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FreeMesh: Boosting Mesh Generation with Coordinates Merging
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Proposes PTME, a training-free entropy-based metric for mesh tokenizers, and coordinate merging (rearrange + BPE merging of coordinates) that compresses serialized meshes and improves point-cloud-conditioned auto-regressive mesh generation.
Problem
Auto-regressive mesh generation depends on how meshes are serialized into token sequences, but there is no efficient, training-free way to measure tokenizer quality, and existing tokenizers yield long sequences that limit face count.
Approach
Defines Per-Token-Mesh-Entropy (PTME) = (substring entropy / average substring length) x compression ratio to score tokenizers without training, and applies BPE (SentencePiece) to coordinate sequences after rearranging coordinates axis-wise in 9-coordinate groups (RMC) so that merges can span axes, reducing PTME and sequence length.
Key results
- EDR+RMC reaches compression ratio 0.212 and PTME 2.231, versus EDR baseline 0.505 and 3.139.
- EDR+RMC lowers Chamfer distance from 0.198 to 0.123 relative to EDR alone in point-cloud conditioned generation.
- PTME correlates with Chamfer distance for EDR+RMC across vocabulary sizes with Pearson r = 0.965.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| apply Merge Coordinates without rearrangement (ablation) | RAW, AMT, and EDR · Mesh tokenization | PTME: 6.742 -> 6.943; 3.349 -> 3.451; 3.139 -> 3.244 | Hurt |
| apply Merge Coordinates without rearrangement (ablation) | RAW, AMT, and EDR · Mesh generation | Chamfer: 0.326 -> 0.334; 0.219 -> 0.232; 0.198 -> 0.204 | Hurt |
| rearrange coordinates without merging (ablation) | RAW, AMT, and EDR · Mesh generation | Chamfer: 0.326 -> 0.329; 0.219 -> 0.226; 0.198 -> 0.202 | Mixed |
| rearrange coordinates, then merge them (ablation) | RAW · Mesh generation | Chamfer: 0.326 -> 0.282 | Helped |
| rearrange coordinates, then merge them (ablation) | AMT · Mesh generation | Chamfer: 0.219 -> 0.164 | Helped |
| rearrange coordinates, then merge them (ablation) | EDR · Mesh generation | Chamfer: 0.198 -> 0.123 | Helped |
| rearrange coordinates, then merge them (ablation) | RAW · Mesh tokenization | PTME: 6.742 -> 4.937 | Helped |
| rearrange coordinates, then merge them (ablation) | AMT · Mesh tokenization | PTME: 3.349 -> 2.537 | Helped |
| rearrange coordinates, then merge them (ablation) | EDR · Mesh tokenization | PTME: 3.139 -> 2.231 | Helped |
| use EDR instead of AMT | Mesh generation · Point-cloud-conditioned generation | Hausdorff: 0.428 vs. 0.408 | Helped |
Surprising findings
- Plain merge coordinates (MC) without rearrangement does not improve generation and even increases PTME for RAW and AMT.
- Training loss correlates poorly with downstream Chamfer distance (r = -0.407 reported), while PTME tracks generation quality.
Limitations
- Gains may diminish at higher quantization levels (e.g., 1024) where identical adjacent coordinate patterns are rarer; evaluated mainly at 7-bit.
- Uses a fixed greedy BPE merging algorithm rather than dynamic merging.
- Qualitative and quantitative results come from a simplified reproduced pipeline rather than the original baseline models.
Experimental setup
Datasets: ShapeNetV2 3D-FUTURE Objaverse Objaverse-XL
Benchmarks: point-cloud conditioned mesh generation test set (sampled meshes at 500, 1000, 2000, 4000 faces)
Metrics: PTME compression ratio Chamfer distance Hausdorff distance
Baselines: MeshXL MeshAnythingV2 EdgeRunner MeshGPT
Builds on: MeshXL MeshAnythingV2 EdgeRunner BPT SentencePiece
Closest papers by meaning
- Scaling Mesh Generation via Compressive Tokenization (CVPR 2025 · similarity 0.89)
- MeshGPT: Generating Triangle Meshes with Decoder-Only Transformers (CVPR 2024 · similarity 0.85)
- TreeMeshGPT: Artistic Mesh Generation with Autoregressive Tree Sequencing (CVPR 2025 · similarity 0.85)
- ARMesh: Autoregressive Mesh Generation via Next-Level-of-Detail Prediction (NeurIPS 2025 · similarity 0.85)
- PivotMesh: Generic 3D Mesh Generation via Pivot Vertices Guidance (ICLR 2025 · similarity 0.85)
- MeshAnything: Artist-Created Mesh Generation with Autoregressive Transformers (ICLR 2025 · similarity 0.83)
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