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Not-So-Optimal Transport Flows for 3D Point Cloud Generation
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Proposes not-so-optimal transport flow matching for 3D point cloud generation, using offline superset OT precomputation with online subsampling plus a hybrid coupling that blends OT with independent noise.
Problem
Generative modeling of 3D point clouds with flow matching: exact or minibatch OT couplings are too costly or ineffective for permutation-invariant, dense point clouds, and straightened OT flows are hard to learn at early timesteps.
Approach
Precompute an approximate OT between a dense point superset and a dense Gaussian noise superset offline (Hungarian for small sets, Wasserstein gradient flow / Sinkhorn for large), subsample coupled pairs online, and perturb the noise with a blending coefficient beta=0.2 so the learned vector field is less complex.
Key results
- With 100 inference steps, the hybrid coupling (beta=0.2) reaches 1-NNA-CD 0.5853 and 1-NNA-EMD 0.5741 on Chair, versus 0.7289 / 0.6647 for pure OT approximation (beta=0) and 0.5989 / 0.5869 for independent coupling.
- The method outperforms prior diffusion and flow baselines at around 10-20 steps, and reaches reasonable shape completion quality within five inference steps while other approaches need about 50.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| increase β from 0 to 0.001 (ablation) | Not-So-Optimal Transport Flow · ShapeNet Chair, 100 steps | 1-NNA-CD: 0.7289 -> 0.6918 | Helped |
| increase β from 0 to 0.01 (ablation) | Not-So-Optimal Transport Flow · ShapeNet Chair, 100 steps | 1-NNA-CD: 0.7289 -> 0.6223 | Helped |
| increase β from 0 to 0.1 (ablation) | Not-So-Optimal Transport Flow · ShapeNet Chair, 100 steps | 1-NNA-CD: 0.7289 -> 0.5968 | Helped |
| increase β from 0 to 0.2 (ablation) | Not-So-Optimal Transport Flow · ShapeNet Chair, 100 steps | 1-NNA-CD: 0.7289 -> 0.5853 | Helped |
| increase β from 0 to 0.5 (ablation) | Not-So-Optimal Transport Flow · ShapeNet Chair, 100 steps | 1-NNA-CD: 0.7289 -> 0.5861 | Helped |
| increase β from 0 to 1.0 (ablation) | Not-So-Optimal Transport Flow · ShapeNet Chair, 100 steps | 1-NNA-CD: 0.7289 -> 0.5989 | Helped |
| increase superset size M from 2048 to 5000 (ablation) | Not-So-Optimal Transport Flow · ShapeNet Chair, 100 steps | 1-NNA-CD: 0.6352 -> 0.5853 | Helped |
| increase superset size M from 2048 to 10000 (ablation) | Not-So-Optimal Transport Flow · ShapeNet Chair, 100 steps | 1-NNA-CD: 0.6352 -> 0.5853 | Helped |
| increase superset size M from 2048 to 20000 (ablation) | Not-So-Optimal Transport Flow · ShapeNet Chair, 100 steps | 1-NNA-CD: 0.6352 -> 0.5853 | Helped |
| increase superset size M from 2048 to 50000 (ablation) | Not-So-Optimal Transport Flow · ShapeNet Chair, 100 steps | 1-NNA-CD: 0.6352 -> 0.5921 | Helped |
| increase superset size M from 2048 to 100000 (ablation) | Not-So-Optimal Transport Flow · ShapeNet Chair, 100 steps | 1-NNA-CD: 0.6352 -> 0.5725 | Helped |
| increase superset size M from 2048 to 5000 (ablation) | Not-So-Optimal Transport Flow · ShapeNet Chair, 100 steps | 1-NNA-EMD: 0.6254 -> 0.5853 | Helped |
Surprising findings
- Pure OT approximation (beta=0) performs worse than independent coupling at 100 steps, showing that less-optimal couplings generate better samples.
- Minibatch OT gives roughly 6% cost reduction even at batch size 256, matching plain flow matching performance.
Limitations
- Does not handle rotational or other invariances present in larger datasets such as Objaverse.
- Only point coordinates are modeled; no colors or other attributes.
- Fixed resolution generation; the theoretical link between beta and model complexity is not established.
Experimental setup
Datasets: ShapeNet GenRe
Benchmarks: ShapeNet
Metrics: 1-NNA-CD 1-NNA-EMD CD EMD COV
Baselines: PVD LION PSF DiT-3D Equivariant OT flow matching Minibatch OT flow matching Independent coupling flow matching v-prediction diffusion
Builds on: flow matching conditional flow matching minibatch optimal transport equivariant OT flow matching rectified flow
Closest papers by meaning
- Diffusion Probabilistic Models for 3D Point Cloud Generation (CVPR 2021 · similarity 0.88)
- Rectified Point Flow: Generic Point Cloud Pose Estimation (NeurIPS 2025 · similarity 0.87)
- Optimal Flow Matching: Learning Straight Trajectories in Just One Step (NeurIPS 2024 · similarity 0.86)
- Accelerating 3D Molecule Generation via Jointly Geometric Optimal Transport (ICLR 2025 · similarity 0.86)
- SE(3)-bi-equivariant Transformers for Point Cloud Assembly (NeurIPS 2024 · similarity 0.86)
- PointInfinity: Resolution-Invariant Point Diffusion Models (CVPR 2024 · similarity 0.85)
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