Equilibrium Matching: Generative Modeling with Implicit Energy-Based Models
This provides a new paradigm for generative modeling with improved performance and flexibility for tasks like denoising and OOD detection, though it builds on existing energy-based and flow models.
The paper tackles generative modeling by introducing Equilibrium Matching (EqM), a framework that learns the equilibrium gradient of an implicit energy landscape, discarding time-conditional dynamics from diffusion and flow models, and achieves an FID of 1.90 on ImageNet 256x256.
We introduce 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 an 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.