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

Zitao Yang (Fudan University) · Amin Ullah (Boeing BR&T) · Shuai Li (Shanxi University) · Fuxin Li (Oregon State University) · Jun Li (Technische Universität München)
complex data distributionsconvergenceconvex potential flowconvex potential mirror langevin algorithmdata manifolddynamic mirror mapenergy-based modelsexponential convergencegeometric explorationinference efficiencylog-concave conditionsmirror langevin dynamicssampling efficiencysampling qualitytarget distributionvanishing bias

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.