When Minimizing the Measurement Residual Selects the Wrong Guidance Strength

When a diffusion or flow prior solves an inverse problem, its trajectory is pulled toward the measurement at every step, and the strength of that pull is a free parameter. Reported scores tune it against reference images; without one, the natural choice is the strength that fits the measurement best. We measure when that choice fails. Under released CIFAR-10 and face diffusion priors, the measurement residual falls as the strength grows, all the way to the strongest setting on every CIFAR-10 blur and mask. Behind binary masks, that setting is also the most accurate. Where the operator measures some directions only weakly, near its noise floor, selecting on the residual fits noise in those directions and gives up 0.099 to 0.514 in correlation and 0.039 to 0.118 under a latent prior. The fraction of such directions, the weak band, is read from the operator and the noise level before any prior is fitted. It tracks the cost. On 10 accelerated-MRI and compressed-sensing forward operators added afterward, it separated the costly operators, which gave up 0.184 to 0.475, from the rest, which gave up at most 0.016. The discrepancy principle, which stops when the residual reaches the noise level, gives up at most 0.028 where the band is not empty. Projected SURE, which estimates the error in all but the weakest directions, gives up at most 0.001 across all 28 operators. Both require the noise level. Most of the loss belongs to the correction rule that replaces the current estimate; the gradient rule stops where its step begins to overshoot. In the real-data task of predicting the brain's response to stimulation with a conditional flow prior, the residual falls the same way, but neither criterion's cost can be distinguished from zero.