mlsanityData to 14 Oct 2026

Score-based Transport Modeling for Mean-Field Fokker-Planck Equations

arXiv 2305.03729 ↗First posted 21 Apr 2023math.NA cs.LG cs.NAcited by 14

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Abstract (arXiv)

We use the score-based transport modeling method to solve the mean-field Fokker-Planck equations, which we call MSBTM. We establish an upper bound on the time derivative of the Kullback-Leibler (KL) divergence to MSBTM numerical estimation from the exact solution, thus validates the MSBTM approach. Besides, we provide an error analysis for the algorithm. In numerical experiments, we study two types of mean-field Fokker-Planck equation and their corresponding dynamics of particles in interacting systems. The MSBTM algorithm is numerically validated through qualitative and quantitative comparison between the MSBTM solutions, the results of integrating the associated stochastic differential equation and the analytical solutions if available.

Key facts. Cited by 14 papers in the map (data through 14 Oct 2026). Builds on 4 of its 15 references that are in the map. First posted on arXiv 21 Apr 2023.

Builds on

4 of 15 references.

References · 4

  1. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  2. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  3. 2022Probability flow solution of the Fokker-Planck equationcited by 47
  4. 2022Self-Consistency of the Fokker-Planck Equationcited by 18

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 7; 2025: 3; 2026: 4.

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  1. 2024Accelerating Diffusion Models with Parallel Sampling: Inference at Sub-Linear Time Complexitycited by 42
  2. 2025Modeling Cell Dynamics and Interactions with Unbalanced Mean Field Schr"odinger Bridgecited by 12
  3. 2024What's the score? Automated Denoising Score Matching for Nonlinear Diffusionscited by 7
  4. 2024Score-based Neural Ordinary Differential Equations for Computing Mean Field Control Problemscited by 7
  5. 2024A score-based particle method for homogeneous Landau equationcited by 6
  6. 2025DiScoFormer: Plug-In Density and Score Estimation with Transformerscited by 6
  7. 2024Transport based particle methods for the Fokker-Planck-Landau equationcited by 4
  8. 2025Score-based deterministic density samplingcited by 4
  9. 2024HJ-sampler: A Bayesian sampler for inverse problems of a stochastic process by leveraging Hamilton-Jacobi PDEs and score-based generative modelscited by 2
  10. 2026Generative Path-Finding Method for Wasserstein Gradient Flowcited by 2
  11. 2026Alternating Diffusion for Proximal Sampling with Zeroth Order Queriescited by 1
  12. 2024Mean-field Chaos Diffusion Modelscited by 0
2 more
  1. 2026A Neural Score-Based Particle Method for the Vlasov-Maxwell-Landau Systemcited by 0
  2. 2026Mean-Field Diffuser: Scaling Offline MARL to Thousands of Agentscited by 0