Equilibrium Matching: Generative Modeling with Implicit Energy-Based
  Models
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 256times256. 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.
68e42cbee4e093a7044e4c40
Runqian Wang
claimed_verified
2025-10-10T09:38:56.172Z
656fd5c7e542334e136d88f6
/avatars/56f960d6b0d64f1cbb7f9f5ba69995e1.svg
Ray Wang
user
raywang4
68e42cbee4e093a7044e4c41
Yilun Du
Equilibrium Matching: Generative Modeling with Implicit Energy-Based
  Models
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 256times256. 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.
Equilibrium Matching (EqM) is a generative modeling framework that learns an equilibrium gradient of an implicit energy landscape, enabling efficient sampling and outperforming traditional diffusion and flow models.
Equilibrium Matching EqM equilibrium dynamics diffusion models flow-based generative models implicit energy landscape gradient descent data manifold partially noised image denoising OOD detection image composition energy-based models