Prior laundering: learned priors with inherited, undetectable overconfidence

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.