After a brief introduction to standard tools in optimal transport and to entropic regularization, we present how to use the tool of entropic regularization to design numerical schemes to learn the diffusion and drift coefficients. Our proposal relies on renormalizing the entropy of a discretized process. We formulate a time-discrete minimization problem for which we show a sort of gamma-convergence result to a continuous functional that makes appear a Bregman divergence associated to the entropy on gaussian processes.

We finish with some numerical simulations illustrating our main result.