PhysNAP: Diffusion Model for Articulated Objects

• PhysNAP is a diffusion-based approach that generates complete articulated 3D object models from partial point clouds using SDF representations and guided reverse diffusion.
• It employs point-cloud, penetration, and mobility losses during inference to improve alignment and physical plausibility while balancing generative quality.
• The method integrates category-aware conditioning and detailed kinematic modeling to overcome previous limitations in articulated-object generation.

PhysNAP is a diffusion model-based approach for generating articulated objects that aligns them with partial point clouds and improves their physical plausibility. It builds on NAP, an unconditional DDPM for articulated objects, represents part shapes by signed distance functions (SDFs), and guides the reverse diffusion process with a point cloud alignment loss together with non-penetration and mobility constraints; a category-aware variant further conditions the denoiser on object class when such information is available (Kreber et al., 1 Aug 2025).

1. Problem formulation and scope

PhysNAP addresses articulated object generation in a setting where the available observation is a partial 3D point cloud from a single viewpoint rather than a complete articulated model. The target output is a full articulated object model comprising the articulation graph, part geometry, joint parameters, and the initial canonical configuration. In the formulation used by PhysNAP, the input is a partial point cloud $\mathbf{P} \in \mathbb{R}^{n_p \times 3}$, optionally accompanied by a category label, and the output includes the number and existence of parts, SDF-based part geometry, part poses, the articulation graph, joint axes in Plücker coordinates, and joint motion ranges (Kreber et al., 1 Aug 2025).

This problem is motivated by the limitations of earlier articulated-object methods. Several earlier systems are restricted to two-part objects with a single joint, while others require the articulation graph as input, operate in multiple disconnected stages, or lack a mechanism for conditioning generation on a partial observation. PhysNAP is explicitly designed to avoid those restrictions: it does not require the articulation graph as input, it uses differentiable SDF-based geometry during guided sampling, and it introduces training-free reverse-diffusion guidance rather than retraining a conditional model for each constraint configuration. In that sense, PhysNAP is both a generative prior over articulated object structure and a constrained inference procedure over that prior.

A central distinction is that PhysNAP is not primarily a training-time physics-informed model. The diffusion model is trained in the standard denoising way, whereas the physical and observational constraints are imposed at inference by modifying the reverse process. This makes the method closer to constrained posterior sampling than to supervised articulated reconstruction.

2. Representation of articulated objects

PhysNAP inherits NAP’s fixed-size articulation-graph representation with up to $K=8$ parts. Each sample is serialized into a real-valued vector $\mathbf{x}_0$ on which the DDPM operates. Nodes represent parts and edges represent potential joints between parts.

Component	Representation
Part existence	$\tilde{o}_i \in \mathbb{R}$
Part pose	translation $\mathbf{t}_i$ with fixed canonical rotation
Bounding box	$\mathbf{b}_i \in \mathbb{R}^3$
Part shape	latent code $\mathbf{s}_i \in \mathbb{R}^{128}$ for an SDF decoder
Joint existence/direction	$c_{i,j} \in \{-1,0,1\}$, stored as $\tilde{\mathbf{c}}_{i,j}$
Joint axis	Plücker coordinates $(\mathbf{l}_{i,j}, \mathbf{m}_{i,j})$
Joint range	$K=8$0

Part geometry is represented by a latent-SDF parameterization. A pretrained decoder takes a local query point together with the part latent code $K=8$1 and returns a signed distance value. Meshes are later extracted from the decoded field with marching cubes. This SDF representation is crucial because it makes both point-cloud alignment and physical-constraint losses differentiable with respect to part shape, existence, and placement.

Joint axes are represented in 6D Plücker coordinates, and joint motion is parameterized by screw-motion ranges for rotation and translation. The graph therefore encodes not just adjacency but a kinematic model suitable for articulated sampling and physical plausibility checks.

3. Diffusion model and guided reverse process

PhysNAP uses a standard DDPM over the vectorized graph representation. The forward diffusion kernel is

$K=8$2

equivalently,

$K=8$3

The reverse process follows the usual DDPM denoising update with a learned noise predictor $K=8$4. PhysNAP then augments this reverse process by approximating conditional sampling from $K=8$5. The posterior-mean estimate of the clean sample is

$K=8$6

Given $K=8$7, PhysNAP defines

$K=8$8

so that the conditional score is approximated by adding $K=8$9 to the reverse step. The total guidance loss is

$\mathbf{x}_0$0

In the experiments, the reverse process uses $\mathbf{x}_0$1 timesteps, with guidance typically applied for $\mathbf{x}_0$2 steps. A hyperparameter sweep yields base weights $\mathbf{x}_0$3, $\mathbf{x}_0$4, and $\mathbf{x}_0$5, which are reduced when several terms are combined (Kreber et al., 1 Aug 2025).

PhysNAP also introduces a category-aware variant. A learnable category embedding is injected into the attentional graph neural network used by the denoiser. When category information is available, this changes the generative prior itself rather than merely changing the guidance objective.

4. Point-cloud alignment and physical plausibility losses

The point-cloud term $\mathbf{x}_0$6 is defined directly from predicted SDFs. For each point $\mathbf{x}_0$7 in the partial point cloud, PhysNAP transforms the point into each part’s local frame and evaluates a signed distance $\mathbf{x}_0$8. Since part membership is unknown, the method uses soft assignments

$\mathbf{x}_0$9

with $\tilde{o}_i \in \mathbb{R}$0 in the reported experiments. The alignment loss is then

$\tilde{o}_i \in \mathbb{R}$1

Because the SDF evaluations depend on shape latent codes, poses, and existence indicators, this loss can steer all of those variables during reverse diffusion.

The penetration term $\tilde{o}_i \in \mathbb{R}$2 penalizes collisions between parts in the initial canonical pose. For each pair of parts, PhysNAP computes the intersection of their axis-aligned bounding boxes, samples a grid inside the intersection region, and accumulates an SDF penetration error

$\tilde{o}_i \in \mathbb{R}$3

The total loss sums these errors over sampled grid points and part pairs, weighted by a volume element and the continuous existence indicators $\tilde{o}_i \in \mathbb{R}$4. This makes the term differentiable with respect to both geometry and graph structure.

The mobility term $\tilde{o}_i \in \mathbb{R}$5 penalizes collisions under articulation. Rather than constructing a global kinematic tree inside the guided loop, which would introduce non-differentiable operations, PhysNAP restricts the check to directly connected part pairs. For each predicted edge, it samples articulation states from the predicted motion limits, transforms one part relative to the other via the predicted screw motion, computes the corresponding intersection volume, and applies the same SDF penetration error. The final mobility loss is defined as twice the summed value so that its scale is comparable to the static penetration term (Kreber et al., 1 Aug 2025).

A common misunderstanding is that these losses provide a hard guarantee of physical validity. They do not. They are differentiable guidance terms that substantially reduce violations, but the paper explicitly notes that PhysNAP does not guarantee completely collision-free articulated objects.

5. Training setup, empirical behavior, and limitations

PhysNAP is trained on PartNet-Mobility using NAP’s train/validation/test splits. The diffusion model is trained in the standard DDPM manner; point clouds are not used during training. For evaluation, a synthetic partial point cloud is created for each test object by sampling a camera pose with elevation in $\tilde{o}_i \in \mathbb{R}$6, azimuth in $\tilde{o}_i \in \mathbb{R}$7, and distance in $\tilde{o}_i \in \mathbb{R}$8, then rendering an RGB-D view and sampling $\tilde{o}_i \in \mathbb{R}$9 3D points from the object silhouette. The main quantitative evaluation uses $\mathbf{t}_i$0 random test models, one point cloud per model, and multiple generated samples per point cloud (Kreber et al., 1 Aug 2025).

The reported metrics separate guidance quality from unconditional generative quality. Guidance metrics include point-cloud SDF error $\mathbf{t}_i$1, point-to-mesh distance $\mathbf{t}_i$2, penetration error $\mathbf{t}_i$3, and mobility error $\mathbf{t}_i$4. Generative metrics inherited from NAP include MMD and $\mathbf{t}_i$5-NNA.

The results show a strong tradeoff. For category-unaware sampling, unguided NAP reports $\mathbf{t}_i$6, $\mathbf{t}_i$7, $\mathbf{t}_i$8, $\mathbf{t}_i$9, $\mathbf{b}_i \in \mathbb{R}^3$0, and $\mathbf{b}_i \in \mathbb{R}^3$1-NNA $\mathbf{b}_i \in \mathbb{R}^3$2. Adding point-cloud guidance alone reduces the alignment error to $\mathbf{b}_i \in \mathbb{R}^3$3 and $\mathbf{b}_i \in \mathbb{R}^3$4, but raises $\mathbf{b}_i \in \mathbb{R}^3$5 to $\mathbf{b}_i \in \mathbb{R}^3$6 and $\mathbf{b}_i \in \mathbb{R}^3$7-NNA to $\mathbf{b}_i \in \mathbb{R}^3$8. In the category-aware variant, point-cloud guidance further improves alignment to $\mathbf{b}_i \in \mathbb{R}^3$9 and $\mathbf{s}_i \in \mathbb{R}^{128}$0, with $\mathbf{s}_i \in \mathbb{R}^{128}$1 and $\mathbf{s}_i \in \mathbb{R}^{128}$2-NNA $\mathbf{s}_i \in \mathbb{R}^{128}$3. When point-cloud, penetration, and mobility guidance are combined, both category-aware and category-unaware PhysNAP reduce $\mathbf{s}_i \in \mathbb{R}^{128}$4 to $\mathbf{s}_i \in \mathbb{R}^{128}$5 and $\mathbf{s}_i \in \mathbb{R}^{128}$6 to $\mathbf{s}_i \in \mathbb{R}^{128}$7 (Kreber et al., 1 Aug 2025).

These numbers support the paper’s central claim: PhysNAP improves constraint consistency and provides a tradeoff with generative ability. Stronger guidance improves alignment and plausibility but moves samples away from the unconditional training distribution.

The main limitations are explicit. PhysNAP assumes the relative pose of the camera or sensor with respect to the canonical object frame is known. It does not guarantee collision-free objects. It incurs a substantial inference-time cost because the guidance losses require repeated SDF evaluations over sampled volumes and articulated states. Reported runtimes are about $\mathbf{s}_i \in \mathbb{R}^{128}$8–$\mathbf{s}_i \in \mathbb{R}^{128}$9 seconds per unguided sample, about $c_{i,j} \in \{-1,0,1\}$0 seconds with point-cloud guidance alone, and up to about $c_{i,j} \in \{-1,0,1\}$1–$c_{i,j} \in \{-1,0,1\}$2 minutes per sample for combined point-cloud, penetration, and mobility guidance on an Nvidia A40. The method also omits NAP’s post-hoc centering and scaling because those operations would complicate differentiability during guidance.

6. Broader interpretive usage of “PhysNAP”

Beyond the specific articulated-object model, the term “PhysNAP-like” appears in later technical summaries as a broader label for physics-aware neural architecture platforms. In those usages, the common pattern is not diffusion over articulated SDF graphs, but the deliberate embedding of physical structure into representation, optimization, or sampling. Examples include deterministic spectral-element neural PDE solving in NSEM (Feugmo et al., 1 Jun 2026), characteristic-based normalizing-flow solvers for Fokker–Planck equations in PINF (Liu et al., 2023), polyconvex neural-additive constitutive discovery with symbolic regression (Bahmani et al., 2023), sparse nonlinear projection for physics-constrained generative sampling in SNAP-FM (Kolli et al., 30 Jun 2026), node-assigned PINNs for thermal-hydraulic system codes (Shin et al., 23 Apr 2025), inverse soft-tissue biomechanics with heterogeneous material-field PINNs (Caforio et al., 2023), and physics-augmented constitutive models for thermo-visco-plasticity and finite-strain viscoelasticity (Jones et al., 10 Dec 2025, Kalina et al., 4 Nov 2025).

This suggests a broader interpretive meaning for “PhysNAP”: not a single architecture class, but a design philosophy in which neural components are coupled to hard or semi-hard physical structure rather than used as unconstrained regressors. In the articulated-object paper, that philosophy takes the form of reverse-diffusion guidance with SDF-based geometric and physical losses. In the broader scientific-ML literature, the same philosophy appears as deterministic quadrature and spectral differentiation, characteristic ODE enforcement, convex neural thermodynamic potentials, sparse nonlinear constraint projection, or node-wise decomposition aligned to physical discretizations. The specific method called PhysNAP remains the articulated-object diffusion model, but its naming has also become a convenient point of reference for a wider family of physics-aware neural methodologies.