Convex Potential Mirror Langevin Algorithm for Efficient Sampling of Energy-Based Models

Yang Zitao, Amin Ullah, Shuai Li, Li Fuxin, Jun Li

Keywords: mirror Langevin dynamics, efficient sampling, energy based models

TL;DR: We introduce a novel approach which leverages a convex potential for efficient sampling of EBMs.

Abstract: This paper introduces the Convex Potential Mirror Langevin Algorithm (CPMLA), a novel method to improve sampling efficiency for Energy-Based Models (EBMs). CPMLA uses mirror Langevin dynamics with a convex potential flow as a dynamic mirror map for EBM sampling. This dynamic mirror map enables targeted geometric exploration on the data manifold, accelerating convergence to the target distribution. Theoretical analysis proves that CPMLA achieves exponential convergence with vanishing bias under relaxed log-concave conditions, supporting its efficiency in adapting to complex data distributions. Experiments on benchmarks like CIFAR-10, SVHN, and CelebA demonstrate CPMLA's improved sampling quality and inference efficiency over existing techniques.

Primary Area: Deep learning (e.g., architectures, generative models, optimization for deep networks, foundation models, LLMs)

Submission Number: 7878