Prior laundering: learned priors with inherited, undetectable overconfidence
Authors: Ali Siahkoohi, Sina Alemohammad
Organizations: Department of Computer Science University of Central Florida · Department of Electrical and Computer Engineering The University of Texas at Austin
Learned generative priors now supply the regularization in ill-posed imaging inverse problems, and the uncertainty read from their posterior samples is taken as evidence earned from data. When examples of the true image are scarce, as in seismic and medical imaging, the widely adopted recourse is to train such a prior not on truths but on an archive of past reconstructions---prior laundering. We show that the uncertainty it then reports can be overconfident, and that no measurement-side check can reveal it. On the directions a forward operator leaves unresolved, this prior reports not what the data support but the assumption built into the older reconstruction method. More specifically, when the archive holds posterior samples, its population law---averaged over the measurements---is exactly the old regularizer advanced a single expectation--maximization step, frozen on the operator's blind subspace. The freeze leaves no signature in the data. Two truths differing only there induce identical data laws, so no goodness-of-fit test separates them, and self-consistency diagnostics, simulation-based calibration among them, pass whatever the prior believes. In the more realistic case, where the archive keeps a single-best reconstruction rather than posterior samples, the blind credible interval collapses to zero width. We prove these statements and demonstrate the inherited overconfidence on deployed seismic and groundwater imaging against a truth-trained control. We recommend reporting which directions the operator resolves---separating the confidence the data support from belief inherited through the pipeline.
Generative (diffusion) priors demonstrate remarkable performance in addressing inverse problems in imaging. Yet, for scientific and medical imaging, it is crucial that reconstruction techniques remain stable and reliable under imperfect settings. Typical definitions of stability encompass the notion of ''convergent regularization'', robustness to out-of-distribution data, and to inaccuracies in the forward operator or noise model. We evaluate these properties numerically. Furthermore, we benchmark generative approaches against modern optimization-based methods inspired by the widely used variational techniques. Our results give insights for which settings and applications generative priors can deliver state-of-the-art reconstructions, and on those in which they fall short or may even be problematic.
Alexander Denker, Johannes Hertrich, Sebastian Neumayer
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.
Generative models are increasingly used as priors for inverse problems, but their ability to produce realistic images creates a basic trust problem: a plausible reconstruction may be supported by the measurements, or it may be filled in by the prior along unobserved directions. This distinction is especially important in medical imaging, where acquisition operators are designed under scan-time, dose, and calibration constraints. We study generative inverse problems from a measurement-geometry perspective. The central question is whether a fixed measurement operator can distinguish nearby images that are plausible under the generative prior, and whether this relationship can guide better measurements. We introduce a local measurement-manifold compatibility measure that quantifies how well the operator observes prior-relevant tangent directions. Under local regularity assumptions, we prove that this quantity controls the stable part of the reconstruction error, while the generative prior controls off-manifold drift. This worst-direction certificate motivates practical fixed and sequential acquisition rules based on overall local volume preservation, including a posterior-cloud design that adapts measurements at test time without training a sampling policy. Across row-sampling, tomographic, and MR acquisition settings, the proposed scores predict failure modes, explain measurement-induced hallucinations, and guide better sampling. In fastMRI Cartesian sampling, posterior-cloud measurement design improves over strong non-learned ACS-preserving baselines, including variable-density and Poisson-like masks.