Towards Diffusion Posteriors for Scientific Inference: Challenges and Opportunities

Diffusion models have transformed generative AI, yet their potential role in scientific inference is only beginning to be realized. In this talk, I will outline a perspective on diffusion models as approximate posterior samplers, situating them within a broader research agenda on the statistical foundations of foundation models. I will begin by briefly discussing my prior work on calibration and ensemble methods for large language models, which illustrates how Bayesian ideas can improve the reliability of foundation models. I will then turn to diffusion models, reviewing their interpretation through the lens of optimal control and highlighting challenges that arise in small-data scientific settings, where informative priors and Bayesian adaptation become essential. The talk will conclude with open problems and potential projects—including anomaly-guided diffusion and Bayesian functional priors—intended to spark discussion and to connect with students interested in pursuing these ideas further.

(This talk is part of the weekly Machine Learning Lunch Meetings (MLLM), held every Tuesday from 12:15 to 1:15 p.m.  Professors from Computer Sciences, Statistics, ECE, the iSchool, and other departments will discuss their latest research in machine learning, covering both theory and applications. This is a great opportunity to network with faculty and fellow researchers, learn about cutting-edge research at our university, and foster new collaborations. For the talk schedule, please visit https://sites.google.com/view/wiscmllm/home. To receive future weekly talk announcements, please subscribe to our UW Google Group at https://groups.google.com/u/1/a/g-groups.wisc.edu/g/mllm.)