Modern Sampling Paradigms: from Posterior Sampling to Generative AI

Sampling from a target distribution is a recurring theme in statistics and generative artificial intelligence (AI). In Bayesian statistics, posterior sampling offers a flexible inferential framework, enabling uncertainty quantification, probabilistic prediction, as well as the estimation of intractable quantities. In generative AI, sampling aims to generate unseen instances that emulate a target population, such as the natural distributions of texts, images, and molecules.
In this talk, I will present my works on designing provably efficient sampling algorithms, addressing challenges in both statistics and generative AI. (1) In the first part, I will focus on posterior sampling for Bayes sparse regression. In general, such posteriors are high-dimensional and contain many modes, making them challenging to sample from. To address this, we develop a novel sampling algorithm based on decomposing the target posterior into a log-concave mixture of simple distributions, reducing sampling from a complex distribution to sampling from a tractable log-concave one. We establish provable guarantees for our method in a challenging regime that was previously intractable. (2) In the second part, I will describe a training-free acceleration method for diffusion models, which are deep generative models that underpin cutting-edge applications such as AlphaFold, DALL-E and Sora. Our approach is simple to implement, wraps around any pre-trained diffusion model, and comes with a provable convergence rate that strengthens prior theoretical results. We demonstrate the effectiveness of our method on several real-world image generation tasks.
Lastly, I will outline my vision for bridging the fields of statistics and generative AI, exploring how insights from one domain can drive progress in the other.