Preconditioned Subspace Langevin Monte Carlo

The Langevin diffusion and its variants have become a fundamental object of study in modern machine learning. On the mathematical side, these diffusions have a deep connection to Wasserstein gradient flows. This connection has been used to study their convergence and to consequently develop new and more efficient diffusions. Practically, discretizations of the Langevin diffusion are highly scalable for generating samples from complex, high-dimensional target distribution. Many examples of the successful application of these methods exist, including denoising diffusion models [1, 2], characterization of complex Bayesian posteriors [3], and differential privacy mechanisms [4].