# Skeletons in Flow: Graph Structured Flow Matching for Human Motion Prediction

arXiv: https://arxiv.org/abs/2609.32231 · HTML: https://mlsanity.com/paper/2609.32231/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 20 of its 23 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)

## Builds on (most cited first, 20 of 20)

- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [AMASS: Archive of Motion Capture as Surface Shapes](https://mlsanity.com/paper/1904.03278/) (2019)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (2023)
- [DLow: Diversifying Latent Flows for Diverse Human Motion Prediction](https://mlsanity.com/paper/2003.08386/) (2020)
- [A Spatio-temporal Transformer for 3D Human Motion Prediction](https://mlsanity.com/paper/2004.08692/) (2020)
- [The Pose Knows: Video Forecasting by Generating Pose Futures](https://mlsanity.com/paper/1705.00053/) (2017)
- [Space-Time-Separable Graph Convolutional Network for Pose Forecasting](https://mlsanity.com/paper/2110.04573/) (2021)
- [BeLFusion: Latent Diffusion for Behavior-Driven Human Motion Prediction](https://mlsanity.com/paper/2211.14304/) (2022)
- [HumanMAC: Masked Motion Completion for Human Motion Prediction](https://mlsanity.com/paper/2302.03665/) (2023)
- [Generating Smooth Pose Sequences for Diverse Human Motion Prediction](https://mlsanity.com/paper/2108.08422/) (2021)
- [Motion Flow Matching for Human Motion Synthesis and Editing](https://mlsanity.com/paper/2312.08895/) (2023)
- [Diverse Human Motion Prediction via Gumbel-Softmax Sampling from an Auxiliary Space](https://mlsanity.com/paper/2207.07351/) (2022)
- [Human Joint Kinematics Diffusion-Refinement for Stochastic Motion Prediction](https://mlsanity.com/paper/2210.05976/) (2022)
- [CoMusion: Towards Consistent Stochastic Human Motion Prediction via Motion Diffusion](https://mlsanity.com/paper/2305.12554/) (2023)
- [Nonisotropic Gaussian Diffusion for Realistic 3D Human Motion Prediction](https://mlsanity.com/paper/2501.06035/) (2025)
- [CacheFlow: Fast Human Motion Prediction by Cached Normalizing Flow](https://mlsanity.com/paper/2505.13140/) (2025)
- [Riemannian Motion Generation: A Unified Framework for Human Motion Representation and Generation via Riemannian Flow Matching](https://mlsanity.com/paper/2603.15016/) (2026)
- [EquiFusion: Kinematics-Agnostic Human Motion Prediction via Equivariant Latent Diffusion](https://mlsanity.com/paper/2607.10984/) (2026)

## Abstract (arXiv)

Human motion prediction requires diverse future trajectories that remain consistent with observed motion and the articulated physical structure of the body. Skeletal constraints restrict individual poses, while coordinated motion depends on spatial interactions (between connected joints) and temporal interactions (between time instants). To facilitate human motion prediction in light of these constraints and interactions, we introduce Graph Structured Flow Matching (GSFM), which transports the complete future skeletal trajectory through a single conditional velocity field. The trajectory produces a spatiotemporal skeleton graph, and spatial and temporal attention couple its evolution according to skeletal relations and physical time offsets. Bone directions lie on unit spheres relative to a root joint, and tangent evolution preserves input bone lengths throughout generation. We train a learned velocity field through conditional flow matching along geodesic paths connecting random trajectories centered on the last-observed pose to recorded future trajectories. Experiments on the Archive of Motion capture As Surface Shapes (AMASS) dataset evaluate prediction accuracy, diversity calibration, and motion statistics. We demonstrate the contributions of spatial and temporal message passing in the developed architecture through an ablation study. GSFM models trained on AMASS also perform competitively on the Human3.6M skeleton without parameter updates or retraining, demonstrating applicability to an unseen skeletal structure.