Is your uncertainty map wrong, or is its target? Exact diagnostics for the Tweedie diagonal, and a gradient-free alternative
Vicent Ribas, Anna Oliveras Tous
Abstract
A diffusion model can predict a follow-up medical scan from a baseline, but a clinician needs a per-voxel map of where that prediction can be trusted. Many such maps approximate the diagonal of the Tweedie posterior covariance, and are evaluated against another approximation of it, so whether the estimator or the target limits them is unclear. We compute the exact diagonal on six checkpoints across fourteen model-corpus conditions. Hutchinson at M=200 tracks it at rank agreement of at least 0.92 everywhere, yet in four of the fourteen the exact diagonal is anti-correlated with the denoising error, reaching -0.13, so a faithful estimator reproduces that reversal. All four are real-image conditions; on the models' own samples the reversal does not appear, so evaluating on generated samples flatters this family. What limits these maps is the target, not the estimator. We then introduce Tweedie Probe-Tangent (T-PT), a gradient-free residual probe that corrupts one model-supported prediction repeatedly and measures the voxel-wise variance of the denoiser's response. T-PT reads a different functional of the same Jacobian, and its exact second-order form ranks with the diagonal wherever the diagonal reverses; at thirty probes it returns a map too unstable to reproduce that ranking, while Hutchinson at M=5 already reproduces it, so T-PT there is not evidence against the reversal. We offer it as an instrument, not a better approximation. On brain MRI at full resolution, where every Jacobian-based estimator we test runs out of memory, T-PT leads a twenty-chain Monte-Carlo ensemble on five of eight endpoints inside tissue and trails it on none, at 16x fewer network evaluations; over the whole volume the ensemble leads, and fifty chains close the tissue gap. On lung CT the ensemble is ahead throughout. Both lose most of their discrimination where the change is, which remains open.