PriorShare: Benchmarking and Understanding Hallucination in Diffusion-Based Scientific Imaging

In scientific imaging, reference images are often unavailable, so a small measurement residual is the main check on a reconstruction from a reusable diffusion prior. The residual is insensitive to errors in source components that the measurement leaves unresolved, which we study as hallucinations. We introduce the prior share, the fraction of source energy in the directions a given operator and noise level leave unobservable. It is computed from the operator and representative source data without a test reference, and unlike operator-only summaries it accounts for how source energy is distributed across unresolved directions. We build the PriorShare benchmark around three new settings: weak-lensing mass mapping, galaxy PSF deconvolution, and reconstruction from real wide-field fluorescence observations. With multi-coil MRI and black-hole imaging added, it evaluates nine diffusion-prior solvers. In a controlled study that varies only the operator, agreement between residual and PSNR rankings decreases as the share grows. At a share of 72%, one solver reaches a relative residual of $0.6\%$ while $99.95\%$ of its squared reconstruction error lies in the discarded directions, mostly in the unmeasured mean level. In the scientific settings, four of nine solvers on BioSR and five on Galaxy incur larger squared error in the unresolved components than zero filling. On noiseless galaxy deconvolution, an untuned inverse without a learned prior outperforms all nine solvers in PSNR and SSIM. PriorShare thus reports, beside data fit and reference fidelity, how much source energy a residual cannot check.