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SketchDNN: Joint Continuous-Discrete Diffusion for CAD Sketch Generation
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Proposes SketchDNN, a joint continuous-discrete diffusion model for CAD sketch primitives using Gaussian-Softmax diffusion over logits, achieving SOA FID and NLL on SketchGraphs.
Problem
Generating parametric CAD sketches whose primitives mix heterogeneous continuous parameterizations and discrete type labels, while being permutation-invariant over primitive orderings; autoregressive and categorical discrete diffusion approaches handle this poorly.
Approach
Gaussian-Softmax diffusion adds Gaussian noise to log-probabilities and projects via softmax onto the simplex, enabling blended (superposed) class labels for discrete variables; combined with a permutation-equivariant diffusion transformer without positional encodings and a variance schedule augmentation.
Key results
- FID improves from 16.04 (Vitruvion) to 7.80 on unconditional primitive generation on SketchGraphs.
- NLL improves from 84.8 (Vitruvion) to 81.33 bits per sketch.
- Categorical diffusion ablation (SketchDNN Cat.) performs worst, with FID 148.93 and NLL 106.10, indicating superposition matters.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use SketchDNN instead of Vitruvion | CAD sketch generation · SketchGraphs test set | Bits/Sketch: 84.80 -> 81.33 | Helped |
| use SketchDNN instead of Vitruvion | unconditional primitive generation · SketchGraphs | FID: 16.04 -> 7.80 | Helped |
| use SketchDNN instead of Vitruvion | unconditional primitive generation · SketchGraphs | Precision: 0.294 -> 0.246 | Hurt |
| use SketchDNN instead of Vitruvion | unconditional primitive generation · SketchGraphs | Recall: 0.176 -> 0.266 | Helped |
| include positional encodings (ablation) | SketchDNN · SketchGraphs test set | Bits/Sketch: 81.33 -> 83.03 | Hurt |
| include positional encodings (ablation) | SketchDNN · Unconditional primitive generation | FID: 7.80 -> 10.26 | Hurt |
| include positional encodings (ablation) | SketchDNN · Unconditional primitive generation | Precision: 0.246 -> 0.230 | Hurt |
| include positional encodings (ablation) | SketchDNN · Unconditional primitive generation | Recall: 0.266 -> 0.245 | Hurt |
| use categorical diffusion instead of Gaussian-Softmax diffusion (ablation) | SketchDNN · SketchGraphs test set | Bits/Sketch: 81.33 -> 106.10 | Hurt |
| use categorical diffusion instead of Gaussian-Softmax diffusion (ablation) | SketchDNN · Unconditional primitive generation | FID: 7.80 -> 148.93 | Hurt |
| use categorical diffusion instead of Gaussian-Softmax diffusion (ablation) | SketchDNN · Unconditional primitive generation | Precision: 0.246 -> 0.117 | Hurt |
| use categorical diffusion instead of Gaussian-Softmax diffusion (ablation) | SketchDNN · Unconditional primitive generation | Recall: 0.266 -> 0.028 | Hurt |
Surprising findings
- The categorical diffusion variant performs worse than both autoregressive baselines Vitruvion and SketchGen, despite having full sketch context at each step.
- Latent diffusion underperforms badly (FID 93.34), suggesting latent-space diffusion is ill suited to CAD sketches.
Limitations
- Only sketches with 8 to 16 primitives were used, excluding the majority of the dataset, and constraints are not generated.
- Failure modes include sketches without discernible structure, large gaps between supposedly coincident endpoints, and redundant overlapping primitives.
- Precision for SketchDNN (0.246) is lower than Vitruvion (0.294).
Experimental setup
Datasets: SketchGraphs
Benchmarks: SketchGraphs test set
Metrics: FID precision recall NLL (bits per sketch) bits per primitive
Baselines: Vitruvion SketchGen SketchDNN (Cat.) Latent diffusion SketchDNN (Pos.)
Builds on: DDPM Multinomial diffusion Diffusion Transformer (DiT) Vitruvion
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