VOILA Lab @ GT / arXiv 2025

Towards Distribution-Shift Uncertainty
for Inverse Problems

A calibration-free, instance-level warning signal for when a generative prior is operating outside its training distribution.

Namhoon KimSara Fridovich-Keil

Georgia Institute of Technology · VOILA Lab

Paper PDF ↗arXiv ↗Code ↗
MNIST digit zero shown as in distribution and digits one through nine shown as out of distribution
Controlled distribution shift. A learned proximal network is trained only on digit “0”, then used for sparse-view CT reconstruction of all ten digits.
0only in-distribution class
1–9out-of-distribution classes
11 / 22 / 33CT projection views
10×random measurement repeats

Core idea

Turn measurement diversity into an uncertainty signal.

Instead of requiring a separate calibration dataset, reuse the measurements already available for the same object.

01

Subsample

Draw several random subsets of the available physical measurements.

→
02

Reconstruct

Apply the same pretrained generative prior to every subset.

→
03

Compare

Measure pixel-wise variation across the resulting reconstructions.

→
04

Warn

High instability flags likely distribution shift and hallucination risk.

Motivation

Strong priors need lightweight guardrails.

Generative priors can reconstruct useful images from dramatically fewer measurements, but their learned assumptions may fail silently when a new patient, scanner, or pathology differs from the training distribution.

We hypothesize that in-distribution targets remain stable when reconstructed from different random measurement subsets, while out-of-distribution targets vary more. That variation becomes an efficient, retraining-free uncertainty indicator for a single imaging instance.

Experiment

A sparse-view CT stress test.

Prior

Learned Proximal Network

An input-convex learned proximal operator supplies the data-driven image prior.

Train

MNIST “0” only

The prior never sees the remaining nine digit classes during training.

Measure

Fan-beam sparse CT

Reconstruction is tested at 11, 22, and 33 projection-angle budgets.

Evaluate

100 targets × 10 seeds

PSNR, SSIM, and reconstruction variance are compared per digit.

Visual evidence

OOD reconstructions move more when measurements change.

Mean sparse-view CT reconstructions for MNIST digits at three projection budgets
The in-distribution zero remains recognizable and consistent even at 11 views; OOD digits are pulled more strongly toward the learned prior.

Key result

Instability tracks distribution shift.

Average reconstruction standard deviation is lowest for the in-distribution digit “0” across all measurement budgets.

The gap is strongest with only 11 projection views—the regime where the learned prior has the greatest influence and distribution mismatch creates the most risk.

High cross-measurement variation → likely OOD
Mean standard deviation by digit for 11, 22, and 33 CT views
Instance-level uncertainty from reconstruction variation.

Scope

A promising guardrail, with honest limits.

Advantages

No calibration set and no retraining.

The indicator wraps around an existing reconstruction prior and uses only repeated measurement subsets.

Initial evidence

Clear behavior in a controlled CT setting.

MNIST makes training distribution and OOD classes explicit, revealing the mechanism cleanly.

Next step

Validate on clinically realistic shifts.

Future work should test diverse modalities, pathologies, priors, and statistically calibrated thresholds.

Citation

If this work is useful, please cite it.

BibTeX
@misc{kim2025distributionshift,
  title         = {Towards Distribution-Shift Uncertainty Estimation
                   for Inverse Problems with Generative Priors},
  author        = {Kim, Namhoon and Fridovich-Keil, Sara},
  year          = {2025},
  eprint        = {2510.10947},
  archivePrefix = {arXiv},
  primaryClass  = {cs.CV}
}