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

TL;DR

This paper introduces a novel method for joint B-Rep generation by representing topological entities as compositional $k$-cell particles, enabling unified, context-aware modeling of geometry and topology.

Contribution

It reformulates B-Reps into shared-latent particles, decoupling hierarchy and allowing joint, context-aware generation of topology and geometry.

Findings

Produces high-fidelity CAD models with superior validity.

Enables joint topology and geometry generation with global context.

Supports downstream tasks like in-painting and non-manifold structure synthesis.

Abstract

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.