HiDiGen: Hierarchical Diffusion for B-Rep Generation with Explicit Topological Constraints

Abstract: Boundary representation (B-rep) is the standard 3D modeling format in CAD systems, encoding both geometric primitives and topological connectivity. Despite its prevalence, deep generative modeling of valid B-rep structures remains challenging due to the intricate interplay between discrete topology and continuous geometry. In this paper, we propose HiDiGen, a hierarchical generation framework that decouples geometry modeling into two stages, each guided by explicitly modeled topological constraints. Specifically, our approach first establishes face-edge incidence relations to define a coherent topological scaffold, upon which face proxies and initial edge curves are generated. Subsequently, multiple Transformer-based diffusion modules are employed to refine the geometry by generating precise face surfaces and vertex positions, with edge-vertex adjacencies dynamically established and enforced to preserve structural consistency. This progressive geometry hierarchy enables the generation of more novel and diverse shapes, while two-stage topological modeling ensures high validity. Experimental results show that HiDiGen achieves strong performance, generating novel, diverse, and topologically sound CAD models.

• The paper introduces a hierarchical diffusion framework that enforces explicit topological constraints to improve the validity and fidelity of B-Rep generation.
• It employs a two-stage bidirectional process with an edge-face-vertex order, ensuring structured synthesis of complex CAD models.
• Experiments on DeepCAD and ABC datasets demonstrate superior performance, including higher model validity, lower failure rates, and enhanced conditional synthesis.

HiDiGen: Hierarchical Diffusion for B-Rep Generation with Explicit Topological Constraints

Introduction

The paper introduces HiDiGen, a hierarchical diffusion framework for Boundary Representation (B-Rep) generation conditioned on explicit topological constraints. The work addresses limitations in previous neural B-Rep generators by modeling both topology and geometry in an interactively coupled, structured manner rather than the common approaches of implicit, decoupled, or unidirectional representations. The primary motivation is to achieve higher topological validity and geometric fidelity in complex Computer-Aided Design (CAD) model synthesis, with evidence across both unconditional and conditioned generation tasks.

Methodological Advancements

The HiDiGen architecture leverages a two-stage hierarchical, diffusion-based autoregressive process, enforcing explicit topological constraints at each generation step. The distinguishing features include:

• Bidirectional Topology-Geometry Interaction: Unlike DTGBrepGen's unidirectional topology-to-geometry pipeline, HiDiGen generates B-Rep elements via explicit feedback between topology (connectivity) and geometry, at both global and local levels. Ablation studies confirm that removing geometric cues in topology evolution leads to a significant decrease in generation validity (−4.73%).
• Edge-Face-Vertex (EFV) Generation Order: The sequence commences with edge generation, followed by face construction, and finally vertex placement, diverging from prior work (e.g., face-edge-vertex in BrepGen). This hierarchy enables staged enforcement of increasingly stringent topological constraints.
• Explicit Constraint Integration: Constraints are not merely implicit in latent representations but are encoded and enforced stage-wise, ensuring that intermediate outputs satisfy structural requirements before subsequent stages.
• Conditioned Generation Capability: HiDiGen incorporates the ability to condition B-Rep generation on external geometric modalities, such as point clouds, without sacrificing topological compliance or geometric detail.

Experimental Results

HiDiGen demonstrates robust improvement over previous state-of-the-art models across several metrics on the DeepCAD and ABC datasets. Key findings include:

• Validity and Diversity: HiDiGen achieves 75.77% validity (DeepCAD) and 65.77% validity (ABC), outperforming BrepDiff by +3.9% and +6.5% respectively. It also excels in diversity (Unique, Novel >99%).
• Geometric Fidelity: HiDiGen yields consistently superior or competitive MMD and JSD scores compared to baselines.
• Topological Complexity: The model achieves significant gains in complexity coverage (CC: 11.03 DeepCAD, 11.27 ABC) and manifold consistency (MC: 1.99 DeepCAD, 1.48 ABC), surpassing BrepGen and DTGBrepGen by large margins (+4.95% and +9.94%).
• Parameter Efficiency: Despite stronger performance, HiDiGen requires fewer parameters than BrepGen (216.8M vs 291.6M), negating the possibility that gains are due to excess capacity.
• Conditional Generation: When conditioned on point clouds, HiDiGen obtains lower Chamfer Distance (CD: 0.719 DeepCAD) and higher IoU (0.71), reflecting more accurate and consistent conditioned synthesis than previous models (e.g., DTGBrepGen: CD 0.817, IoU 0.62).
• Rebuilding Failure Rate: The approach reduces failure rates to 33.75%, lower than BrepGen (45.94%) and DTGBrepGen (40.16%).

Theoretical and Practical Implications

By explicitly factorizing the B-Rep synthesis process and integrating staged, bidirectional constraint enforcement, HiDiGen delivers improved guarantees on the validity and utility of synthesized representations. This enables the generation of more complex, structurally rigorous CAD models suitable for downstream engineering and design automation.

From a theoretical standpoint, the hierarchical bidirectional architecture can be viewed as a paradigm shift, offering better alignment with how mature CAD algorithms build up representations while maintaining the critical topological invariants. The explicit constraint incorporation also makes the framework robust to degenerate or ambiguous examples that can derail unidirectional or implicit approaches.

Practically, the improved conditional generation performance has direct implications for CAD reverse engineering, shape completion, and augmented generative design, where external geometric cues (point clouds, partial scans) must be respected. Reduced model complexity and reconstruction failure bode well for scalable deployment in industrial contexts.

Future Directions

HiDiGen opens several avenues for further inquiry:

• Generalization to Other Schema: Extension of this bidirectional hierarchical design to other forms of topological generative models (manifold meshes, volumetric data) may be promising.
• Global Context and Long-Range Constraints: The current two-stage design could be expanded to better capture long-range dependencies and global symmetries inherent in engineering models.
• Learning with Scarce Data: The explicit constraint pipeline potentially enables integrating additional human-in-the-loop or rule-based topological priors, reducing data requirements.
• Integration with Downstream Workflows: Exploring post-processing toolchains directly compatible with HiDiGen outputs for end-to-end design automation would be valuable.

Conclusion

HiDiGen establishes a new standard for neural B-Rep generation by enforcing explicit topological constraints in a hierarchical, bidirectionally coupled diffusion process. This enables the consistent synthesis of CAD models exhibiting both geometric fidelity and topological validity, outperforming previous implicit or unidirectional pipelines in both unconditional and point cloud conditioned tasks. The explicit, structured approach paves the way for further methodological innovation and practical deployments in automated geometric design systems.

Reference: "HiDiGen: Hierarchical Diffusion for B-Rep Generation with Explicit Topological Constraints" (2604.02847)