Benchmarking Uncertainty Quantification of Plug-and-Play Diffusion Priors for Inverse Problems Solving

2026-02-04

AI Summary

Existing evaluations of Plug-and-Play Diffusion Prior (PnPDP) solvers focus solely on point estimation accuracy, overlooking the stochastic nature of their outputs and the inherent uncertainty of inverse problems, thereby failing to capture the true posterior distribution. This work presents the first uncertainty quantification (UQ)-oriented evaluation framework for PnPDP solvers, introducing a UQ-driven categorization scheme to systematically analyze their behavior at the distributional level. Through toy-model simulations, multiple PnPDP methods, comprehensive UQ metrics, and real-world scientific datasets, experiments validate the efficacy of the proposed classification and reveal distinct uncertainty characteristics across different solvers. The study establishes a novel evaluation paradigm that enables more reliable reconstructions in scientific inverse problems by explicitly accounting for uncertainty.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Uncertainty Representations
• Planning, Routing, and Scheduling: Planning under Uncertainty

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• User Modeling, Personalization and Recommendation: User model development and evaluation
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Plug-and-play diffusion priors (PnPDP) have become a powerful paradigm for solving inverse problems in scientific and engineering domains. Yet, current evaluations of reconstruction quality emphasize point-estimate accuracy metrics on a single sample, which do not reflect the stochastic nature of PnPDP solvers and the intrinsic uncertainty of inverse problems, critical for scientific tasks. This creates a fundamental mismatch: in inverse problems, the desired output is typically a posterior distribution and most PnPDP solvers induce a distribution over reconstructions, but existing benchmarks only evaluate a single reconstruction, ignoring distributional characterization such as uncertainty. To address this gap, we conduct a systematic study to benchmark the uncertainty quantification (UQ) of existing diffusion inverse solvers. Specifically, we design a rigorous toy model simulation to evaluate the uncertainty behavior of various PnPDP solvers, and propose a UQ-driven categorization. Through extensive experiments on toy simulations and diverse real-world scientific inverse problems, we observe uncertainty behaviors consistent with our taxonomy and theoretical justification, providing new insights for evaluating and understanding the uncertainty for PnPDPs.

Problem

• uncertainty quantification
• inverse problems
• plug-and-play diffusion priors
• posterior distribution
• benchmarking

Innovation

• uncertainty quantification
• plug-and-play diffusion priors
• inverse problems
• posterior distribution
• benchmarking