# Flatten The Complex: Joint B-Rep Generation via Compositional k-Cell Particles

arXiv: https://arxiv.org/abs/2601.17733 · HTML: https://mlsanity.com/paper/2601.17733/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 36 of its 51 references that are in the map.
- First posted on arXiv 25 Jan 2026.

## Builds on (most cited first, 30 of 36)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Structured 3D Latents for Scalable and Versatile 3D Generation](https://mlsanity.com/paper/2412.01506/) (2024)
- [LION: Latent Point Diffusion Models for 3D Shape Generation](https://mlsanity.com/paper/2210.06978/) (2022)
- [3DShape2VecSet: A 3D Shape Representation for Neural Fields and Generative Diffusion Models](https://mlsanity.com/paper/2301.11445/) (2023)
- [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018)
- [DeepCAD: A Deep Generative Network for Computer-Aided Design Models](https://mlsanity.com/paper/2105.09492/) (2021)
- [PolyGen: An Autoregressive Generative Model of 3D Meshes](https://mlsanity.com/paper/2002.10880/) (2020)
- [Sonata: Self-Supervised Learning of Reliable Point Representations](https://mlsanity.com/paper/2503.16429/) (2025)
- [CSGNet: Neural Shape Parser for Constructive Solid Geometry](https://mlsanity.com/paper/1712.08290/) (2017)
- [BrepGen: A B-rep Generative Diffusion Model with Structured Latent Geometry](https://mlsanity.com/paper/2401.15563/) (2024)
- [Computer-Aided Design as Language](https://mlsanity.com/paper/2105.02769/) (2021)
- [UCSG-Net -- Unsupervised Discovering of Constructive Solid Geometry Tree](https://mlsanity.com/paper/2006.09102/) (2020)
- [PolyDiff: Generating 3D Polygonal Meshes with Diffusion Models](https://mlsanity.com/paper/2312.11417/) (2023)
- [CAD-Recode: Reverse Engineering CAD Code from Point Clouds](https://mlsanity.com/paper/2412.14042/) (2024)
- [FasterDiT: Towards Faster Diffusion Transformers Training without Architecture Modification](https://mlsanity.com/paper/2410.10356/) (2024)
- [Generating CAD Code with Vision-Language Models for 3D Designs](https://mlsanity.com/paper/2410.05340/) (2024)
- [CSG-Stump: A Learning Friendly CSG-Like Representation for Interpretable Shape Parsing](https://mlsanity.com/paper/2108.11305/) (2021)
- [Inferring CAD Modeling Sequences Using Zone Graphs](https://mlsanity.com/paper/2104.03900/) (2021)
- [Intriguing Properties of Quantization at Scale](https://mlsanity.com/paper/2305.19268/) (2023)
- [Reconstructing editable prismatic CAD from rounded voxel models](https://mlsanity.com/paper/2209.01161/) (2022)
- [D2CSG: Unsupervised Learning of Compact CSG Trees with Dual Complements and Dropouts](https://mlsanity.com/paper/2301.11497/) (2023)
- [PolyDiffuse: Polygonal Shape Reconstruction via Guided Set Diffusion Models](https://mlsanity.com/paper/2306.01461/) (2023)
- [CADCrafter: Generating Computer-Aided Design Models from Unconstrained Images](https://mlsanity.com/paper/2504.04753/) (2025)
- [HoLa: B-Rep Generation using a Holistic Latent Representation](https://mlsanity.com/paper/2504.14257/) (2025)
- [Neurosymbolic Models for Computer Graphics](https://mlsanity.com/paper/2304.10320/) (2023)
- [CadVLM: Bridging Language and Vision in the Generation of Parametric CAD Sketches](https://mlsanity.com/paper/2409.17457/) (2024)
- [CADDreamer: CAD Object Generation from Single-view Images](https://mlsanity.com/paper/2502.20732/) (2025)

## Abstract (arXiv)

Boundary Representation (B-Rep) is the widely adopted standard in Computer-Aided Design (CAD) and manufacturing. However, generative modeling of B-Reps remains a formidable challenge due to their inherent heterogeneity as geometric cell complexes, which entangles topology with geometry across cells of varying orders (i.e., k-cells such as vertices, edges, faces). Previous methods typically rely on cascaded sequences to handle this hierarchy, which fails to fully exploit the geometric relationships between cells, such as adjacency and sharing, limiting context awareness and error recovery. To fill this gap, we introduce a novel paradigm that reformulates B-Reps into sets of compositional k-cell particles. Our approach encodes each topological entity as a composition of particles, where adjacent cells share identical latents at their interfaces, thereby promoting geometric coupling along shared boundaries. By decoupling the rigid hierarchy, our representation unifies vertices, edges, and faces, enabling the joint generation of topology and geometry with global context awareness. We synthesize these particle sets using a multi-modal flow matching framework to handle unconditional generation as well as precise conditional tasks, such as 3D reconstruction from single-view or point cloud. Furthermore, the explicit and localized nature of our representation naturally extends to downstream tasks like local in-painting and enables the direct synthesis of non-manifold structures (e.g., wireframes). Extensive experiments demonstrate that our method produces high-fidelity CAD models with superior validity and editability compared to state-of-the-art methods.