Abstract: Priors are essential for solving ill-posed imaging problems, affecting both the quality and uncertainty of reconstructed images. Diffusion models can express complex image priors, but recent approaches extending diffusion models to inverse problems do not capture a true Bayesian posterior of images conditioned on measurements. We propose turning score-based diffusion models into principled image priors (“score-based priors”) for analyzing an image posterior. In particular, we appeal to the log-probability function of a score-based diffusion model as a standalone prior function that can be plugged into any established algorithm for Bayesian inference. We demonstrate this with a variational-inference approach for sampling from an approximate image posterior. Our approach is hyperparameter-free, and we show that it results in more-accurate posteriors than other diffusion-model-based methods. To incorporate physics knowledge in the prior, we propose neural approximate mirror maps for constrained diffusion models. Our method results in diffusion models that satisfy a prescribed constraint (e.g., following a PDE) by construction. These constrained diffusion models can then be used as physics-informed priors for computational imaging.

Bio: Berthy Feng is a sixth-year PhD student working with Prof. Katie Bouman at Caltech. She earned her bachelor’s degree in computer science summa cum laude from Princeton University. Her research interests include computational imaging, computer vision, and generative modeling. She is currently interested in incorporating data-driven and physics-based knowledge into principled computational imaging approaches. She has received the Kortschak Scholarship and NSF GRFP Fellowship.