Separating Intrinsic Ambiguity from Estimation Uncertainty in Deep Generative Models for Linear Inverse Problems

TL;DR

This paper introduces a structural decomposition method to distinguish intrinsic ambiguity from estimation uncertainty in deep generative models for inverse problems, enhancing interpretability and calibration.

Contribution

It presents a novel decomposition framework and calibration diagnostics for posterior uncertainty in inverse problems, validated on MRI and EEG data.

Findings

Decomposition isolates intrinsic ambiguity in posterior uncertainty.

Calibration diagnostics reveal failure modes hidden by reconstruction quality.

Validated approach on MRI and EEG inverse problems.

Abstract

Recently, deep generative models have been used for posterior inference in inverse problems, including high-stakes applications in medical imaging and scientific discovery, where the uncertainty of a prediction can matter as much as the prediction itself. However, posterior uncertainty is difficult to interpret because it can mix ambiguity inherent to the forward operator with uncertainty propagated through inference. We introduce a structural decomposition of posterior uncertainty that isolates intrinsic ambiguity. A cascade formulation makes this ambiguity accessible for calibration analysis, enabling qualitative diagnostics and simulation-based calibration tests that reveal failure modes that remain hidden when models are selected by reconstruction quality alone. We first validate the approach on a Gaussian example with analytical posterior structure, then illustrate the decomposition on accelerated magnetic resonance imaging (MRI), and finally apply the calibration diagnostics to electroencephalography (EEG) source imaging.