# Task-Driven Uncertainty Quantification in Inverse Problems via Conformal Prediction

arXiv: https://arxiv.org/abs/2405.18527 · HTML: https://mlsanity.com/paper/2405.18527/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 64 references that are in the map.
- First posted on arXiv 28 May 2024.

## Builds on (most cited first, 30 of 39)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Image Quality Assessment: Unifying Structure and Texture Similarity](https://mlsanity.com/paper/2004.07728/) (2020)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [Uncertainty Sets for Image Classifiers using Conformal Prediction](https://mlsanity.com/paper/2009.14193/) (2020)
- [Score-based diffusion models for accelerated MRI](https://mlsanity.com/paper/2110.05243/) (2021)
- [Distribution-Free, Risk-Controlling Prediction Sets](https://mlsanity.com/paper/2101.02703/) (2021)
- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [Analyzing Inverse Problems with Invertible Neural Networks](https://mlsanity.com/paper/1808.04730/) (2018)
- [End-to-End Variational Networks for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2004.06688/) (2020)
- [Image-to-Image Regression with Distribution-Free Uncertainty Quantification and Applications in Imaging](https://mlsanity.com/paper/2202.05265/) (2022)
- [Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreau](https://mlsanity.com/paper/1612.07471/) (2016)
- [Deep Learning Methods for Parallel Magnetic Resonance Image Reconstruction](https://mlsanity.com/paper/1904.01112/) (2019)
- [Deep Bayesian Inversion](https://mlsanity.com/paper/1811.05910/) (2018)
- [Physics-Driven Deep Learning for Computational Magnetic Resonance Imaging](https://mlsanity.com/paper/2203.12215/) (2022)
- [How to Trust Your Diffusion Model: A Convex Optimization Approach to Conformal Risk Control](https://mlsanity.com/paper/2302.03791/) (2023)
- [Uncertainty Quantification in Deep MRI Reconstruction](https://mlsanity.com/paper/1901.11228/) (2019)
- [Improving Trustworthiness of AI Disease Severity Rating in Medical Imaging with Ordinal Conformal Prediction Sets](https://mlsanity.com/paper/2207.02238/) (2022)
- [Conffusion: Confidence Intervals for Diffusion Models](https://mlsanity.com/paper/2211.09795/) (2022)
- [Bayesian Uncertainty Estimation of Learned Variational MRI Reconstruction](https://mlsanity.com/paper/2102.06665/) (2021)

## Built on by (most cited first, 8 of 8)

- [Conformal Bounds on Full-Reference Image Quality for Imaging Inverse Problems](https://mlsanity.com/paper/2505.09528/) (2025)
- [Towards Distribution-Shift Uncertainty Estimation for Inverse Problems with Generative Priors](https://mlsanity.com/paper/2510.10947/) (2025)
- [Minimax Multi-Target Conformal Prediction with Applications to Imaging Inverse Problems](https://mlsanity.com/paper/2511.13533/) (2025)
- [Evaluating structural uncertainty in accelerated MRI: are voxelwise measures useful surrogates?](https://mlsanity.com/paper/2503.10527/) (2025)
- [QUTCC: Quantile Uncertainty Training and Conformal Calibration for Imaging Inverse Problems](https://mlsanity.com/paper/2507.14760/) (2025)
- [KLIP: localized distribution shift detection via KL-divergence with diffusion priors in Inverse Problems](https://mlsanity.com/paper/2605.31596/) (2026)
- [SafeRestore: Detector-Relative Risk Certificates for Selective Industrial Image Restoration](https://mlsanity.com/paper/2609.03475/) (2026)
- [How Many Posterior Samples? Calibrated Stopping for Adaptive Sensing](https://mlsanity.com/paper/2609.21813/) (2026)

## Abstract (arXiv)

In imaging inverse problems, one seeks to recover an image from missing/corrupted measurements. Because such problems are ill-posed, there is great motivation to quantify the uncertainty induced by the measurement-and-recovery process. Motivated by applications where the recovered image is used for a downstream task, such as soft-output classification, we propose a task-centered approach to uncertainty quantification. In particular, we use conformal prediction to construct an interval that is guaranteed to contain the task output from the true image up to a user-specified probability, and we use the width of that interval to quantify the uncertainty contributed by measurement-and-recovery. For posterior-sampling-based image recovery, we construct locally adaptive prediction intervals. Furthermore, we propose to collect measurements over multiple rounds, stopping as soon as the task uncertainty falls below an acceptable level. We demonstrate our methodology on accelerated magnetic resonance imaging (MRI): https://github.com/jwen307/TaskUQ.