We present Pose-NDF, a method that learns a continuous model of plausible human poses as the zero level set of a neural implicit function. We extend the idea of modeling implicit surfaces in 3D to the high-dimensional domain SO(3)^K, where a human pose is defined by a single data point, represented by K quaternions corresponding to K body joints. The neural distance field provides a smooth and continuous representation of the pose manifold, enabling gradient-based optimization for pose estimation and generation tasks. We demonstrate that Pose-NDF outperforms existing pose priors on multiple downstream tasks including pose estimation from noisy observations, pose completion, and motion denoising.

Modeling the space of plausible human poses is fundamental to many applications in computer vision, including human pose estimation, motion capture, animation, and action recognition. Existing approaches typically represent pose priors as Gaussian Mixture Models (GMMs), Variational Autoencoders (VAEs), or normalizing flows. While effective in certain settings, these methods often struggle with the complex topology of the pose manifold, produce blurry or overly smooth samples, or require expensive sampling procedures. We propose a fundamentally different approach: representing the pose manifold as an implicit function that assigns a distance value to any point in the pose space.

The key insight of our work is that the manifold of plausible human poses can be characterized by its distance field. Given a query pose (potentially noisy or incomplete), the neural distance field provides the distance to the nearest plausible pose on the manifold. This distance field is differentiable everywhere, enabling efficient gradient-based projection onto the manifold. This is in contrast to explicit representations which require either sampling from a learned distribution or solving a complex optimization problem to find the nearest valid pose.

We represent each human pose as a point in SO(3)^K, where K is the number of body joints. Each joint rotation is parameterized as a unit quaternion q_i in S^3. The full pose is then a point on the product manifold p = (q_1, q_2, ..., q_K) in (S^3)^K. We train a neural network f_theta: (S^3)^K -> R that maps any pose to its unsigned distance to the nearest plausible pose on the manifold. The network is trained such that f_theta(p) = 0 for plausible poses and f_theta(p) > 0 for implausible poses, with the value indicating how far the pose deviates from plausibility.

To leverage the Riemannian structure of SO(3), we compute geodesic distances on the rotation manifold rather than Euclidean distances in the embedding space. Specifically, the distance between two quaternions is computed as d(q_i, q_j) = 2 arccos(|q_i . q_j|), respecting the topology of the rotation group. For downstream tasks, we formulate pose estimation as an optimization problem: minimize f_theta(p) subject to data consistency constraints, using gradient descent on the manifold to project noisy observations onto plausible poses.

We train Pose-NDF using the AMASS dataset, which contains over 11,000 motion sequences spanning 40 hours of motion data. We sample training poses both on the manifold (plausible poses from the dataset) and off the manifold (generated by adding controlled noise to plausible poses). For off-manifold points, the ground truth distance is computed as the geodesic distance to the nearest on-manifold point using k-nearest neighbor search in the quaternion space. The network is trained with an L1 loss on the predicted distances, combined with an Eikonal regularization term that encourages the gradient magnitude to be close to one, ensuring the learned function behaves like a proper distance field.

We evaluate Pose-NDF on three downstream tasks. For pose estimation from noisy observations, we compare against VPoser, GMM-based priors, and normalizing flow priors. Pose-NDF achieves the lowest reconstruction error across all noise levels, with particularly significant improvements at high noise levels (above 30 degrees per joint). The smooth gradient field enables robust convergence even from poor initializations, where competing methods frequently get stuck in local minima.

For pose completion (recovering a full body pose from partial joint observations), Pose-NDF demonstrates superior ability to infer occluded joint positions. When only 50% of joints are observed, Pose-NDF achieves a mean error of 4.8 degrees compared to 7.2 degrees for VPoser and 6.1 degrees for the normalizing flow baseline. For motion denoising, we apply Pose-NDF independently to each frame of a noisy motion sequence, projecting each pose onto the manifold. The resulting sequences are temporally smoother and more physically plausible than those produced by frame-independent baseline methods.

We have introduced Pose-NDF, a novel representation of human pose manifolds using neural distance fields. By extending implicit surface modeling to the high-dimensional rotation space SO(3)^K, we provide a continuous, differentiable, and geometry-aware prior for human poses. Our experiments demonstrate consistent improvements over existing pose priors across pose estimation, completion, and denoising tasks. The distance field representation offers unique advantages: it naturally supports gradient-based optimization, provides a meaningful measure of pose plausibility, and generalizes well to unseen poses. Future work may extend this approach to dynamic pose manifolds and incorporate temporal coherence directly into the distance field formulation.