007.15240/) (2020)
- [MoMask: Generative Masked Modeling of 3D Human Motions](https://mlsanity.com/paper/2312.00063/) (2023)
- [Flow Matching Guide and Code](https://mlsanity.com/paper/2412.06264/) (2024)
- [EDGE: Editable Dance Generation From Music](https://mlsanity.com/paper/2211.10658/) (2022)
- [Z-Image: An Efficient Image Generation Foundation Model with Single-Stream Diffusion Transformer](https://mlsanity.com/paper/2511.22699/) (2025)
- [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (2023)
- [MoFusion: A Framework for Denoising-Diffusion-based Motion Synthesis](https://mlsanity.com/paper/2212.04495/) (2022)
- [FLAME: Free-form Language-based Motion Synthesis & Editing](https://mlsanity.com/paper/2209.00349/) (2022)
- [MotionLCM: Real-time Controllable Motion Generation via Latent Consistency Model](https://mlsanity.com/paper/2404.19759/) (2024)
- [Human Motion Generation: A Survey](https://mlsanity.com/paper/2307.10894/) (2023)
- [MotionStreamer: Streaming Motion Generation via Diffusion-based Autoregressive Model in Causal Latent Space](https://mlsanity.com/paper/2503.15451/) (2025)
- [Rethinking Diffusion for Text-Driven Human Motion Generation: Redundant Representations, Evaluation, and Masked Autoregression](https://mlsanity.com/paper/2411.16575/) (2024)

## Built on by (most cited first, 2 of 2)

- [Spatial Temporal Synergy: Balancing Change and Invariance in Text Driven 3D Human Motion Editing](https://mlsanity.com/paper/2608.16008/) (2026)
- [Skeletons in Flow: Graph Structured Flow Matching for Human Motion Prediction](https://mlsanity.com/paper/2609.32231/) (2026)

## Abstract (arXiv)

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 mathscrT+mathscrR (translation + rotations) representation is the most stable and effective, highlighting geometry-aware modeling as a practical and scalable route to high-fidelity motion generation.