# Field Matching: an Electrostatic Paradigm to Generate and Transfer Data

arXiv: https://arxiv.org/abs/2502.02367 · HTML: https://mlsanity.com/paper/2502.02367/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 29 references that are in the map.
- First posted on arXiv 4 Feb 2025.

## Builds on (most cited first, 18 of 18)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [How to Train Your Energy-Based Models](https://mlsanity.com/paper/2101.03288/) (2021)
- [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (2023)
- [Dual Diffusion Implicit Bridges for Image-to-Image Translation](https://mlsanity.com/paper/2203.08382/) (2022)
- [Equivariant flow matching](https://mlsanity.com/paper/2306.15030/) (2023)
- [Poisson Flow Generative Models](https://mlsanity.com/paper/2209.11178/) (2022)
- [Diffusion Bridge Mixture Transports, Schr"odinger Bridge Problems and Generative Modeling](https://mlsanity.com/paper/2304.00917/) (2023)
- [PFGM++: Unlocking the Potential of Physics-Inspired Generative Models](https://mlsanity.com/paper/2302.04265/) (2023)
- [Entropic Neural Optimal Transport via Diffusion Processes](https://mlsanity.com/paper/2211.01156/) (2022)
- [Schr"odinger Bridge Flow for Unpaired Data Translation](https://mlsanity.com/paper/2409.09347/) (2024)
- [Reflected Flow Matching](https://mlsanity.com/paper/2405.16577/) (2024)

## Built on by (most cited first, 6 of 6)

- [Interaction Field Matching: Overcoming Limitations of Electrostatic Models](https://mlsanity.com/paper/2506.02950/) (2025)
- [Overclocking Electrostatic Generative Models](https://mlsanity.com/paper/2509.22454/) (2025)
- [Data Generation without Function Estimation](https://mlsanity.com/paper/2507.08239/) (2025)
- [Unlocking the Duality between Flow and Field Matching](https://mlsanity.com/paper/2602.02261/) (2026)
- [Electric Currents for Discrete Data Generation](https://mlsanity.com/paper/2509.23825/) (2025)
- [Bridge Graphical Models: Coupling, Projection, and Current-Preserving Dynamics for Generative Modeling](https://mlsanity.com/paper/2608.19144/) (2026)

## Abstract (arXiv)

We propose Electrostatic Field Matching (EFM), a novel method that is suitable for both generative modeling and distribution transfer tasks. Our approach is inspired by the physics of an electrical capacitor. We place source and target distributions on the capacitor plates and assign them positive and negative charges, respectively. Then we learn the electrostatic field of the capacitor using a neural network approximator. To map the distributions to each other, we start at one plate of the capacitor and move the samples along the learned electrostatic field lines until they reach the other plate. We theoretically justify that this approach provably yields the distribution transfer. In practice, we demonstrate the performance of our EFM in toy and image data experiments. Our code is available at https://github.com/justkolesov/FieldMatching