Diffusion bridge models in both continuous and discrete state spaces have recently become powerful tools in the field of generative modeling. In this work, we leverage the discrete state space formulation of bridge matching models to address another important problem in machine learning and information theory: the estimation of the mutual information (MI) between discrete random variables. By neatly framing MI estimation as a domain transfer problem, we construct a Discrete Bridge Mutual Information (DBMI) estimator suitable for discrete data, which poses difficulties for conventional MI estimators. We showcase the performance of our estimator on two MI estimation settings: low-dimensional and image-based.
@article{arxiv.2602.08894,
title = {Discrete Bridges for Mutual Information Estimation},
author = {Iryna Zabarianska and Sergei Kholkin and Grigoriy Ksenofontov and Ivan Butakov and Alexander Korotin},
journal= {arXiv preprint arXiv:2602.08894},
year = {2026}
}