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

arXiv: https://arxiv.org/abs/2305.03729 · HTML: https://mlsanity.com/paper/2305.03729/

## 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 (most cited first, 4 of 4)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Probability flow solution of the Fokker-Planck equation](https://mlsanity.com/paper/2206.04642/) (2022)
- [Self-Consistency of the Fokker-Planck Equation](https://mlsanity.com/paper/2206.00860/) (2022)

## Built on by (most cited first, 14 of 14)

- [Accelerating Diffusion Models with Parallel Sampling: Inference at Sub-Linear Time Complexity](https://mlsanity.com/paper/2405.15986/) (2024)
- [Modeling Cell Dynamics and Interactions with Unbalanced Mean Field Schr"odinger Bridge](https://mlsanity.com/paper/2505.11197/) (2025)
- [What's the score? Automated Denoising Score Matching for Nonlinear Diffusions](https://mlsanity.com/paper/2407.07998/) (2024)
- [Score-based Neural Ordinary Differential Equations for Computing Mean Field Control Problems](https://mlsanity.com/paper/2409.16471/) (2024)
- [A score-based particle method for homogeneous Landau equation](https://mlsanity.com/paper/2405.05187/) (2024)
- [DiScoFormer: Plug-In Density and Score Estimation with Transformers](https://mlsanity.com/paper/2511.05924/) (2025)
- [Transport based particle methods for the Fokker-Planck-Landau equation](https://mlsanity.com/paper/2405.10392/) (2024)
- [Score-based deterministic density sampling](https://mlsanity.com/paper/2504.18130/) (2025)
- [HJ-sampler: A Bayesian sampler for inverse problems of a stochastic process by leveraging Hamilton-Jacobi PDEs and score-based generative models](https://mlsanity.com/paper/2409.09614/) (2024)
- [Generative Path-Finding Method for Wasserstein Gradient Flow](https://mlsanity.com/paper/2604.11519/) (2026)
- [Alternating Diffusion for Proximal Sampling with Zeroth Order Queries](https://mlsanity.com/paper/2603.19633/) (2026)
- [Mean-field Chaos Diffusion Models](https://mlsanity.com/paper/2406.05396/) (2024)
- [A Neural Score-Based Particle Method for the Vlasov-Maxwell-Landau System](https://mlsanity.com/paper/2603.25832/) (2026)
- [Mean-Field Diffuser: Scaling Offline MARL to Thousands of Agents](https://mlsanity.com/paper/2605.30190/) (2026)

## 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.