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Score-based generative modeling, informally referred to as diffusion models,continue to grow in popularity across several important domains and tasks.While they provide high-quality and diverse samples from empiricaldistributions, important questions remain on the reliability andtrustworthiness of these sampling procedures for their responsible use incritical scenarios. Conformal prediction is a modern tool to constructfinite-sample, distribution-free uncertainty guarantees for any black-boxpredictor. In this work, we focus on image-to-image regression tasks and wepresent a generalization of the Risk-Controlling Prediction Sets (RCPS)procedure, that we term $K$-RCPS, which allows to $(i)$ provide entrywisecalibrated intervals for future samples of any diffusion model, and $(ii)$control a certain notion of risk with respect to a ground truth image withminimal mean interval length. Differently from existing conformal risk controlprocedures, ours relies on a novel convex optimization approach that allows formultidimensional risk control while provably minimizing the mean intervallength. We illustrate our approach on two real-world image denoising problems:on natural images of faces as well as on computed tomography (CT) scans of theabdomen, demonstrating state of the art performance.

How to Trust Your Diffusion Model: A Convex Optimization Approach to Conformal Risk Control