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 empirical distributions, important questions remain on the reliability and trustworthiness of these sampling procedures for their responsible use in critical scenarios. Conformal prediction is a modern tool to construct finite-sample, distribution-free uncertainty guarantees for any black-box predictor. In this work, we focus on image-to-image regression tasks and we present a generalization of the Risk-Controlling Prediction Sets (RCPS) procedure, that we term $K$-RCPS, which allows to $(i)$ provide entrywise calibrated intervals for future samples of any diffusion model, and $(ii)$ control a certain notion of risk with respect to a ground truth image with minimal mean interval length. Differently from existing conformal risk control procedures, ours relies on a novel convex optimization approach that allows for multidimensional risk control while provably minimizing the mean interval length. 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 the abdomen, demonstrating state of the art performance.

翻译：基于分数的生成建模（俗称扩散模型）在多个重要领域和任务中持续受到广泛关注。尽管这些模型能够从经验分布中生成高质量且多样化的样本，但在关键场景中负责任地使用这些采样过程时，其可靠性和可信度仍存在重要问题。共形预测是一种现代工具，可为任何黑箱预测器提供有限样本、无分布假设的不确定性保证。本文聚焦于图像到图像的回归任务，提出了一种名为$K$-RCPS的风险控制预测集（RCPS）程序的泛化方法，该方法能够：（i）为任何扩散模型的未来样本提供逐元素校准的区间；（ii）在保证最小区间长度的前提下，控制相对于真实图像的特定风险度量。与现有共形风险控制程序不同，本文方法基于一种新颖的凸优化方法，可在多维风险控制的同时以可证明方式最小化平均区间长度。我们通过两个真实世界的图像去噪问题——自然人脸图像以及腹部计算机断层扫描（CT）影像——验证了该方法，展示了其最先进的性能。