Field Matching: an Electrostatic Paradigm to Generate and Transfer Data

TL;DR

This paper introduces Electrostatic Field Matching (EFM), a physics-inspired method for generative modeling and distribution transfer that learns electrostatic fields to map data distributions effectively.

Contribution

EFM is a novel electrostatics-inspired approach that theoretically guarantees distribution transfer and demonstrates practical effectiveness in toy and image data experiments.

Findings

Proves distribution transfer theoretically

Performs well on toy data

Effective in image data tasks

Abstract

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