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

Yang Zitao, Amin Ullah, Shuai Li, Fuxin Li, 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 designed to optimize sampling efficiency within Energy-Based Models (EBMs). CPMLA employs mirror Langevin dynamics in conjunction with convex potential flow as a dynamic mirror map for sampling in EBMs. By leveraging this dynamic mirror map, CPMLA enables targeted geometric exploration on the data manifold, enhancing the convergence process towards the target distribution. Theoretical analysis proves that CPMLA achieves exponential convergence with vanishing bias under relaxed log-concave conditions, supporting its efficiency and effectiveness in adapting to complex data distributions. Experimental results on established benchmarks like CIFAR-10, SVHN, and CelebA showcase CPMLA's enhanced sampling quality and inference efficiency compared to existing techniques.

Primary Area: generative models

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Submission Number: 2745