Despite the advancements in 3D full-shape generation, acurately modeling complex geometries and semantics of shape parts remains a significant challenge, particularly for shapes with varying numbers of parts. Current methods struggle to effectively integrate the contextual and struc- tural information of 3D shapes into their generative pro- cesses. We address these limitations with PRISM, a novel compositional approach for 3D shape generation that in- tegrates categorical diffusion models with Statistical Shape Models (SSM) and Gaussian Mixture Models (GMM). Our method employs compositional SSMs to capture part-level geometric variations and uses GMM to represent part se- mantics in a continuous space. This integration enables both high fidelity and diversity in generated shapes while preserving structural coherence. Through extensive experiments on shape generation and manipulation tasks, we demonstrate that our approach significantly outperforms previous methods in both quality and controllability of part-level operations. Our code will be made publicly available.
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