# Geometric Neural Distance Fields for Learning Human Motion Priors

arXiv: https://arxiv.org/abs/2509.09667 · HTML: https://mlsanity.com/paper/2509.09667/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 61 references that are in the map.
- First posted on arXiv 11 Sep 2025.

## Builds on (most cited first, 30 of 44)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [Rethinking Atrous Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1706.05587/) (2017)
- [Expressive Body Capture: 3D Hands, Face, and Body from a Single Image](https://mlsanity.com/paper/1904.05866/) (2019)
- [AMASS: Archive of Motion Capture as Surface Shapes](https://mlsanity.com/paper/1904.03278/) (2019)
- [OpenPose: Realtime Multi-Person 2D Pose Estimation using Part Affinity Fields](https://mlsanity.com/paper/1812.08008/) (2018)
- [Human Motion Diffusion Model](https://mlsanity.com/paper/2209.14916/) (2022)
- [Keep it SMPL: Automatic Estimation of 3D Human Pose and Shape from a Single Image](https://mlsanity.com/paper/1607.08128/) (2016)
- [VIBE: Video Inference for Human Body Pose and Shape Estimation](https://mlsanity.com/paper/1912.05656/) (2019)
- [Human Motion Diffusion as a Generative Prior](https://mlsanity.com/paper/2303.01418/) (2023)
- [Humans in 4D: Reconstructing and Tracking Humans with Transformers](https://mlsanity.com/paper/2305.20091/) (2023)
- [PARE: Part Attention Regressor for 3D Human Body Estimation](https://mlsanity.com/paper/2104.08527/) (2021)
- [HuMoR: 3D Human Motion Model for Robust Pose Estimation](https://mlsanity.com/paper/2105.04668/) (2021)
- [Resolving 3D Human Pose Ambiguities with 3D Scene Constraints](https://mlsanity.com/paper/1908.06963/) (2019)
- [Neural Unsigned Distance Fields for Implicit Function Learning](https://mlsanity.com/paper/2010.13938/) (2020)
- [CLIFF: Carrying Location Information in Full Frames into Human Pose and Shape Estimation](https://mlsanity.com/paper/2208.00571/) (2022)
- [TMR: Text-to-Motion Retrieval Using Contrastive 3D Human Motion Synthesis](https://mlsanity.com/paper/2305.00976/) (2023)
- [Character Controllers Using Motion VAEs](https://mlsanity.com/paper/2103.14274/) (2021)
- [SMPLer-X: Scaling Up Expressive Human Pose and Shape Estimation](https://mlsanity.com/paper/2309.17448/) (2023)
- [PyMAF-X: Towards Well-aligned Full-body Model Regression from Monocular Images](https://mlsanity.com/paper/2207.06400/) (2022)
- [EgoBody: Human Body Shape and Motion of Interacting People from Head-Mounted Devices](https://mlsanity.com/paper/2112.07642/) (2021)
- [Collaborative Regression of Expressive Bodies using Moderation](https://mlsanity.com/paper/2105.05301/) (2021)
- [PlaneRCNN: 3D Plane Detection and Reconstruction from a Single Image](https://mlsanity.com/paper/1812.04072/) (2018)
- [Pymanopt: A Python Toolbox for Optimization on Manifolds using Automatic Differentiation](https://mlsanity.com/paper/1603.03236/) (2016)
- [TRACE: 5D Temporal Regression of Avatars with Dynamic Cameras in 3D Environments](https://mlsanity.com/paper/2306.02850/) (2023)
- [Pose-NDF: Modeling Human Pose Manifolds with Neural Distance Fields](https://mlsanity.com/paper/2207.13807/) (2022)
- [NIFTY: Neural Object Interaction Fields for Guided Human Motion Synthesis](https://mlsanity.com/paper/2307.07511/) (2023)
- [NeMF: Neural Motion Fields for Kinematic Animation](https://mlsanity.com/paper/2206.03287/) (2022)
- [GFPose: Learning 3D Human Pose Prior with Gradient Fields](https://mlsanity.com/paper/2212.08641/) (2022)
- [Make-An-Animation: Large-Scale Text-conditional 3D Human Motion Generation](https://mlsanity.com/paper/2305.09662/) (2023)

## Built on by (most cited first, 6 of 6)

- [MoLingo: Motion-Language Alignment for Text-to-Human Motion Generation](https://mlsanity.com/paper/2512.13840/) (2025)
- [Parallelised Differentiable Straightest Geodesics for 3D Meshes](https://mlsanity.com/paper/2603.15780/) (2026)
- [PDF-HR: Pose Distance Fields for Humanoid Robots](https://mlsanity.com/paper/2602.04851/) (2026)
- [SAMoR: Motion Modelling for Articulated Objects of Any Skeleton and Topology](https://mlsanity.com/paper/2607.02148/) (2026)
- [Spatial Temporal Synergy: Balancing Change and Invariance in Text Driven 3D Human Motion Editing](https://mlsanity.com/paper/2608.16008/) (2026)
- [PFM-HR: Pose Flow Matching for Humanoid Robots](https://mlsanity.com/paper/2608.03227/) (2026)

## Abstract (arXiv)

We introduce Neural Riemannian Motion Fields (NRMF), a novel 3D generative human motion prior that enables robust, temporally consistent, and physically plausible 3D motion recovery. Unlike existing VAE or diffusion-based methods, our higher-order motion prior explicitly models the human motion in the zero level set of a collection of neural distance fields (NDFs) corresponding to pose, transition (velocity), and acceleration dynamics. Our framework is rigorous in the sense that our NDFs are constructed on the product space of joint rotations, their angular velocities, and angular accelerations, respecting the geometry of the underlying articulations. We further introduce: (i) a novel adaptive-step hybrid algorithm for projecting onto the set of plausible motions, and (ii) a novel geometric integrator to "roll out" realistic motion trajectories during test-time-optimization and generation. Our experiments show significant and consistent gains: trained on the AMASS dataset, NRMF remarkably generalizes across multiple input modalities and to diverse tasks ranging from denoising to motion in-betweening and fitting to partial 2D / 3D observations.