# NRDF: Neural Riemannian Distance Fields for Learning Articulated Pose Priors

arXiv: https://arxiv.org/abs/2403.03122 · HTML: https://mlsanity.com/paper/2403.03122/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 74 references that are in the map.
- First posted on arXiv 5 Mar 2024.

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

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (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)
- [Human Motion Diffusion Model](https://mlsanity.com/paper/2209.14916/) (2022)
- [End-to-end Recovery of Human Shape and Pose](https://mlsanity.com/paper/1712.06584/) (2017)
- [Keep it SMPL: Automatic Estimation of 3D Human Pose and Shape from a Single Image](https://mlsanity.com/paper/1607.08128/) (2016)
- [Learning to Reconstruct 3D Human Pose and Shape via Model-fitting in the Loop](https://mlsanity.com/paper/1909.12828/) (2019)
- [VIBE: Video Inference for Human Body Pose and Shape Estimation](https://mlsanity.com/paper/1912.05656/) (2019)
- [Action-Conditioned 3D Human Motion Synthesis with Transformer VAE](https://mlsanity.com/paper/2104.05670/) (2021)
- [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020)
- [HuMoR: 3D Human Motion Model for Robust Pose Estimation](https://mlsanity.com/paper/2105.04668/) (2021)
- [3D Menagerie: Modeling the 3D shape and pose of animals](https://mlsanity.com/paper/1611.07700/) (2016)
- [Neural Unsigned Distance Fields for Implicit Function Learning](https://mlsanity.com/paper/2010.13938/) (2020)
- [BEHAVE: Dataset and Method for Tracking Human Object Interactions](https://mlsanity.com/paper/2204.06950/) (2022)
- [Multi-Garment Net: Learning to Dress 3D People from Images](https://mlsanity.com/paper/1908.06903/) (2019)
- [Learning Gradient Fields for Shape Generation](https://mlsanity.com/paper/2008.06520/) (2020)
- [MoFusion: A Framework for Denoising-Diffusion-based Motion Synthesis](https://mlsanity.com/paper/2212.04495/) (2022)
- [Neural Body Fitting: Unifying Deep Learning and Model-Based Human Pose and Shape Estimation](https://mlsanity.com/paper/1808.05942/) (2018)
- [HP-GAN: Probabilistic 3D human motion prediction via GAN](https://mlsanity.com/paper/1711.09561/) (2017)
- [Learning to Reconstruct People in Clothing from a Single RGB Camera](https://mlsanity.com/paper/1903.05885/) (2019)
- [SMPLer-X: Scaling Up Expressive Human Pose and Shape Estimation](https://mlsanity.com/paper/2309.17448/) (2023)
- [Human POSEitioning System (HPS): 3D Human Pose Estimation and Self-localization in Large Scenes from Body-Mounted Sensors](https://mlsanity.com/paper/2103.17265/) (2021)
- [Neural-GIF: Neural Generalized Implicit Functions for Animating People in Clothing](https://mlsanity.com/paper/2108.08807/) (2021)
- [Learning Motion Priors for 4D Human Body Capture in 3D Scenes](https://mlsanity.com/paper/2108.10399/) (2021)

## Built on by (most cited first, 27 of 27)

- [Dyn-HaMR: Recovering 4D Interacting Hand Motion from a Dynamic Camera](https://mlsanity.com/paper/2412.12861/) (2024)
- [InterTrack: Tracking Human Object Interaction without Object Templates](https://mlsanity.com/paper/2408.13953/) (2024)
- [The Quest for Generalizable Motion Generation: Data, Model, and Evaluation](https://mlsanity.com/paper/2510.26794/) (2025)
- [MEGA: Masked Generative Autoencoder for Human Mesh Recovery](https://mlsanity.com/paper/2405.18839/) (2024)
- [PRIMAL: Physically Reactive and Interactive Motor Model for Avatar Learning](https://mlsanity.com/paper/2503.17544/) (2025)
- [DPoser-X: Diffusion Model as Robust 3D Whole-body Human Pose Prior](https://mlsanity.com/paper/2508.00599/) (2025)
- [Riemann2: Learning Riemannian Submanifolds from Riemannian Data](https://mlsanity.com/paper/2503.05540/) (2025)
- [Geometric Neural Distance Fields for Learning Human Motion Priors](https://mlsanity.com/paper/2509.09667/) (2025)
- [CoMoVi: Co-Generation of 3D Human Motions and Realistic Videos](https://mlsanity.com/paper/2601.10632/) (2026)
- [PUMPS: Skeleton-Agnostic Point-based Universal Motion Pre-Training for Synthesis in Human Motion Tasks](https://mlsanity.com/paper/2507.20170/) (2025)
- [Forecasting Continuous Non-Conservative Dynamical Systems in SO(3)](https://mlsanity.com/paper/2508.07775/) (2025)
- [Multi-modal Pose Diffuser: A Multimodal Generative Conditional Pose Prior](https://mlsanity.com/paper/2410.14540/) (2024)
- [MeshMamba: State Space Models for Articulated 3D Mesh Generation and Reconstruction](https://mlsanity.com/paper/2507.15212/) (2025)
- [PHD: Personalized 3D Human Body Fitting with Point Diffusion](https://mlsanity.com/paper/2508.21257/) (2025)
- [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)
- [GRAFT: Geometric Refinement and Fitting Transformer for Human Scene Reconstruction](https://mlsanity.com/paper/2604.19624/) (2026)
- [PDF-HR: Pose Distance Fields for Humanoid Robots](https://mlsanity.com/paper/2602.04851/) (2026)
- [T2MBench: A Benchmark for Out-of-Distribution Text-to-Motion Generation](https://mlsanity.com/paper/2602.13751/) (2026)
- [SAMoR: Motion Modelling for Articulated Objects of Any Skeleton and Topology](https://mlsanity.com/paper/2607.02148/) (2026)
- [Latent Riemannian Flow Matching for Geometry-Grounded 3D Foundation Models](https://mlsanity.com/paper/2607.19120/) (2026)
- [Neural Human Pose Prior](https://mlsanity.com/paper/2507.12138/) (2025)
- [LieHMR: Autoregressive Human Mesh Recovery with SO(3) Diffusion](https://mlsanity.com/paper/2509.25739/) (2025)
- [Skeleton2Stage: Reward-Guided Fine-Tuning for Physically Plausible Dance Generation](https://mlsanity.com/paper/2602.13778/) (2026)
- [Non-intrusive Body Composition Assessment from Full-body mmWave Scans](https://mlsanity.com/paper/2605.08306/) (2026)
- [PoseShield: Neural Collision Fields for Human Self-Collision Resolution](https://mlsanity.com/paper/2606.29686/) (2026)
- [PFM-HR: Pose Flow Matching for Humanoid Robots](https://mlsanity.com/paper/2608.03227/) (2026)

## Abstract (arXiv)

Faithfully modeling the space of articulations is a crucial task that allows recovery and generation of realistic poses, and remains a notorious challenge. To this end, we introduce Neural Riemannian Distance Fields (NRDFs), data-driven priors modeling the space of plausible articulations, represented as the zero-level-set of a neural field in a high-dimensional product-quaternion space. To train NRDFs only on positive examples, we introduce a new sampling algorithm, ensuring that the geodesic distances follow a desired distribution, yielding a principled distance field learning paradigm. We then devise a projection algorithm to map any random pose onto the level-set by an adaptive-step Riemannian optimizer, adhering to the product manifold of joint rotations at all times. NRDFs can compute the Riemannian gradient via backpropagation and by mathematical analogy, are related to Riemannian flow matching, a recent generative model. We conduct a comprehensive evaluation of NRDF against other pose priors in various downstream tasks, i.e., pose generation, image-based pose estimation, and solving inverse kinematics, highlighting NRDF's superior performance. Besides humans, NRDF's versatility extends to hand and animal poses, as it can effectively represent any articulation.