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In this work we present a new method for the estimation of Mutual Information(MI) between random variables. Our approach is based on an originalinterpretation of the Girsanov theorem, which allows us to use score-baseddiffusion models to estimate the Kullback Leibler divergence between twodensities as a difference between their score functions. As a by-product, ourmethod also enables the estimation of the entropy of random variables. Armedwith such building blocks, we present a general recipe to measure MI, whichunfolds in two directions: one uses conditional diffusion process, whereas theother uses joint diffusion processes that allow simultaneous modelling of tworandom variables. Our results, which derive from a thorough experimentalprotocol over all the variants of our approach, indicate that our method ismore accurate than the main alternatives from the literature, especially forchallenging distributions. Furthermore, our methods pass MI self-consistencytests, including data processing and additivity under independence, whichinstead are a pain-point of existing methods.

MINDE: Mutual Information Neural Diffusion Estimation