Title: Equilibrium Matching: Generative Modeling with Implicit Energy-Based Models
Primary area: generative models
Keywords: Energy-Based Model, Flow Matching, Diffusion, Generative Model

Abstract: We introduce $\textit{Equilibrium Matching}$ (EqM), a generative modeling framework built from an equilibrium dynamics perspective. EqM discards the non-equilibrium, time-conditional dynamics in traditional diffusion and flow-based generative models and instead learns the equilibrium gradient of an implicit energy landscape. Through this approach, we can adopt an optimization-based sampling process at inference time, where samples are obtained by gradient descent on the learned landscape with adjustable step sizes, adaptive optimizers, and adaptive compute. EqM surpasses the generation performance of diffusion/flow models empirically, achieving a FID of 1.90 on ImageNet 256$\times$256. EqM is also theoretically justified to learn and sample from the data manifold. Beyond generation, EqM is a flexible framework that naturally handles tasks including partially noised image denoising, OOD detection, and image composition. By replacing time-conditional velocities with a unified equilibrium landscape, EqM offers a tighter bridge between flow and energy-based models and a simple route to optimization-driven inference.

TL;DR: An equilibrium-based generative model that supports optimization-driven sampling, exceeds Diffusion/Flow in generation quality, and offers flexibility for downstream tasks