arXiv:2604.20301v1 Announce Type: new Abstract: We consider the problem of sampling from a probability distribution $\pi$. It is well known that this can be written as an optimisation problem over the space of probability distributions in which we aim to minimise the Kullback--Leibler divergence from $\pi$. We consider the effect of replacing $\pi$ with a sequence of moving targets $(\pi_t)_{t\ge0