Abstract
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.
Abstract (translated)
我们介绍了一种新的生成模型框架——平衡匹配（EqM），该框架从平衡动力学的角度构建。与传统的扩散和基于流的生成模型不同，EqM摒弃了非平衡的时间条件动力学，并学习隐式能量景观的平衡梯度。通过这种方法，在推理过程中可以采用基于优化的采样过程，即通过对学习到的能量景观进行可调整步长、自适应优化器及计算量的梯度下降来获取样本。 实验结果表明，EqM在生成性能上超过了扩散和流模型，在ImageNet 256×256数据集上的FID（Frechet Inception Distance）得分为1.90。从理论上讲，EqM被证明可以从数据流形中学习并进行采样。除生成任务外，EqM还是一个灵活的框架，能够自然地处理部分噪声图像去噪、异常检测和图像合成等任务。 通过用统一的能量景观取代时间条件速度，EqM建立了流模型与能量模型之间更紧密的联系，并提供了一条简单且基于优化推断的方法路径。
URL
https://arxiv.org/abs/2510.02300
