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NRDF: Neural Riemannian Distance Fields for Learning Articulated Pose Priors
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Introduces Neural Riemannian Distance Fields (NRDFs), neural distance fields on a product-quaternion manifold that act as articulated pose priors, trained with a new Riemannian sampling scheme and projected with an adaptive Riemannian gradient descent (RDFGrad).
Problem
Modeling the space of plausible articulated poses (humans, hands, animals) so that realistic poses can be generated, recovered from partial observations, and used as priors for pose estimation, while respecting joint-rotation geometry.
Approach
Represent plausible poses as the zero level set of a neural distance field defined on the product manifold of unit quaternions with geodesic distance, train it on positive examples using a Riemannian sampling scheme that controls the distance distribution, and project poses onto the manifold with a Riemannian gradient descent that stays on the manifold at every step.
Key results
- On pose denoising, NRDF reaches 14.32 cm m2m error versus 24.43 cm for GFPose-Q and 25.04 cm for Pose-NDF, with 8 convergence steps versus 40 for Pose-NDF.
- In SMPLer-X refinement on 3DPW, NRDF reduces PA-MPJPE from 77.82 mm to 68.47 mm and raises PCK@50mm from 59.30 to 66.17.
- Pose generation: NRDF gives FID 0.636 and APD 23.116 cm, a balance between VPoser (FID 0.048, APD 14.684) and Pose-NDF (FID 3.920, APD 37.813).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use NRDF rather than Pose-NDF for pose denoising | NRDF · Pose denoising | ∆q +m2m: 0.349 -> 0.170 | Helped |
| Use NRDF rather than FM-Grad for pose denoising | NRDF · Pose denoising | ∆q +m2m: 0.216 -> 0.170 | Helped |
| Use NRDF rather than VPoser for pose generation | NRDF · Pose generation | APD (in cm): 14.684±.138 -> 23.116±.105 | Helped |
| Use NRDF rather than VPoser for pose generation | NRDF · Pose generation | FID: 0.048±.002 -> 0.636±.007 | Hurt |
| Use NRDF rather than Pose-NDF for pose generation | NRDF · Pose generation | FID: 3.920±.034 -> 0.636±.007 | Helped |
| Use NRDF rather than Pose-NDF for pose generation | NRDF · Pose generation | APD (in cm): 37.813±.085 -> 23.116±.105 | Hurt |
| Refine SMPLer-X predictions with NRDF optimization instead of no prior | SMPLer-X · 3DPW | PA-MPJPE (in mm): 77.97 -> 68.47 | Helped |
| Add RDFGrad-based projection (ablation) | NRDF pose denoising · Pose denoising | ∆q +m2m: 0.171 -> 0.170 | No clear effect |
| Add quaternion geodesic distance dq and RDFGrad-based projection (ablation) | NRDF pose denoising · Pose denoising | ∆q +m2m: 0.179 -> 0.170 | Helped |
| Set α to 0.5 instead of 1.0 (ablation) | NRDF pose denoising · Pose denoising | ∆q +m2m: 0.170 -> 0.180 | Hurt |
| Set α to 0.01 instead of 1.0 (ablation) | NRDF pose denoising · Pose denoising | ∆q +m2m: 0.170 -> 0.201 | Hurt |
| Add the new training-data sampling method (ablation) | NRDF pose denoising · Pose denoising | ∆q +m2m | Helped |
Surprising findings
- Pose-NDF's Euclidean-gradient projection with re-projection converges more slowly and produces unrealistic poses, while distance-field gradients from the proposed sampler improve realism.
- GFPose trained on quaternion representations collapses to near-mean poses when denoising.
Limitations
- Iterative sampling scheme may reduce generation efficiency compared to direct latent-to-pose mapping.
- Model does not explicitly represent uncertainty over the manifold.
- Pose generation FID and dNN are higher than VPoser and GAN-S, showing a realism-diversity trade-off.
Experimental setup
Datasets: AMASS DART Animal3D 3DPW H3.6M
Benchmarks: 3DPW AMASS
Metrics: Average Pairwise Distance (APD) FID dNN PA-MPJPE PA-PVE PCK@50mm quaternion + marker-to-marker distance marker-to-marker distance
Baselines: VPoser Pose-NDF GFPose GAN-S GMM FM-Dis FM-Grad SMPLer-X
Builds on: Pose-NDF Riemannian flow matching VPoser neural distance fields
Closest papers by meaning
- PDF-HR: Pose Distance Fields for Humanoid Robots (NeurIPS 2026 · similarity 0.86)
- PORF: POSE RESIDUAL FIELD FOR ACCURATE NEURAL SURFACE RECONSTRUCTION (ICLR 2024 · similarity 0.85)
- Normalizing Flows on the Product Space of SO(3) Manifolds for Probabilistic Human Pose Modeling (CVPR 2024 · similarity 0.85)
- Neural Localizer Fields for Continuous 3D Human Pose and Shape Estimation (NeurIPS 2024 · similarity 0.85)
- Follow the Energy, Find the Path: Riemannian Metrics from Energy-Based Models (NeurIPS 2025 · similarity 0.84)
- Small Steps and Level Sets: Fitting Neural Surface Models with Point Guidance (CVPR 2024 · similarity 0.84)
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