Abstract: Diffusion models can learn strong image priors and use them to solve inverse problems. However, standard methods come with many challenges in medical and scientific applications: they are computationally expensive, they require lots of training data, and they may not be robust to distribution shifts between the training data and the test data. This talk will describe methods for tackling these challenges, focusing on medical imaging inverse problems like MRI and low-dose Xray CT image reconstruction. Work with Jason Hu, Bowen Song, Xiaojian Xu and Liyue Shen.