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GraphCAD: Geometry-Aware Diffusion on Edge-Adjacency Graphs for CAD Generation
Wenhao Zheng, Xianggen Liu, Li Yue, Jiancheng Shi, Jiancheng Lv
TL;DR
B-rep generation must reconcile discrete topology with continuous geometry, a challenge for direct synthesis. GraphCAD uses hybrid diffusion on an edge-adjacency graph, with geometry-aware denoising. It achieves state-of-the-art validity and fidelity against existing sequence-based and graph-based baselines.
Problem
Direct B-rep synthesis is difficult because it must model continuous geometric parameters and discrete topological connectivity together.
Source: §1 · p. 1Method
GraphCAD performs hybrid graph diffusion on EAGs, using geometry-aware denoising that renders edge attributes into spatial geometry for an SE(3)-equivariant network.
Source: §1 · p. 2Results
GraphCAD achieves state-of-the-art performance in both validity and fidelity compared with existing sequence-based and graph-based baselines.
Source: §6 · p. 8Takeaways & Limitations
GraphCAD grounds abstract EAG node attributes in spatial geometry while promoting robust topological and geometric consistency.
Source: §6 · p. 8EAG models 1D boundary curves rather than explicit surface patches, and reconstruction may introduce errors in regions with complex curvature.
Source: §5 · p. 8
Abstract
from arXiv · showhide
Generative modeling for Computer-Aided Design (CAD) remains fundamentally challenged by the need to capture the intricate interplay between discrete topological connectivity and precise spatial geometry inherent in Boundary Representations (B-reps). Existing generative approaches largely formulate CAD construction as a sequence modeling problem, but consequently lack an explicit topological inductive bias. In this work, we present GraphCAD, a geometry-aware generative framework that centers modeling on the Edge-Adjacency Graph (EAG), a novel graph-based CAD representation tailored for generative tasks. GraphCAD adopts a hybrid graph diffusion formulation to jointly model the discrete and continuous components of EAG and introduces a geometry-aware denoising mechanism that renders node attributes into spatial point sets. These point sets are encoded by an SE(3)-equivariant backbone and fused into the node representations, thereby grounding the generative process in physical geometry. To support this study, we construct EAGBench, a large-scale dataset of engineering CAD models. Extensive experiments show that GraphCAD can generate complex CAD models with more than 50 faces and achieves state-of-the-art performance in geometric fidelity and distributional alignment compared with sequence-based baselines.
1 Introduction
Generating B-reps requires modeling discrete topology and continuous geometry together, while prevailing sequence and CSG approaches can struggle to preserve topological integrity. GraphCAD instead builds generation around an edge-based graph and geometry-aware diffusion.
1 Introduction
- B-rep generation must jointly model continuous geometric parameters and discrete topological connectivity, a combination that makes direct synthesis difficult.B-reps describe solids through parameterized faces, edges, and vertices.Source: §1 · p. 1
- Sequence and CSG approaches can struggle to preserve topological integrity, while face-adjacency graph methods remain limited in enforcing precise 1D boundary constraints.In sequence-based generation, an early error can propagate into disjoint loops, non-manifold edges, or invalid geometries.Source: §1 · p. 1
- EAG makes topological edges its nodes, with curve types and spatial parameters as hybrid attributes.Its graph connectivity represents shared B-rep vertices.Source: §1 · p. 2, Figure 1 · p. 2
- GraphCAD uses geometry-aware hybrid graph diffusion and an SE(3)-equivariant denoising network to model EAG's discrete and continuous attributes.The network renders node attributes into curves and samples spatial point sets for geometric encoding.Source: §1 · p. 2
- On EAGBench, GraphCAD achieves state-of-the-art geometric fidelity and distributional alignment while maintaining highly competitive topological validity against leading sequence-based baselines.EAGBench is a large-scale unified benchmark built on the EAG representation.Source: §1 · p. 2
2 Related Work
Prior CAD generation spans CSG, command sequences, and graph representations of B-reps, while graph diffusion and SE(3)-equivariant networks provide relevant modeling tools for GraphCAD.
2.1 Generative CAD Modeling
- Feature-based command sequences have improved controllability and geometric fidelity, but encode command histories rather than explicit geometric-topological structure.Earlier CSG methods are described as overly complex and insufficiently flexible for typical industrial design scenarios.Source: §2.1 · p. 2
2.2 Representation Learning for B-reps
- B-rep graph methods use face-adjacency graphs with UV-domain surface features, but their complex trimmed-surface nodes and multistage generation can impede precise 1D boundary constraints.The text identifies computational redundancy and error accumulation across stages as additional difficulties.Source: §2.2 · pp. 2–3
2.3 Graph Diffusion and Equivariance
- Graph diffusion methods model discrete or continuous graph structures, while SE(3)-equivariant networks address rotational robustness; GraphCAD applies these ideas to hybrid EAG generation.The paper presents invariant likelihoods for rigorous engineering geometries as a property of this design.Source: §2.3 · p. 3
3 Method
GraphCAD models CAD generation on an Edge-Adjacency Graph (EAG), combining edge-level topology with spatial geometry. Its hybrid diffusion and geometry-aware denoising operate on this representation, with the denoising network designed to be SE(3)-equivariant.
3 Method
- GraphCAD shifts from parametric CAD sequences to EAGs and uses hybrid graph diffusion to generate structural connectivity and precise 3D geometry.The framework treats geometry as spatial entities rather than independent abstract variables.Source: §3 · p. 3
3.1 Edge-Adjacency Graph Representation
- EAG nodes represent topological edges with curve-type and spatial attributes, while graph edges connect CAD edges that share a B-rep vertex.The representation uses line, arc, and circle primitives; splines are represented as sequences of arc segments.Source: §3.1 · pp. 3–4, Figure 3 · p. 4
3.2 Hybrid Graph Diffusion
- Hybrid graph diffusion jointly models discrete node types and edge connectivity with continuous geometric parameters.The reverse process is conditionally factorized, but a shared denoising network processes the complete noisy graph and predicts all three components.Source: §3.2 · p. 4
3.3 Geometry-Aware Denoising
- The denoiser renders noisy node parameters as curves, samples local point sets, and encodes them to ground node representations in geometry.Noisy parameters are interpreted as control points for quadratic Bézier curves, with 100 points sampled per curve.Source: §3.3 · pp. 4–5
- A semantic-aware mask suppresses geometry-loss terms for attributes undefined by a curve type, preventing gradients for nonexistent geometry.The hybrid loss combines cross-entropy for node types and edge connectivity with masked supervision of continuous geometry.Source: §3.3 · p. 5
3.4 SE(3) Equivariance
- The denoising network is SE(3)-equivariant: transforming an input EAG yields a correspondingly transformed prediction.Translation is handled by input canonicalization and rotation by an SO(3)-equivariant backbone; the claim does not extend to sampling or B-rep reconstruction.Source: §3.4 · p. 5
4.1 Setup
The setup introduces EAGBench’s two datasets and evaluates graph generation and reconstructed CAD using structural and geometric measures. It also specifies a shared reconstruction pipeline and catalogs the failure modes that prevent valid solid construction.
4.1.1 Dataset Construction.
- EAGBench combines DeepCAD and Fusion 360 Gallery models; its subsets contain 95,392 and 2,839 models, respectively, with the latter featuring more curved primitives.Models are deduplicated and filtered for parseable surface area and volume before edge attributes are extracted and normalized.Source: §4.1.1 · p. 5
4.1.2 Baselines.
- Baselines cover graph-generation models, sequence-based CAD generation, and graph-based CAD generation.The comparisons include GraphNVP, GDSS, ConGress, DiGress, DeepCAD, Text2CAD, TGBFN, BrepGiff, and GraphBRep.Source: §4.1.2 · p. 6
4.1.3 Metrics.
- Evaluation measures graph validity, uniqueness, novelty, and distributional structure, alongside reconstructed CAD invalidity, geometric fidelity, and distributional quality.CAD geometry uses squared Chamfer and Hausdorff distances on 8,192 sampled surface points; Table 1 Validity and Tables 2–3 IR are complementary measures from the same reconstruction pipeline.Source: §4.1.3 · p. 6
4.1.4 B-rep Reconstruction.
- Generated EAGs are reconstructed into B-reps by instantiating edge primitives, assembling closed wires, stitching faces into shells, and checking watertightness.Valid shells are converted to solids for uniform surface sampling; graph-based methods share this pipeline, while sequence-based baselines use their official implementations.Source: §4.1.4 · p. 6
4.1.5 Implementation Details.
- The hybrid diffusion implementation uses 500 timesteps and an SE(3)-equivariant point-set encoder with a three-stage hierarchy.Discrete variables use Markov transition matrices, while continuous parameters use a Gaussian variance schedule.Source: §4.1.5 · p. 6
4.1.6 Failure Mode Analysis of EAG-to-B-rep Reconstruction.
- Four reconstruction failures are identified: degenerate primitives, undefined arc parametrization, geometric inconsistency, and topological mismatch.They arise respectively from coincident endpoints, collinear arc-defining points, unequal center-to-endpoint distances beyond tolerance, and graph-connected edges with non-coincident endpoints that leave an open wire.Source: §4.1.6 · p. 6
4.2 Unconditional Topological Generation
GraphCAD generates EAGs that better match reference topology than the compared graph-generation baselines, with a particularly large validity advantage on EAGBench-FS. Its samples also show high uniqueness and novelty, while qualitative examples depict complex geometry and topology.
4.2 Unconditional Topological Generation
- 96.58% validity on EAGBench-FS exceeds DiGress’s 77.45%, and GraphCAD achieves the lowest Deg, Clus, and Orb scores across the evaluated graph-generation baselines.The comparison reports consistent outperformance of GraphNVP, GDSS, ConGress, and DiGress across evaluation metrics, with the validity margin especially pronounced on EAGBench-FS.Source: §4.2 · pp. 6–7
- Uniqueness exceeds 95% and Novelty exceeds 92% across both datasets, while Figure 5 depicts realistic CAD B-reps with complex geometry and topology.The authors describe the samples as diverse and report no evident overfitting or mode collapse.Source: §4.2 · p. 7, Figure 5 · p. 7
4.3 Conditional CAD Generation
GraphCAD performs strongly in conditional CAD generation on both EAGBench-FS and EAGBench-DC. Its results show stronger geometric and distributional metrics than baselines, while TGBFN retains the lowest invalidity ratio on EAGBench-DC.
4.3 Conditional CAD Generation
- 0.78% IR for TGBFN is lower than GraphCAD’s 1.67% IR on EAGBench-DC, although GraphCAD provides stronger geometric reconstruction quality.The comparison describes a balance between topological validity and geometric accuracy.Source: §4.3 · pp. 7–8
- CD decreases from 2.34 to 1.73 and JSD from 65.92 to 33.22 for GraphCAD versus TGBFN on EAGBench-DC.GraphCAD achieves the best geometric and distributional metrics on EAGBench-DC.Source: §4.3 · pp. 7–8
- 5.42% IR, 3.37 CD, 0.59 HD, 64.97 JSD, and 3.52 MMD are GraphCAD’s best EAGBench-FS scores across all five metrics.It surpasses sequence-based Text2CAD and graph-based GraphBRep and BrepGiff on this more challenging benchmark.Source: §4.3 · p. 8
4.4 Ablation Study
The ablations identify geometric rendering as the most consequential module for GraphCAD’s validity, geometric fidelity, and distributional alignment. Point-sampling results also show large gains from sparse rendering and a quality-efficiency trade-off at higher density.
4.4 Ablation Study
- Removing geometric rendering causes the largest deterioration in validity, geometric fidelity, and distributional alignment; the full GraphCAD model performs best overall.Removing SE(3) equivariance leads to a moderate decline, while removing loss masking causes a much larger validity drop and weaker geometric consistency.Source: §4.4 · p. 8
- Without explicit rendering (K=0), invalidity is 27.59%; introducing even a sparse point set (K=10) reduces it to 2.52%, underscoring the importance of spatial grounding.Source: §4.4 · p. 8
- At K=100, CD is 1.94 and IR is 1.78%, while VRAM rises by 0.66 GB from 4.40 GB to 5.06 GB.The authors identify K=100 as a practical trade-off between reconstruction quality and efficiency.Source: §4.4 · p. 8
5 Limitations
The limitations concern surface reconstruction, inference speed, and scaling beyond component-level parts.
5 Limitations
- EAG models 1D boundary curves rather than explicit 2D surface patches, and post-processing recovery of complete surface definitions may introduce errors in complex-curvature regions.The paper names NURBS control points as an example of surface definitions recovered during post-processing.Source: §5 · p. 8
- The iterative diffusion process requires T denoising steps, making inference slower than single-pass generative methods.Source: §5 · p. 8
- Experiments focus on component-level parts, and scaling EAG generation to assemblies with thousands of topological edges remains challenging because of the larger discrete state space.Source: §5 · p. 8
6 Conclusion
The conclusion presents GraphCAD as a geometry-aware hybrid graph diffusion framework built on EAG. Experiments on EAGBench report strong validity and fidelity against sequence-based and graph-based baselines, while future work targets full surface definitions.
6 Conclusion
- GraphCAD combines a curve-rendering mechanism with an SE(3)-equivariant backbone to ground abstract node attributes in spatial geometry.Source: §6 · p. 8
- Experiments on EAGBench show state-of-the-art performance in validity and fidelity compared with existing sequence-based and graph-based baselines.Source: §6 · p. 8
- Future work will extend the probabilistic formulation to infer full surface definitions, moving beyond wireframe generation toward complete solid reconstruction.Source: §6 · p. 8