# QUTCC: Quantile Uncertainty Training and Conformal Calibration for Imaging Inverse Problems

arXiv: https://arxiv.org/abs/2507.14760 · HTML: https://mlsanity.com/paper/2507.14760/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 54 of its 72 references that are in the map.
- First posted on arXiv 19 Jul 2025.

## Builds on (most cited first, 30 of 54)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Attention U-Net: Learning Where to Look for the Pancreas](https://mlsanity.com/paper/1804.03999/) (2018)
- [Deep Bayesian Active Learning with Image Data](https://mlsanity.com/paper/1703.02910/) (2017)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Distributional Reinforcement Learning with Quantile Regression](https://mlsanity.com/paper/1710.10044/) (2017)
- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [Implicit Quantile Networks for Distributional Reinforcement Learning](https://mlsanity.com/paper/1806.06923/) (2018)
- [Uncertainty Sets for Image Classifiers using Conformal Prediction](https://mlsanity.com/paper/2009.14193/) (2020)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [Distribution-Free, Risk-Controlling Prediction Sets](https://mlsanity.com/paper/2101.02703/) (2021)
- [Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control](https://mlsanity.com/paper/2110.01052/) (2021)
- [Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisons](https://mlsanity.com/paper/2201.07766/) (2022)
- [Conformal Language Modeling](https://mlsanity.com/paper/2306.10193/) (2023)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [Bayesian Convolutional Neural Networks with Bernoulli Approximate Variational Inference](https://mlsanity.com/paper/1506.02158/) (2015)
- [Uncertainty Estimates and Multi-Hypotheses Networks for Optical Flow](https://mlsanity.com/paper/1802.07095/) (2018)
- [Score-Based Diffusion Models as Principled Priors for Inverse Imaging](https://mlsanity.com/paper/2304.11751/) (2023)
- [Safe Planning in Dynamic Environments using Conformal Prediction](https://mlsanity.com/paper/2210.10254/) (2022)
- [Class-Conditional Conformal Prediction with Many Classes](https://mlsanity.com/paper/2306.09335/) (2023)
- [Image-to-Image Regression with Distribution-Free Uncertainty Quantification and Applications in Imaging](https://mlsanity.com/paper/2202.05265/) (2022)
- [Learning in an Uncertain World: Representing Ambiguity Through Multiple Hypotheses](https://mlsanity.com/paper/1612.00197/) (2016)
- [Beyond Pinball Loss: Quantile Methods for Calibrated Uncertainty Quantification](https://mlsanity.com/paper/2011.09588/) (2020)
- [Sequential Predictive Conformal Inference for Time Series](https://mlsanity.com/paper/2212.03463/) (2022)
- [A Poisson-Gaussian Denoising Dataset with Real Fluorescence Microscopy Images](https://mlsanity.com/paper/1812.10366/) (2018)

## Abstract (arXiv)

While deep learning offers tremendous promise for scientific and medical imaging, any failures and hallucinations (predictions that do not coincide with reality) are hard to pinpoint and can have serious downstream consequences. Uncertainty estimation techniques, such as conformal prediction, can help by predicting statistically valid error bars for a model's prediction. However, popular conformal prediction methods were not designed for high-dimensional image-valued problems and do not take into account spatial correlations within an image during conformal calibration, resulting in larger-than-necessary uncertainty intervals. We propose a practical simultaneous quantile regression method that enables non-linear, spatially-adaptive scaling during conformal calibration. Our method, QUTCC uses a U-Net architecture with a quantile embedding to learn a full conditional quantile distribution during training, and then leverages this non-linear, learned function for spatially-adaptive conformal calibration. At test time, our method can efficiently estimate uncertainty intervals with pixel-marginal coverage guarantees. In addition, QUTCC can also predict pixel-wise conditional probability density estimates without any built-in distributional assumptions. We evaluate our method on several denoising problems, accelerated magnetic resonance imaging, and quantitative phase microscopy. Our method consistently produces tighter uncertainty intervals than prior conformal methods at the same coverage level, can predict plausible conditional distributions for different tasks, and in some cases, high-uncertainty regions can help us locate hallucinations in a model's prediction.