Equilibrium Matching (raywang4.github.io)

Equilibrium Matching (EqM) is a new generative modeling framework that abandons the time-conditional, non-equilibrium dynamics used by diffusion and many flow models and instead learns the equilibrium gradient of an implicit energy landscape. Rather than simulating a noise-to-data trajectory, EqM performs optimization-based sampling at inference: images are produced by gradient descent on the learned energy with tunable step sizes, adaptive optimizers, and variable compute. The method is theoretically grounded to learn and sample from the data manifold, and it empirically outperforms prior diffusion/flow approaches — notably achieving an FID of 1.90 on ImageNet 256×256. The shift from time-conditional velocities to a single equilibrium landscape has two practical implications for the AI/ML community. First, sampling becomes an optimization problem, allowing flexible, compute-aware inference (early stopping, adaptive steps, alternative optimizers) and potentially tighter sample quality control. Second, EqM bridges flow models and energy-based models by unifying their perspectives into a single learned landscape, while naturally extending to tasks beyond unconditional generation such as partially-noised image denoising, OOD detection, and image composition. In short, EqM offers a simpler, more adaptable route to high-fidelity generative modeling with strong theoretical and empirical support.