mlsanityData to 7 Oct 2026

Image-to-Image Regression with Distribution-Free Uncertainty Quantification and Applications in Imaging

arXiv 2202.05265 ↗First posted 10 Feb 2022cs.LG cs.CV eess.IVcited by 107

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Abstract (arXiv)

Image-to-image regression is an important learning task, used frequently in biological imaging. Current algorithms, however, do not generally offer statistical guarantees that protect against a model's mistakes and hallucinations. To address this, we develop uncertainty quantification techniques with rigorous statistical guarantees for image-to-image regression problems. In particular, we show how to derive uncertainty intervals around each pixel that are guaranteed to contain the true value with a user-specified confidence probability. Our methods work in conjunction with any base machine learning model, such as a neural network, and endow it with formal mathematical guarantees -- regardless of the true unknown data distribution or choice of model. Furthermore, they are simple to implement and computationally inexpensive. We evaluate our procedure on three image-to-image regression tasks: quantitative phase microscopy, accelerated magnetic resonance imaging, and super-resolution transmission electron microscopy of a Drosophila melanogaster brain.

Key facts. Cited by 107 papers in the map (data through 7 Oct 2026). Builds on 31 of its 82 references that are in the map. First posted on arXiv 10 Feb 2022.

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31 of 82 references.

References · 31

  1. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  2. 2016Image-to-Image Translation with Conditional Adversarial Networkscited by 4,510
  3. 2015Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learningcited by 4,416
  4. 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,888
  5. 2016Perceptual Losses for Real-Time Style Transfer and Super-Resolutioncited by 2,678
  6. 2016Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Networkcited by 1,898
  7. 2018Attention U-Net: Learning Where to Look for the Pancreascited by 1,420
  8. 2018On the Spectral Bias of Neural Networkscited by 1,321
  9. 2014Image Super-Resolution Using Deep Convolutional Networkscited by 1,218
  10. 2016Colorful Image Colorizationcited by 1,113
  11. 2021A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantificationcited by 777
  12. 2017Unpaired Image-to-Image Translation using Cycle-Consistent Adversarial Networkscited by 707
19 more
  1. 2019Conformalized Quantile Regressioncited by 620
  2. 2018fastMRI: An Open Dataset and Benchmarks for Accelerated MRIcited by 464
  3. 2019Deep Ensembles: A Loss Landscape Perspectivecited by 438
  4. 2020Classification with Valid and Adaptive Coveragecited by 390
  5. 2020Uncertainty Sets for Image Classifiers using Conformal Predictioncited by 365
  6. 2021Distribution-Free, Risk-Controlling Prediction Setscited by 278
  7. 2016Least Ambiguous Set-Valued Classifiers with Bounded Error Levelscited by 270
  8. 2021Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Controlcited by 256
  9. 2017Neural Style Transfer: A Reviewcited by 199
  10. 2018Uncertainty Estimates and Multi-Hypotheses Networks for Optical Flowcited by 135
  11. 2019Deep Learning on Image Denoising: An overviewcited by 128
  12. 2013A Conformal Prediction Approach to Explore Functional Datacited by 85
  13. 2021Fair Conformal Predictors for Applications in Medical Imagingcited by 74
  14. 2021Improving Conditional Coverage via Orthogonal Quantile Regressioncited by 48
  15. 2018Cautious Deep Learningcited by 35
  16. 2019Quantifying Point-Prediction Uncertainty in Neural Networks via Residual Estimation with an I/O Kernelcited by 19
  17. 2021Private Prediction Setscited by 16
  18. 2020Interval Neural Networks: Uncertainty Scorescited by 14
  19. 2018Quantitative Phase Imaging and Artificial Intelligence: A Reviewcited by 13

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 14; 2023: 24; 2024: 26; 2025: 20; 2026: 23.

107 papers.

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  1. 2022Confident Adaptive Language Modelingcited by 297
  2. 2022Conformal Risk Controlcited by 290
  3. 2023Class-Conditional Conformal Prediction with Many Classescited by 109
  4. 2023Improved Online Conformal Prediction via Strongly Adaptive Online Learningcited by 76
  5. 2022Training Uncertainty-Aware Classifiers with Conformalized Deep Learningcited by 62
  6. 2024Estimating Epistemic and Aleatoric Uncertainty with a Single Modelcited by 52
  7. 2023How to Trust Your Diffusion Model: A Convex Optimization Approach to Conformal Risk Controlcited by 50
  8. 2023Federated Conformal Predictors for Distributed Uncertainty Quantificationcited by 46
  9. 2022Achieving Risk Control in Online Learning Settingscited by 38
  10. 2022Improving Trustworthiness of AI Disease Severity Rating in Medical Imaging with Ordinal Conformal Prediction Setscited by 38
  11. 2024Conformal Prediction Sets Improve Human Decision Makingcited by 35
  12. 2022Predictive Inference with Feature Conformal Predictioncited by 33
38 more
  1. 2022Conffusion: Confidence Intervals for Diffusion Modelscited by 33
  2. 2023On the Posterior Distribution in Denoising: Application to Uncertainty Quantificationcited by 31
  3. 2023Principal Uncertainty Quantification with Spatial Correlation for Image Restoration Problemscited by 28
  4. 2024Fast yet Safe: Early-Exiting with Risk Controlcited by 27
  5. 2022Conformal Prediction with Temporal Quantile Adjustmentscited by 25
  6. 2023Conformal Contextual Robust Optimizationcited by 25
  7. 2024Calibrated Uncertainty Quantification for Operator Learning via Conformal Predictioncited by 25
  8. 2024Conformal Prediction: A Data Perspectivecited by 25
  9. 2023What's in a Prior? Learned Proximal Networks for Inverse Problemscited by 24
  10. 2024Adaptive Bounding Box Uncertainties via Two-Step Conformal Predictioncited by 23
  11. 2022Semantic uncertainty intervals for disentangled latent spacescited by 22
  12. 2025Generative Uncertainty in Diffusion Modelscited by 20
  13. 2022Integrative conformal p-values for powerful out-of-distribution testing with labeled outlierscited by 19
  14. 2024Conformal Semantic Image Segmentation: Post-hoc Quantification of Predictive Uncertaintycited by 19
  15. 2023Equivariant Bootstrapping for Uncertainty Quantification in Imaging Inverse Problemscited by 17
  16. 2023Uncertainty Quantification via Neural Posterior Principal Componentscited by 16
  17. 2023Safe Perception-Based Control under Stochastic Sensor Uncertainty using Conformal Predictioncited by 15
  18. 2023Fortuna: A Library for Uncertainty Quantification in Deep Learningcited by 14
  19. 2023Kandinsky Conformal Prediction: Efficient Calibration of Image Segmentation Algorithmscited by 14
  20. 2024Active, anytime-valid risk controlling prediction setscited by 14
  21. 2022Posterior-Variance-Based Error Quantification for Inverse Problems in Imagingcited by 12
  22. 2023From Posterior Sampling to Meaningful Diversity in Image Restorationcited by 12
  23. 2024Looks Too Good To Be True: An Information-Theoretic Analysis of Hallucinations in Generative Restoration Modelscited by 12
  24. 2022Conformal Methods for Quantifying Uncertainty in Spatiotemporal Data: A Surveycited by 11
  25. 2023Empirical Validation of Conformal Prediction for Trustworthy Skin Lesions Classificationcited by 11
  26. 2025Uncertainty Quantification for Machine Learning in Healthcare: A Surveycited by 11
  27. 2023Uncertainty Estimation and Propagation in Accelerated MRI Reconstructioncited by 10
  28. 2022Conformal Prediction Intervals with Temporal Dependencecited by 9
  29. 2024Implicit Neural Representations for Robust Joint Sparse-View CT Reconstructioncited by 9
  30. 2024Uncertainty-Aware PPG-2-ECG for Enhanced Cardiovascular Diagnosis using Diffusion Modelscited by 8
  31. 2024Task-Driven Uncertainty Quantification in Inverse Problems via Conformal Predictioncited by 8
  32. 2024Conformal Performance Range Prediction for Segmentation Output Quality Controlcited by 8
  33. 2025Direct Prediction Set Minimization via Bilevel Conformal Classifier Trainingcited by 8
  34. 2023Digital staining in optical microscopy using deep learning -- a reviewcited by 7
  35. 2025Conformal Risk Control for Semantic Uncertainty Quantification in Computed Tomographycited by 7
  36. 2025Uncertainty-Aware Online Extrinsic Calibration: A Conformal Prediction Approachcited by 6
  37. 2022What's Behind the Mask: Estimating Uncertainty in Image-to-Image Problemscited by 5
  38. 2023dugMatting: Decomposed-Uncertainty-Guided Mattingcited by 4

50 most cited of 107 All 107 (JSON)