Field Matching: an Electrostatic Paradigm to Generate and Transfer Data

We propose Electrostatic Field Matching (EFM), a novel method that is suitable for both generative modelling 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. We then learn the capacitor's electrostatic field 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.

Modern AI systems that transform one image to another or generate images often rely on a class of generative models based on thermodynamics such as Diffusion Models. Despite producing high-quality samples these models are relatively slow, taking many steps during the inference. An alternative among the physics-inspired generative models is PFGM which uses the electrostatic theory. However it is suited only for unconditional generation tasks.Our research focuses on a new physics-based methodology called Electrostatic field matching (EFM). Contrary to PFGM it is well-suited for unpaired translation as well as image generation tasks. The methodology uses the idea of multi-dimensional capacitor with equally charged plates. The movement along the corresponding electrostatic field lines transforms one data distribution into another.Provided the ground-truth field in the capacitor our approach accelerates the inference process. This opens the door to making powerful AI-based image editing tools much more practical and accessible in everyday applications.