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.

翻译：连续与离散状态空间中的扩散桥模型近来已成为生成建模领域的强大工具。本研究利用桥匹配模型的离散状态空间表述，解决了机器学习与信息论中的另一个重要问题：离散随机变量间互信息的估计。通过将互信息估计巧妙地构建为领域迁移问题，我们构建了适用于离散数据的离散桥互信息估计器，该估计器能够应对传统互信息估计方法在处理离散数据时面临的困难。我们在两种互信息估计场景中展示了所提估计器的性能：低维场景与基于图像的场景。