Yale Institute for Foundations of Data Science Common Area, Kline Tower 13th Floor, Common Area 1307, New Haven, CT 06511

**Title: **Using Log Concavity and Differential Expressions to Compute Score Diffusions

**Abstract:** Reverse diffusions based on the score provide a method to generate samples from difficult densities not well suited to classical MCMC methods. Core to implementing these reverse SDE is the computation of the score. Here we discuss two useful techniques to compute the score. First, when is the score expressible as the expectation of a log concave distribution, thus can be efficiently estimated empirically by MCMC estimates? Second, knowing the score at one point in time, can we use that information to compute that score at a different time in the SDE by setting up a differential expression d/dt (score) = F(score) relating the change in the score to a function of its current value.