# Towards Distribution-Shift Uncertainty Estimation for Inverse Problems with Generative Priors

arXiv: https://arxiv.org/abs/2510.10947 · HTML: https://mlsanity.com/paper/2510.10947/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 28 references that are in the map.
- First posted on arXiv 13 Oct 2025.

## Builds on (most cited first, 13 of 13)

- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Image-to-Image Regression with Distribution-Free Uncertainty Quantification and Applications in Imaging](https://mlsanity.com/paper/2202.05265/) (2022)
- [On hallucinations in tomographic image reconstruction](https://mlsanity.com/paper/2012.00646/) (2020)
- [How to Trust Your Diffusion Model: A Convex Optimization Approach to Conformal Risk Control](https://mlsanity.com/paper/2302.03791/) (2023)
- [Conffusion: Confidence Intervals for Diffusion Models](https://mlsanity.com/paper/2211.09795/) (2022)
- [Generative Modeling in Sinogram Domain for Sparse-view CT Reconstruction](https://mlsanity.com/paper/2211.13926/) (2022)
- [What's in a Prior? Learned Proximal Networks for Inverse Problems](https://mlsanity.com/paper/2310.14344/) (2023)
- [Equivariant Bootstrapping for Uncertainty Quantification in Imaging Inverse Problems](https://mlsanity.com/paper/2310.11838/) (2023)
- [Denoising Score-Matching for Uncertainty Quantification in Inverse Problems](https://mlsanity.com/paper/2011.08698/) (2020)
- [Uncertainty Quantification for Forward and Inverse Problems of PDEs via Latent Global Evolution](https://mlsanity.com/paper/2402.08383/) (2024)
- [Task-Driven Uncertainty Quantification in Inverse Problems via Conformal Prediction](https://mlsanity.com/paper/2405.18527/) (2024)
- [Randomized Physics-Informed Machine Learning for Uncertainty Quantification in High-Dimensional Inverse Problems](https://mlsanity.com/paper/2312.06177/) (2023)

## Built on by (most cited first, 1 of 1)

- [Beyond Accuracy: Evaluating Posterior Fidelity of Diffusion Inverse Solvers](https://mlsanity.com/paper/2602.04189/) (2026)

## Abstract (arXiv)

Generative models have shown strong potential as data-driven priors for solving inverse problems such as reconstructing medical images from undersampled measurements. While these priors improve reconstruction quality with fewer measurements, they risk hallucinating features when test images lie outside the training distribution. Existing uncertainty quantification methods in this setting (i) require an in-distribution calibration dataset, which may not be available, (ii) provide heuristic rather than statistical estimates, or (iii) quantify uncertainty from model capacity or limited measurements rather than distribution shift. We propose an instance-level, calibration-free uncertainty indicator that is sensitive to distribution shift, requires no knowledge of the training distribution, and incurs no retraining cost. Our key hypothesis is that reconstructions of in-distribution images remain stable under random measurement variations, while reconstructions of out-of-distribution (OOD) images exhibit greater instability. We use this stability as a proxy for detecting distribution shift. Our proposed OOD indicator is efficiently computable for any computational imaging inverse problem; we demonstrate it on tomographic reconstruction of MNIST digits, where a learned proximal network trained only on digit "0" is evaluated on all ten digits. Reconstructions of OOD digits show higher variability and correspondingly higher reconstruction error, validating this indicator. These results suggest a deployment strategy that pairs generative priors with lightweight guardrails, enabling aggressive measurement reduction for in-distribution cases while automatically warning when priors are applied out of distribution.