Separating Intrinsic Ambiguity from Estimation Uncertainty in Deep Generative Models for Linear Inverse Problems
For practitioners in medical imaging and scientific discovery, this work provides a diagnostic tool to assess and interpret uncertainty in deep generative models, revealing failure modes that reconstruction quality alone misses.
The paper introduces a structural decomposition of posterior uncertainty in deep generative models for linear inverse problems, isolating intrinsic ambiguity from estimation uncertainty. The method enables calibration diagnostics that reveal failure modes hidden by reconstruction quality metrics, validated on Gaussian examples, accelerated MRI, and EEG source imaging.
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.