Sampling from high-dimensional distributions is a notoriously difficult problem, especially when the distribution isn't logconcave or has multiple modes. While Markov Chain Monte Carlo is a powerful approach, new tools are much needed. I will present a different class of algorithms related to diffusions method in generative AI, and to the stochastic localization technique in probability theory. I will use this approach to establish new sampling guarantees in a problems in Bayesian estimation and statistical physics.