mlsanityData to 7 Oct 2026

Mean-field Chaos Diffusion Models

arXiv 2406.05396 ↗First posted 8 Jun 2024cs.LG cs.AI cs.CVcited by 0

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

In this paper, we introduce a new class of score-based generative models (SGMs) designed to handle high-cardinality data distributions by leveraging concepts from mean-field theory. We present mean-field chaos diffusion models (MF-CDMs), which address the curse of dimensionality inherent in high-cardinality data by utilizing the propagation of chaos property of interacting particles. By treating high-cardinality data as a large stochastic system of interacting particles, we develop a novel score-matching method for infinite-dimensional chaotic particle systems and propose an approximation scheme that employs a subdivision strategy for efficient training. Our theoretical and empirical results demonstrate the scalability and effectiveness of MF-CDMs for managing large high-cardinality data structures, such as 3D point clouds.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 37 of its 94 references that are in the map. First posted on arXiv 8 Jun 2024.

Builds on

37 of 94 references.

Closest ancestors · 11

Same direction, newest first

  1. 2023Multilevel Diffusion: Infinite Dimensional Score-Based Diffusion Models for Image Generation8 Mar
  2. 2022Diffusion Generative Models in Infinite Dimensions1 Dec
  3. 2022Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions3 Nov
  4. 2022Convergence of denoising diffusion models under the manifold hypothesis10 Aug
  5. 2022Maximum Likelihood Training for Score-Based Diffusion ODEs by High-Order Denoising Score Matching16 Jun
  6. 2022Convergence for score-based generative modeling with polynomial complexity13 Jun
  7. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  8. 2021Score-Based Generative Modeling with Critically-Damped Langevin Diffusion14 Dec
  9. 2021Maximum Likelihood Training of Score-Based Diffusion Models22 Jan
  10. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  11. 2020Denoising Diffusion Implicit Models6 Oct

Other references · 26

  1. 2017PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Spacecited by 4,384
  2. 2017Progressive Growing of GANs for Improved Quality, Stability, and Variationcited by 2,967
  3. 2015ShapeNet: An Information-Rich 3D Model Repositorycited by 2,880
  4. 2018Dynamic Graph CNN for Learning on Point Cloudscited by 2,220
  5. 2015Variational Inference with Normalizing Flowscited by 2,161
  6. 2021Diffusion Probabilistic Models for 3D Point Cloud Generationcited by 734
  7. 2022Equivariant Diffusion for Molecule Generation in 3Dcited by 666
  8. 2021CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputationcited by 577
  9. 2022LION: Latent Point Diffusion Models for 3D Shape Generationcited by 552
  10. 20213D Shape Generation and Completion through Point-Voxel Diffusioncited by 516
  11. 2019PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flowscited by 487
  12. 2022Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equationscited by 273
14 more
  1. 2020Permutation Invariant Graph Generation via Score-Based Generative Modelingcited by 263
  2. 2021Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theorycited by 216
  3. 2019Generalized Sliced Wasserstein Distancescited by 205
  4. 2023Geometric Latent Diffusion Models for 3D Molecule Generationcited by 185
  5. 2019A Machine Learning Framework for Solving High-Dimensional Mean Field Game and Mean Field Control Problemscited by 95
  6. 2021SetVAE: Learning Hierarchical Composition for Generative Modeling of Set-Structured Datacited by 78
  7. 2019Convergence Analysis of Machine Learning Algorithms for the Numerical Solution of Mean Field Control and Games: II -- The Finite Horizon Casecited by 34
  8. 2023MedShapeNet -- A Large-Scale Dataset of 3D Medical Shapes for Computer Visioncited by 31
  9. 2016Mean Field Game of Controls and An Application To Trade Crowdingcited by 22
  10. 2019Numerical resolution of McKean-Vlasov FBSDEs using neural networkscited by 19
  11. 2022Learning High-Dimensional McKean-Vlasov Forward-Backward Stochastic Differential Equations with General Distribution Dependencecited by 13
  12. 2023Score-based Transport Modeling for Mean-Field Fokker-Planck Equationscited by 13
  13. 2020Ito's formula for flows of measures on semimartingalescited by 6
  14. 2015On The Interpretation Of The Master Equationcited by 1

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