SQuadGen: Generating Simple Quad Layouts via Chart Distance Fields

Abstract: 3D shapes from scanning, reconstruction, or AI-generated content often lack simple quad mesh layouts -- critical for efficient editing and modeling. Existing quad-remeshing techniques typically produce complex layouts with irregular loops, leading to tedious manual cleanup and extensive algorithm tuning. We introduce SQuadGen, a diffusion-based generative framework that leverages Chart Distance Fields (CDF) to synthesize simple quad layouts on 3D shapes. Our approach addresses two key challenges: (1) the discrete nature of mesh connectivity, which hinders learning, and (2) the scarcity of large-scale datasets with simple quad meshes. To overcome the first, we propose CDF, a continuous surface-based representation enabling effective learning and synthesis of quad layouts. To address the second, we define loop-aware simplicity metrics and construct a large-scale dataset of high-quality quad layouts recovered from public 3D repositories through a robust quad-recovery pipeline. Extensive evaluations across diverse 3D inputs show that SQuadGen consistently outperforms existing methods, producing robust, artist-friendly simple quad layouts.

• The paper presents a novel diffusion-based framework that generates simple, artist-friendly quad mesh layouts via continuous Chart Distance Fields.
• It introduces a unique scalar field formulation that bypasses direct connectivity prediction by representing quad charts through smooth distance mappings.
• Experimental results show that SQuadGen outperforms existing methods with higher loop simplicity and lower chart counts for efficient 3D modeling workflows.

Generating Simple Quad Mesh Layouts with Diffusion and Chart Distance Fields

Motivation and Problem Statement

The problem of quadrilateral (quad) mesh layout generation underlies key workflows in digital geometry processing, modeling, and animation. Simple quad layouts—those with minimal singularities, clear loop structures, and alignment with feature lines—are essential for efficient downstream editing, deformation, and simulation. However, current quad-remeshing approaches often produce complex, spiral-prone layouts that are suboptimal for artist-centric surface editing, requiring significant manual post-processing. Furthermore, most mesh generation and processing pipelines natively output triangle meshes or point clouds, exacerbating the gap between automated mesh generation and practical usability.

Contributions and Methodology

The paper "SQuadGen: Generating Simple Quad Layouts via Chart Distance Fields" (2604.27329) introduces SQUADGEN, a diffusion-based generative model that synthesizes simple, artist-friendly quad layouts directly on input triangle meshes. The central contributions of the work are:

• Chart Distance Field (CDF) Representation: A novel continuous scalar field formulation that encodes discrete quad mesh layout structures as smooth fields over surfaces, bypassing the difficulties of learning combinatorial mesh connectivity directly.
• Geometry-Conditioned Latent Diffusion: A sophisticated generative pipeline employing geometry-aware autoencoding, variational latent representation, and diffusion over latents to synthesize the chart distance field aligned with a given 3D surface.
• Large-Scale Quad Layout Dataset and Simplicity Metrics: A robust pipeline for extracting and curating a dataset (>230k samples) of simple quad mesh layouts from common 3D model repositories using loop-aware metrics quantifying face-loop and edge-loop simplicity.
• Efficient Layout Extraction and Refinement: A region-growing and feature-aware procedure for extracting regular quad layouts from generated CDFs, with further refinement for mesh quality and feature alignment.

Loop Simplicity Metrics and Quad Layout Quality

Traditional measures of quad mesh quality, such as singularity or irregular vertex count, do not adequately capture editing-friendly layouts. This work introduces explicit loop simplicity metrics—namely, the area-ratio of regions controlled by simple face-loops and edge-loops (where "simple" means non-self-intersecting and nonspiraling). The overall loop simplicity score is:

$$S_\text{simplicity}(Q) = \min(S_\text{face-loop}(Q), S_\text{edge-loop}(Q))$$

These loop-aware metrics serve both to filter training data and to rigorously benchmark outputs, aligning empirical evaluation with the demands of practical modeling.

Chart Distance Fields (CDF) as Continuous Representation

A key innovation is the Chart Distance Field representation, which maps each chart (patch) in the quad layout to a continuous field, with scalar values decreasing smoothly from chart centers to chart boundaries. By splitting charts into subcharts—with centers determined by flow lines along edge-rings—this method provides a smooth, grid-like signal (with extensions to dual charts, DCDF) that is naturally periodic and encodes global layout structure. This approach greatly simplifies the learning and inference of layout structure, sidestepping direct prediction of connectivity or frame fields.

SQUADGEN Architecture

SQUADGEN comprises several tightly-integrated neural modules:

• Geom-AE: A VectorSet-based autoencoder that compresses surface geometry into global latent codes.
• SQ-VAE: A geometry-conditioned variational autoencoder that maps quad layouts into a compatible latent space.
• SQ-Diffuse: A geometry-conditioned latent diffusion transformer (based on Scalable Interpolant Transformer) for synthesizing latents representing the CDF given an input geometry.
• Layout Extraction: An algorithm that clusters faces based on synthesized CDF maxima to recover quad chart boundaries, followed by edge collapse and refinement to ensure quad-dominant meshes.

A notable design is the use of global (VecSet) attention, enabling non-local interactions necessary for capturing the inherently global structure of quad layouts.

Dataset Curation and Loop-Aware Triangle Merging

The abundance of triangle meshes in public 3D datasets motivated a custom triangle-to-quad merging algorithm, which prioritizes rectangularity, edge-flow alignment, and face-loop simplicity. Combined with remeshing tools (QuadRemesher, QuadWild), alpha wrapping, and feature-line preservation, this pipeline yields a large corpus of pure-quad meshes, strictly filtered via loop simplicity, distortion, chart count, and geometric criteria. This depth of dataset construction was indispensable both for supervised learning and quantitative benchmarking.

Experimental Results and Empirical Evaluation

On a suite of diverse test sets—including in-domain, CAD, and complex high-detail shapes—SQUADGEN demonstrates strong numerical performance compared to both classical and contemporary methods:

Metric	Ground Truth	QuadriFlow	QuadWild	QuadRemesher	FSCP	SQUADGEN
Loop Simplicity (↑ Part1k)	1.00	0.55	0.86	0.82	0.79	0.95
Chart Count (↓)	23.3	1645.7	127.2	558.8	685.1	47.7
Irregular Vertices (↓)	10.9	49.0	11.5	12.9	12.7	18.2

(Sample results for the Part1k dataset; see (2604.27329), Table 1.)

Key findings:

• SQUADGEN outputs demonstrate substantially higher loop simplicity and lower chart count than strong baselines, indicating simpler and more editable quad layouts.
• The method generalizes robustly to both CAD and organic test shapes, though with some degradation on highly detailed or out-of-distribution inputs.
• Regularized inference and increased latent resolution further improve output simplicity and regularity.

Qualitatively, SQUADGEN’s outputs are characterized by clear boundary alignment, large coherent patches, and minimal spiral or tangled loops, ideal for modeling and animation workflows.

Theoretical and Practical Implications

The reconceptualization of quad layout generation as scalar field synthesis, rather than direct connectivity prediction or field interpolation, opens new methodological vistas for mesh generation and surface layout in geometry processing.

• Theoretically, CDFs provide a low-frequency, learnable surrogate to frame fields, facilitating robust generalization, data-driven synthesis, and extensibility to volumetric (hexahedral) domains.
• Practically, artist workflows for 3D asset retopology, character modeling, and simulation mesh generation can benefit directly from the simplicity, editability, and structural alignment of SQUADGEN outputs.

Limitations and Future Directions

The current approach is primarily limited by the restrictiveness of training data—layouts with complex geometric detail are largely filtered out, limiting generalization to high-frequency or intricate surfaces. Furthermore, the stochasticity of the diffusion process, necessary post-hoc selection of best samples, and heuristic nature of layout extraction introduce inefficiencies and potential failure modes.

Promising future directions include:

• Data enrichment: Incorporating complex layouts or optimizing existing mesh data to improve coverage.
• User conditioning: Allowing direct user constraints (e.g., guiding strokes, partial layout specification) to steer generation.
• Integration of layout optimization: Post-processing generated layouts via existing optimization algorithms to further improve structural and geometric quality.
• Methodological unification: Extending the chart distance field formalism to volumetric hexahedral or tetrahedral meshing.

Conclusion

SQUADGEN introduces a paradigm shift in quad mesh layout generation by reframing the problem as scalar field synthesis using diffusion models over a continuous chart distance field representation. Through rigorous dataset construction, innovative loop simplicity metrics, a geometry-conditioned diffusion architecture, and robust extraction procedures, the method delivers consistently simple, artist-friendly quad layouts. This framework presents new opportunities for data-driven mesh generation in computer graphics, geometric modeling, and downstream AI-driven 3D content creation (2604.27329).