We build on the view of the Exact Renormalization Group (ERG) as an instantiation of Optimal Transport described by a functional convection-diffusion equation. We provide a new information theoretic perspective for understanding the ERG through the intermediary of Bayesian Statistical Inference. This connection is facilitated by the Dynamical Bayesian Inference scheme, which encodes Bayesian inference in the form of a one parameter family of probability distributions solving an integro-differential equation derived from Bayes' law. In this note, we demonstrate how the Dynamical Bayesian Inference equation is, itself, equivalent to a diffusion equation which we dub Bayesian Diffusion. Identifying the features that define Bayesian Diffusion, and mapping them onto the features that define the ERG, we obtain a dictionary outlining how renormalization can be understood as the inverse of statistical inference.

翻译：我们基于将精确重整化群（ERG）视为最优传输的一种实例的观点，该观点由泛函对流-扩散方程描述。通过贝叶斯统计推断这一中介，我们为理解ERG提供了新的信息论视角。这种联系由动态贝叶斯推断方案促成，该方案将贝叶斯推断编码为求解由贝叶斯定律导出的积分-微分方程的一族单参数概率分布。本文中，我们演示了动态贝叶斯推断方程本身等价于一个扩散方程，我们将其称为贝叶斯扩散。通过识别定义贝叶斯扩散的特征，并将其映射到定义ERG的特征，我们得到了一份词典，概述了重整化如何被理解为统计推断的逆过程。