Sampling from a probability distribution is a ubiquitous challenge in machine learning, ranging from generative AI to approximate Bayesian inference. This talk will show how to leverage low-precision compute to accelerate Markov chain Monte Carlo (MCMC) sampling with theoretical guarantees on the convergence. First, I will introduce a general and theoretically grounded framework to enable low-precision sampling, with applications to Stochastic Gradient Langevin Dynamics and Stochastic Gradient Hamiltonian Monte Carlo. Then I will present an approach for binary sampling---operating at 1-bit precision. Finally, I will show the experimental results of low-precision sampling on various deep learning tasks.