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Hallucinations are an inescapable consequence of solving inverse problemswith deep neural networks. The expressiveness of recent generative models isthe reason why they can yield results far superior to conventionalregularizers; it can also lead to realistic-looking but incorrect features,potentially undermining the trust in important aspects of the reconstruction.We present a practical and computationally efficient method to determine, whichregions in the solutions of inverse problems with data-driven priors are proneto hallucinations. By computing the diagonal elements of the Fisher informationmatrix of the likelihood and the data-driven prior separately, we can flagregions where the information is prior-dominated. Our diagnostic can directlybe compared to the reconstructed solutions and enables users to decide ifmeasurements in such regions are robust for their application. Our methodscales linearly with the number of parameters and is thus applicable inhigh-dimensional settings, allowing it to be rolled out broadly for thelarge-volume data products of future wide-field surveys.

Spotting Hallucinations in Inverse Problems with Data-Driven Priors