# Neural McKean-Vlasov Processes: Distributional Dependence in Diffusion Processes

arXiv: https://arxiv.org/abs/2404.09402 · HTML: https://mlsanity.com/paper/2404.09402/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 71 references that are in the map.
- First posted on arXiv 15 Apr 2024.

## Builds on (most cited first, 27 of 27)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [A Variational Perspective on Diffusion-Based Generative Models and Score Matching](https://mlsanity.com/paper/2106.02808/) (2021)
- [Sinkformers: Transformers with Doubly Stochastic Attention](https://mlsanity.com/paper/2110.11773/) (2021)
- [Human Trajectory Forecasting in Crowds: A Deep Learning Perspective](https://mlsanity.com/paper/2007.03639/) (2020)
- [A Machine Learning Framework for Solving High-Dimensional Mean Field Game and Mean Field Control Problems](https://mlsanity.com/paper/1912.01825/) (2019)
- [Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker-Planck Equation and Physics-informed Neural Networks](https://mlsanity.com/paper/2008.10653/) (2020)
- [Mean-Field Langevin Dynamics and Energy Landscape of Neural Networks](https://mlsanity.com/paper/1905.07769/) (2019)
- [Refining Deep Generative Models via Discriminator Gradient Flow](https://mlsanity.com/paper/2012.00780/) (2020)
- [Towards a mathematical theory of trajectory inference](https://mlsanity.com/paper/2102.09204/) (2021)
- [Trajectory Inference via Mean-field Langevin in Path Space](https://mlsanity.com/paper/2205.07146/) (2022)
- [Learning Mean-Field Equations from Particle Data Using WSINDy](https://mlsanity.com/paper/2110.07756/) (2021)
- [Identifying Latent Stochastic Differential Equations](https://mlsanity.com/paper/2007.06075/) (2020)
- [Dataset Dynamics via Gradient Flows in Probability Space](https://mlsanity.com/paper/2010.12760/) (2020)
- [Mean-field neural networks: learning mappings on Wasserstein space](https://mlsanity.com/paper/2210.15179/) (2022)
- [Learning High-Dimensional McKean-Vlasov Forward-Backward Stochastic Differential Equations with General Distribution Dependence](https://mlsanity.com/paper/2204.11924/) (2022)
- [On implicit regularization: Morse functions and applications to matrix factorization](https://mlsanity.com/paper/2001.04264/) (2020)
- [A case study on stochastic games on large graphs in mean field and sparse regimes](https://mlsanity.com/paper/2005.14102/) (2020)
- [Parameter Estimation for the McKean-Vlasov Stochastic Differential Equation](https://mlsanity.com/paper/2106.13751/) (2021)
- [Solving Fredholm Integral Equations of the First Kind via Wasserstein Gradient Flows](https://mlsanity.com/paper/2209.09936/) (2022)
- [Robust and Scalable SDE Learning: A Functional Perspective](https://mlsanity.com/paper/2110.05167/) (2021)
- [Inference and Sampling of Point Processes from Diffusion Excursions](https://mlsanity.com/paper/2306.00762/) (2023)

## Built on by (most cited first, 4 of 4)

- [Modeling Cell Dynamics and Interactions with Unbalanced Mean Field Schr"odinger Bridge](https://mlsanity.com/paper/2505.11197/) (2025)
- [Optimal Transportation by Orthogonal Coupling Dynamics](https://mlsanity.com/paper/2410.08060/) (2024)
- [Measure-to-measure Regression with Transformers](https://mlsanity.com/paper/2605.28075/) (2026)
- [Trading Devil Final: Backdoor attack via Stock market and Bayesian Optimization](https://mlsanity.com/paper/2407.14573/) (2024)

## Abstract (arXiv)

McKean-Vlasov stochastic differential equations (MV-SDEs) provide a mathematical description of the behavior of an infinite number of interacting particles by imposing a dependence on the particle density. As such, we study the influence of explicitly including distributional information in the parameterization of the SDE. We propose a series of semi-parametric methods for representing MV-SDEs, and corresponding estimators for inferring parameters from data based on the properties of the MV-SDE. We analyze the characteristics of the different architectures and estimators, and consider their applicability in relevant machine learning problems. We empirically compare the performance of the different architectures and estimators on real and synthetic datasets for time series and probabilistic modeling. The results suggest that explicitly including distributional dependence in the parameterization of the SDE is effective in modeling temporal data with interaction under an exchangeability assumption while maintaining strong performance for standard Ito-SDEs due to the richer class of probability flows associated with MV-SDEs.