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

2026-05-14

AI Summary

This work addresses the challenge of interpreting predictive uncertainty in posterior inference with deep generative models for linear inverse problems, where uncertainty conflates the intrinsic ambiguity inherent in the forward operator with estimation uncertainty introduced by the inference process. To resolve this, the authors propose a structured decomposition approach that explicitly disentangles posterior uncertainty into these two distinct components through cascaded modeling, enabling analytically tractable and calibratable characterization of intrinsic ambiguity. This method constitutes the first structural separation of posterior uncertainty in deep generative models, revealing failure modes invisible to reconstruction quality alone. Validation on Gaussian analytic cases, accelerated magnetic resonance imaging, and electroencephalographic source imaging demonstrates that the approach effectively isolates and calibrates intrinsic ambiguity, facilitating qualitative diagnosis and simulation-based calibration tests.

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.

Problem

• intrinsic ambiguity
• estimation uncertainty
• posterior inference
• inverse problems
• uncertainty decomposition

Innovation

• intrinsic ambiguity
• estimation uncertainty
• posterior decomposition
• simulation-based calibration
• deep generative models