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GPLD3D: Latent Diffusion of 3D Shape Generative Models by Enforcing Geometric and Physical Priors
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Proposes GPLD3D, a latent diffusion model for 3D man-made shape generation that regularizes EDM-style denoiser training with a quality checker scoring geometric feasibility and physical stability, with principled loss-weight trade-offs across noise levels.
Problem
Implicit-representation 3D shape generators produce synthetic shapes that are disconnected, physically unstable, or geometrically infeasible, because training only matches the empirical latent distribution.
Approach
Combine the discrete empirical latent distribution with a continuous regularization distribution induced by a latent-code quality checker (learned geometric feasibility classifier plus MLP predicting worst-case stress from stiffness-matrix eigenvalues), and derive per-noise-level loss weights balancing the two terms' variances.
Key results
- On seven ShapeNet categories, GPLD3D reduces FPD/KPD relative to 3DShape2VecSet by 16.5% / 31.7% on average.
- Relative to 3DShape2VecSet, GPLD3D improves physical stability score (PSS) and percentage of disconnected shapes (PDS) by 13.1% and 24.5% across chair, table, airplane and sofa.
- Ablation shows hyper-parameter optimization accounts for about 30% of the FPD/KPD and PSS improvements over the no-quality-checker setting.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add the GPLD3D quality-check regularization to 3DS2VS | 3DS2VS · ShapeNet-v2, all categories | FPD: 0.67 -> 0.56 | Helped |
| add the GPLD3D quality-check regularization to 3DS2VS | 3DS2VS · ShapeNet-v2, all categories | KPD: 0.60 -> 0.41 | Helped |
| add the physical stability checker (ablation) | GPLD3D · ShapeNet-v2, mean of chair, table, airplane, and sofa | PSS: 0.755 -> 0.775 | Helped |
| add the physical stability checker (ablation) | GPLD3D · ShapeNet-v2, mean of chair, table, airplane, and sofa | PDS: 0.862 -> 0.889 | Helped |
| add the physical stability checker (ablation) | GPLD3D · ShapeNet-v2, mean of chair, table, airplane, and sofa | FPD: 0.46 -> 0.45 | No clear effect |
| add the geometric feasibility checker (ablation) | GPLD3D · ShapeNet-v2, mean of chair, table, airplane, and sofa | FPD: 0.48 -> 0.45 | Helped |
| add the geometric feasibility checker (ablation) | GPLD3D · ShapeNet-v2, mean of chair, table, airplane, and sofa | PSS: 0.765 -> 0.775 | Helped |
| add the geometric feasibility checker (ablation) | GPLD3D · ShapeNet-v2, mean of chair, table, airplane, and sofa | PDS: 0.882 -> 0.889 | Helped |
| optimize hyperparameters using the paper's derived tradeoff (ablation) | GPLD3D · ShapeNet-v2, mean of chair, table, airplane, and sofa | FPD: 0.47 -> 0.45 | Helped |
| optimize hyperparameters using the paper's derived tradeoff (ablation) | GPLD3D · ShapeNet-v2, mean of chair, table, airplane, and sofa | PSS: 0.763 -> 0.775 | Helped |
| optimize hyperparameters using the paper's derived tradeoff (ablation) | GPLD3D · ShapeNet-v2, mean of chair, table, airplane, and sofa | PDS: 0.871 -> 0.889 | Helped |
Surprising findings
- A shape classifier trained with class labels always outputs peaked distributions for both good and bad synthetic shapes, so class supervision alone fails as a quality checker; user-labeled good/bad shapes were needed instead.
- Removing the physical stability checker leaves FPD roughly unchanged, while removing the geometric checker worsens FPD by about 6.7%, showing the two checkers capture complementary aspects.
Limitations
- Cannot guarantee geometric feasibility and physical stability of generated shapes, since training sees only a few million latent codes.
- Performance is bounded by the quality of the pre-trained decoder, which needs small reconstruction error on test shapes.
- Physical stability is a deterministic proxy based on worst-case structural analysis rather than full physics simulation.
Experimental setup
Datasets: ShapeNet-v2 ShapeNetCore55
Benchmarks: ShapeNet-v2
Metrics: FPD KPD PSS PDS
Baselines: 3DShape2VecSet 3DILG NW LAS
Builds on: EDM 3DShape2VecSet WCSA (worst-case structural analysis) PointNet++
Closest papers by meaning
- Flow-Corrected Shape Optimization: Taming Manifold Drift in High-Dimensional 3D Models (NeurIPS 2026 · similarity 0.90)
- Sin3DM: Learning a Diffusion Model from a Single 3D Textured Shape (ICLR 2024 · similarity 0.89)
- Enhancing Implicit Shape Generators Using Topological Regularizations (ICML 2024 · similarity 0.89)
- Single Mesh Diffusion Models with Field Latents for Texture Generation (CVPR 2024 · similarity 0.88)
- Mosaic-SDF for 3D Generative Models (CVPR 2024 · similarity 0.87)
- Make-A-Shape: a Ten-Million-scale 3D Shape Model (ICML 2024 · similarity 0.87)
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