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

TL;DR

This paper introduces a convex optimization-based conformal prediction method for diffusion models, enabling calibrated uncertainty intervals and risk control in image-to-image regression tasks, with demonstrated state-of-the-art results.

Contribution

It generalizes the RCPS procedure to multidimensional risk control using convex optimization, providing calibrated intervals and minimal mean length for diffusion model predictions.

Findings

Achieves state-of-the-art uncertainty quantification in image denoising.

Provides calibrated, risk-controlled prediction intervals for diffusion models.

Demonstrates effectiveness on face images and CT scans.

Abstract

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.