PRISM: Articulated Object Modeling with Precise Structural Control

Articulated objects are fundamental to robotics, simulation, and interactive virtual environments, where generated assets must satisfy not only visual realism but also structural and functional validity. Although recent generation methods have made substantial progress through 2D diffusion priors, sparse-view reconstruction, and native 3D generative models, their semantic or appearance-level conditions leave part topology and articulation underdetermined. Consequently, visually plausible assets can exhibit incorrect connectivity, joint placement, or functional organization. We present Prism, an Analytic-Concept-guided framework for articulated object modeling with strict structural control, together with an automated Analytic Concept construction module that instantiates the executable concepts used for conditioning. Prism uses Analytic Concept as a procedural control interface that specifies part geometry, topological relations, articulation constraints, and affordance functions in an executable form. Given a target brief, procedural templates, and a small set of valid instances, the construction module infers parameter dependencies, proposes an instance in dependency order, and repairs only the parameters implicated by failed execution checks. A validated concept and an appearance reference image are then converted into a multi-modal prior representation from concept-rendered images, concept-derived language descriptions, and image-based appearance features. Adaptive modulation and cross-attention integrate these complementary modalities before a conditional diffusion transformer maps the resulting representation into a latent space. The predicted latent is then decoded into a mesh that preserves the specified articulated organization while maintaining realistic geometric details. We evaluate Prism on PartNet-Mobility and downstream robotic manipulation tasks. Under their respective input conditions, comparisons with general-purpose and articulated-generation baselines show improved geometric quality and structural fidelity. Controlled condition ablations further show that gains depend on how Prism integrates the explicit concept with appearance evidence, rather than on structural specification alone. Evaluating automatically constructed concepts across unseen categories remains a separate question.