Equilibrium Matching (EqM) is a generative modeling framework built from the perspective of equilibrium dynamics. It abandons the non-equilibrium, time-conditional dynamics of conventional diffusion- and flow-based generative models and instead learns the equilibrium gradient of an implicit energy landscape. This approach allows for an optimization-based sampling process at inference time, using variable step sizes, an adaptive optimizer, and adaptive operations to obtain samples via gradient descent over the learned landscape. EqM achieves a FID of 1.90 on ImageNet 256×256, outperforming the generative performance of diffusion/flow models. Furthermore, EqM is theoretically justified by learning and sampling from a data manifold. Beyond generative models, EqM is a flexible framework that naturally addresses tasks such as partially noisy image denoising, OOD detection, and image synthesis. By replacing time-conditional velocities with an integrated equilibrium landscape, EqM provides a closer connection between flow and energy-based models, offering a straightforward path to optimization-based inference.
