# PRISM: Probabilistic Representation for Integrated Shape Modeling and Generation

arXiv: https://arxiv.org/abs/2504.04454 · HTML: https://mlsanity.com/paper/2504.04454/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 33 of its 45 references that are in the map.
- First posted on arXiv 6 Apr 2025.

## Builds on (most cited first, 30 of 33)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [GET3D: A Generative Model of High Quality 3D Textured Shapes Learned from Images](https://mlsanity.com/paper/2209.11163/) (2022)
- [PolyGen: An Autoregressive Generative Model of 3D Meshes](https://mlsanity.com/paper/2002.10880/) (2020)
- [MeshGPT: Generating Triangle Meshes with Decoder-Only Transformers](https://mlsanity.com/paper/2311.15475/) (2023)
- [Learning Gradient Fields for Shape Generation](https://mlsanity.com/paper/2008.06520/) (2020)
- [Learning Shape Templates with Structured Implicit Functions](https://mlsanity.com/paper/1904.06447/) (2019)
- [AutoSDF: Shape Priors for 3D Completion, Reconstruction and Generation](https://mlsanity.com/paper/2203.09516/) (2022)
- [Text2Shape: Generating Shapes from Natural Language by Learning Joint Embeddings](https://mlsanity.com/paper/1803.08495/) (2018)
- [Ditto: Building Digital Twins of Articulated Objects from Interaction](https://mlsanity.com/paper/2202.08227/) (2022)
- [Neural Wavelet-domain Diffusion for 3D Shape Generation](https://mlsanity.com/paper/2209.08725/) (2022)
- [PQ-NET: A Generative Part Seq2Seq Network for 3D Shapes](https://mlsanity.com/paper/1911.10949/) (2019)
- [PARIS: Part-level Reconstruction and Motion Analysis for Articulated Objects](https://mlsanity.com/paper/2308.07391/) (2023)
- [SDM-NET: Deep Generative Network for Structured Deformable Mesh](https://mlsanity.com/paper/1908.04520/) (2019)
- [ShapeFormer: Transformer-based Shape Completion via Sparse Representation](https://mlsanity.com/paper/2201.10326/) (2022)
- [SALAD: Part-Level Latent Diffusion for 3D Shape Generation and Manipulation](https://mlsanity.com/paper/2303.12236/) (2023)
- [PolyDiff: Generating 3D Polygonal Meshes with Diffusion Models](https://mlsanity.com/paper/2312.11417/) (2023)
- [Part123: Part-aware 3D Reconstruction from a Single-view Image](https://mlsanity.com/paper/2405.16888/) (2024)
- [CAGE: Controllable Articulation GEneration](https://mlsanity.com/paper/2312.09570/) (2023)
- [DiffFacto: Controllable Part-Based 3D Point Cloud Generation with Cross Diffusion](https://mlsanity.com/paper/2305.01921/) (2023)
- [3DCoMPaT++: An improved Large-scale 3D Vision Dataset for Compositional Recognition](https://mlsanity.com/paper/2310.18511/) (2023)

## Abstract (arXiv)

Despite the advancements in 3D full-shape generation, accurately 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 structural information of 3D shapes into their generative processes. We address these limitations with PRISM, a novel compositional approach for 3D shape generation that integrates 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 semantics 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.