Rate-Distortion Theory by and for Energy-Based Models

In this work, we examine the relationship between rate-distortion theory and energy-based models (EBMs). We demonstrate that EBMs can be used to approximate the rate-distortion approaching posterior, as in the Blahut-Arimoto (BA) algorithm, and to solve batch denoising problems using the posterior distribution learned by EBMs. Our results highlight the potential of EBMs to enhance the efficiency of rate-distortion theory analysis and vice versa.