Research map / Probabilistic and scientific modeling / Variational and generative sampling
Normalizing Flows on the Product Space of SO(3) Manifolds for Probabilistic Human Pose Modeling
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Introduces HuProSO3, a normalizing flow on a product space of SO(3) manifolds (MobiusCoupling + quaternion affine layers with autoregressive nonlinear conditioning) for probabilistic human pose modeling, evaluated as a pose prior, IK, and 2D-to-3D uplifting.
Problem
Normalized densities over joint rotations of the human pose (a product of SO(3) manifolds) are hard to learn with normalizing flows because Euclidean flows do not respect the rotational manifold structure.
Approach
Flow layers that operate directly on SO(3) (Möbius coupling on sphere columns plus quaternion affine transforms), lifted to a product of N SO(3) manifolds via permuted, nonlinear autoregressive conditioning in 6D representation, giving exact normalized likelihoods.
Key results
- On AMASS test IK, HuProSO3 reaches MPJPE 8.2 mm and MGEO 0.163 rad (single sample) vs. GAN-S 12.1 mm / 0.224 rad.
- For 2D-to-3D uplifting, HuProSO3 achieves MPJPE 32.8 mm (single sample) vs. GAN-S 61.5 mm and HF-AC 74.4 mm.
- For unconditional pose prior, HuProSO3 gives the best train and test precision/recall means versus GAN-S and a 6D normalizing flow.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a normalizing flow defined on the SO(3) product space rather than a 6D Euclidean normalizing flow | HuProSO3 pose prior · AMASS test | recall (mean): 3.66 -> 3.44 | Helped |
| Use a normalizing flow defined on the SO(3) product space rather than a 6D Euclidean normalizing flow | HuProSO3 pose prior · AMASS test | precision (mean): 4.50 -> 4.24 | Helped |
| Use HuProSO3 instead of HF-AC | Probabilistic inverse kinematics · AMASS test inverse kinematics | MPJPE (1 sample): 33.2 -> 8.2 | Helped |
| Use HuProSO3 instead of HF-AC | Probabilistic inverse kinematics · AMASS test inverse kinematics | MGEO (1 sample): 0.308 -> 0.163 | Helped |
| Use HuProSO3 instead of GAN-S | Partial-observation inverse kinematics · Left leg occlusion | MPJPE: 16.8 -> 13.9 | Helped |
| Use HuProSO3 instead of GAN-S | Partial-observation inverse kinematics · Left arm and hand occlusion | MPJPE: 29.6 -> 30.2 | Hurt |
| Use HuProSO3 instead of Pose-NDF | Partial-observation inverse kinematics · Right shoulder and upper arm occlusion | MPJPE: 2.1 -> 12.7 | Hurt |
| Use HuProSO3 instead of Pose-NDF | 2D-to-3D uplifting · AMASS test 2D-to-3D uplifting | MPJPE: 133.1 -> 32.8 | Helped |
Surprising findings
- Pose-NDF achieves the best MPJPE in IK despite worse MGEO, since it does not penalize realistic poses that differ from ground truth.
Limitations
- Autoregressive structure depends heavily on the permutation of conditioning order and may not capture all dependencies.
- Sampling scales linearly with the number of manifolds and is slow in high dimensions.
- Only supports products of SO(3) manifolds.
Experimental setup
Datasets: AMASS
Benchmarks: AMASS test split (precision/recall, IK, occlusion IK, 5-point evaluation, 2D-to-3D uplifting)
Metrics: precision recall MPJPE MGEO log-likelihood
Baselines: GAN-S Pose-NDF HF-AC VPoser 6D normalizing flow
Builds on: Möbius coupling layer (Liu et al.) masked autoregressive flow neural spline flow HuManiFlow
Closest papers by meaning
- Delving Into Discrete Normalizing Flows on SO(3) Manifold for Probabilistic Rotation Modeling (CVPR 2023 · similarity 0.90)
- ProPose: Probabilistic 3D Human Pose Estimation with Instance-Level Distribution and Normalizing Flow (AAAI 2025 · similarity 0.87)
- ManiPose: Manifold-Constrained Multi-Hypothesis 3D Human Pose Estimation (NeurIPS 2024 · similarity 0.86)
- Neural Localizer Fields for Continuous 3D Human Pose and Shape Estimation (NeurIPS 2024 · similarity 0.85)
- NRDF: Neural Riemannian Distance Fields for Learning Articulated Pose Priors (CVPR 2024 · similarity 0.85)
- $\text{Di}^2\text{Pose}$: Discrete Diffusion Model for Occluded 3D Human Pose Estimation (NeurIPS 2024 · similarity 0.85)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.