Score-Based Diffusion Models as Principled Priors for Inverse Imaging

Figure 1 . A score-based prior is a hyperparameter-free, probabilistic prior that is also expressive and data-driven. Paired with a set of measurements, the prior can be used for principled inference of a full posterior. In this example, a score-based prior was trained on face images ("Prior" shows samples from the learned prior). The inverse problem is interferometic imaging of a synthetic black hole. We simulated interferometric measurements from the actual telescope array used to capture the first black-hole image [17] and sampled images from the posterior via variational inference. From the top to bottom row, the posterior stably moves away from the prior given more constraining measurements. With measurements from only three telescopes, the posterior shows strong influence from the prior and contains images resembling faces that are brighter on the left half. As more telescopes (measurements) are added, the posterior reveals the ring-like structure of the underlying image. Our framework finds the proper relative strengths of the prior and measurements automatically.