A Very Effective and Simple Diffusion Reconstruction for the Diluted Ising Model

Abstract: Diffusion-based generative models are machine learning models that use diffusion processes to learn the probability distribution of high-dimensional data. In recent years, they have become extremely successful in generating multimedia content. However, it is still unknown if such models can be used to generate high-quality datasets of physical models. In this work, we use a Landau-Ginzburg-like diffusion model to infer the distribution of a $2D$ bond-diluted Ising model. Our approach is simple and effective, and we show that the generated samples reproduce correctly the statistical and critical properties of the physical model.