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Denoising Functional Maps: Diffusion Models for Shape Correspondence
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Proposes DenoisFM, a DDPM-based model that predicts template-wise functional maps for shape correspondence, trained on 230k synthetic SURREAL human meshes with an unsupervised Laplacian eigenvector sign corrector.
Problem
Deformable 3D shape correspondence lacks broad generalization and typically requires category-specific training data.
Approach
Use a denoising diffusion model (2D U-Net) to directly predict template-wise functional maps conditioned on sign-corrected Laplacian eigenbasis and learned per-vertex features, with the sign ambiguity resolved by an unsupervised sign correction network and Dirichlet-energy-based sample selection.
Key results
- On the remeshed SHREC'19, Ours (64x64) achieves 3.5 mean geodesic error (x100), best among compared methods including ConsistentFMaps (3.8).
- On FAUST/SCAPE, DenoisFM is on par with descriptor-based methods (e.g., 1.7 FAUST and 2.1 SCAPE for 96x96 vs ULRSSM 1.6 and 2.2).
- On SMAL animal shapes, DenoisFM reaches mean error 4.3, matching ULRSSM and beating ConsistentFMaps (4.8).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Predict functional maps with a diffusion model trained on SURREAL (template-wise maps) instead of descriptor-based pipelines | DenoisFM · FAUST, SCAPE, SHREC'19 (near-isometric) | mean geodesic error | Mixed |
| Train on SURREAL with diffusion and generalize to SCAPE rather than FAUST-trained descriptor methods | DenoisFM vs TransMatch and 3D-CODED · SCAPE and SHREC'19 | mean geodesic error | Helped |
| Increase functional map resolution from 64x64 to 96x96 | DenoisFM · FAUST, SCAPE, SHREC'19 | mean geodesic error: FAUST 1.8→1.7, SCAPE 2.3→2.1, SHREC'19 3.5→3.9 | Mixed |
| Diffusion-based approach with anisotropic remeshing robustness (training with varied connectivity, vertex-count independent conditioning) | DenoisFM · FAUST anisotropic and SCAPE anisotropic | mean geodesic error | Mixed |
| Learned unsupervised sign correction of Laplacian eigenvectors | DenoisFM · Overall (qualitative claim) | mean geodesic error | No clear effect |
| Zero-shot training on human SURREAL, testing on DT4D humanoid classes | DenoisFM · SMAL animal shapes (64x64) | mean geodesic error | No clear effect |
Surprising findings
- Large-scale template-based baselines trained on SURREAL (3D-CODED, TransMatch) perform much worse on SCAPE and SHREC'19 than descriptor-based methods, while DenoisFM generalizes well.
Limitations
- DDPM inference is slow, taking hours for high-dimensional functional maps.
- Animal generalization is limited by the small diversity of the generated SMAL training data.
- Map selection via Dirichlet energy has a major impact on accuracy, relying on multiple samples.
Experimental setup
Datasets: SURREAL FAUST SCAPE SHREC'19 FAUST anisotropic SCAPE anisotropic DT4D SMAL
Benchmarks: FAUST SCAPE SHREC'19 FAUST anisotropic SCAPE anisotropic DT4D SMAL
Metrics: mean geodesic error
Baselines: 3D-CODED TransMatch DUO-FMNet GeomFMaps AttentiveFMaps ConsistentFMaps SSL DiffZO ULRSSM SmS
Builds on: DDPM functional maps DiffusionNet 3D-CODED ZoomOut
Closest papers by meaning
- Memory-Scalable and Simplified Functional Map Learning (CVPR 2024 · similarity 0.88)
- Spectral Meets Spatial: Harmonising 3D Shape Matching and Interpolation (CVPR 2024 · similarity 0.88)
- Hybrid Functional Maps for Crease-Aware Non-Isometric Shape Matching (CVPR 2024 · similarity 0.88)
- Locality Preserving Refinement for Shape Matching with Functional Maps (AAAI 2024 · similarity 0.88)
- Integrating Efficient Optimal Transport and Functional Maps For Unsupervised Shape Correspondence Learning (CVPR 2024 · similarity 0.87)
- Generative Perception of Shape and Material from Differential Motion (NeurIPS 2025 · similarity 0.87)
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