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Mean-field Chaos Diffusion Models
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Proposes mean-field chaos diffusion models (MF-CDMs), a score-based generative model for high-cardinality unstructured data (point clouds) that treats data as an interacting particle system, using mean-field score matching and a particle-subdivision training scheme.
Problem
Score-based generative models scale poorly in dimensionality and cardinality when modeling high-cardinality unstructured data such as large point clouds; existing point-cloud diffusion models rely on rigid localization modules that cap the number of points.
Approach
Model a data instance as an empirical measure of N exchangeable interacting particles, derive a mean-field score-matching objective on Wasserstein space (via Itô-Wentzell-Lions), use propagation of chaos so that a finite number of particles suffices, and grow particle count during sampling via a branching function with a subdivided (piecewise) training objective.
Key results
- On ShapeNet with 1e4-point clouds, MF-CDMs reach EMD 2.627 and CD 1.877 (x1e2), beating the best baseline DPM (3.058 / 3.269).
- On MedShapeNet (2e4 points), MF-CDMs reach EMD 4.046 and CD 2.764 versus DPM's 6.139 / 3.248.
- On the synthetic benchmark at N=1e5, MF-CDMs achieve the lowest sliced W2 (3.167 at d=5, 4.059 at d=32), but at N=1e3 LION and DPM are better.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use MF-CDMs instead of LION | Synthetic data generation · Synthetic (N=10^3, d=5) | sliced 2-Wasserstein distance: 1.841 -> 2.017 | Hurt |
| Use MF-CDMs instead of LION | Synthetic data generation · Synthetic (N=10^3, d=32) | sliced 2-Wasserstein distance: 1.919 -> 2.413 | Hurt |
| Use MF-CDMs instead of LION | Synthetic data generation · Synthetic (N=10^5, d=5) | sliced 2-Wasserstein distance: 5.234 -> 3.167 | Helped |
| Use MF-CDMs instead of LION | Synthetic data generation · Synthetic (N=10^5, d=32) | sliced 2-Wasserstein distance: 6.105 -> 4.059 | Helped |
| Use MF-CDMs instead of DPM | 3D point-cloud generation · ShapeNet | EMD: 3.058 -> 2.627 | Helped |
| Use MF-CDMs instead of PVD | 3D point-cloud generation · ShapeNet | CD: 3.032 -> 1.877 | Helped |
| Use MF-CDMs instead of DPM | 3D point-cloud generation · MedShapeNet | EMD: 6.139 -> 4.046 | Helped |
| Use MF-CDMs instead of DPM | 3D point-cloud generation · MedShapeNet | CD: 3.248 -> 2.764 | Helped |
Surprising findings
- At small cardinality (N=1e3), MF-CDMs underperform LION and DPM on the synthetic benchmark, which the authors attribute to excessive complexity of the mean-field modeling.
Limitations
- Underperforms existing methods at small cardinality (N=1e3) on the synthetic benchmark.
- Theoretical results rely on strong assumptions (Lipschitz, uniform convexity, reducibility of score networks) and are stated informally.
- Evaluated only on synthetic data and two point-cloud datasets.
Experimental setup
Datasets: ShapeNet MedShapeNet synthetic Gaussian mixture
Benchmarks: ShapeNet MedShapeNet synthetic Gaussian mixture
Metrics: sliced 2-Wasserstein distance MMD-EMD MMD-CD
Baselines: VP-SDE CLD DPM LION PVD
Builds on: score-based generative models variance-preserving SDE Critical Langevin Dynamics LION
Closest papers by meaning
- Improved Particle Approximation Error for Mean Field Neural Networks (NeurIPS 2024 · similarity 0.85)
- Adapting to Unknown Low-Dimensional Structures in Score-Based Diffusion Models (NeurIPS 2024 · similarity 0.85)
- Propagation of Chaos for Mean-Field Langevin Dynamics and its Application to Model Ensemble (ICML 2025 · similarity 0.85)
- Universal Approximation of Mean-Field Models via Transformers (ICML 2025 · similarity 0.84)
- Generative Fractional Diffusion Models (NeurIPS 2024 · similarity 0.84)
- Unified Framework for Diffusion Generative Models in SO(3): Applications in Computer Vision and Astrophysics (AAAI 2024 · similarity 0.84)
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