# Cycle Consistency-based Uncertainty Quantification of Neural Networks in Inverse Imaging Problems

arXiv: https://arxiv.org/abs/2305.12852 · HTML: https://mlsanity.com/paper/2305.12852/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 58 references that are in the map.
- First posted on arXiv 22 May 2023.

## Builds on (most cited first, 30 of 38)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks](https://mlsanity.com/paper/1809.00219/) (2018)
- [Real-ESRGAN: Training Real-World Blind Super-Resolution with Pure Synthetic Data](https://mlsanity.com/paper/2107.10833/) (2021)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [Deep Multi-scale Convolutional Neural Network for Dynamic Scene Deblurring](https://mlsanity.com/paper/1612.02177/) (2016)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [A Survey of Deep Learning Techniques for Autonomous Driving](https://mlsanity.com/paper/1910.07738/) (2019)
- [Adversarial Attacks on Neural Network Policies](https://mlsanity.com/paper/1702.02284/) (2017)
- [Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks](https://mlsanity.com/paper/1906.04893/) (2019)
- [Unsolved Problems in ML Safety](https://mlsanity.com/paper/2109.13916/) (2021)
- [A Probabilistic U-Net for Segmentation of Ambiguous Images](https://mlsanity.com/paper/1806.05034/) (2018)
- [Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification](https://mlsanity.com/paper/1801.06879/) (2018)
- [Deep Learning on Image Denoising: An overview](https://mlsanity.com/paper/1912.13171/) (2019)
- [A Study and Comparison of Human and Deep Learning Recognition Performance Under Visual Distortions](https://mlsanity.com/paper/1705.02498/) (2017)
- [Lipschitz constant estimation of Neural Networks via sparse polynomial optimization](https://mlsanity.com/paper/2004.08688/) (2020)
- [Intriguing Findings of Frequency Selection for Image Deblurring](https://mlsanity.com/paper/2111.11745/) (2021)
- [Deep learning-based virtual histology staining using auto-fluorescence of label-free tissue](https://mlsanity.com/paper/1803.11293/) (2018)
- [Uncertainty-Informed Deep Learning Models Enable High-Confidence Predictions for Digital Histopathology](https://mlsanity.com/paper/2204.04516/) (2022)
- [Bayesian Triplet Loss: Uncertainty Quantification in Image Retrieval](https://mlsanity.com/paper/2011.12663/) (2020)
- [Digital synthesis of histological stains using micro-structured and multiplexed virtual staining of label-free tissue](https://mlsanity.com/paper/2001.07267/) (2020)
- [Reliable deep-learning-based phase imaging with uncertainty quantification](https://mlsanity.com/paper/1901.02038/) (2019)

## Built on by (most cited first, 4 of 4)

- [A robust and scalable framework for hallucination detection in virtual tissue staining and digital pathology](https://mlsanity.com/paper/2404.18458/) (2024)
- [Neural Network-Based Processing and Reconstruction of Compromised Biophotonic Image Data](https://mlsanity.com/paper/2403.14324/) (2024)
- [Hybrid Neural World Models](https://mlsanity.com/paper/2605.28317/) (2026)
- [Round-Trip Consistency: Bidirectional Diffusion Models Can Predict Their Own Rollout Errors](https://mlsanity.com/paper/2608.00675/) (2026)

## Abstract (arXiv)

Uncertainty estimation is critical for numerous applications of deep neural networks and draws growing attention from researchers. Here, we demonstrate an uncertainty quantification approach for deep neural networks used in inverse problems based on cycle consistency. We build forward-backward cycles using the physical forward model available and a trained deep neural network solving the inverse problem at hand, and accordingly derive uncertainty estimators through regression analysis on the consistency of these forward-backward cycles. We theoretically analyze cycle consistency metrics and derive their relationship with respect to uncertainty, bias, and robustness of the neural network inference. To demonstrate the effectiveness of these cycle consistency-based uncertainty estimators, we classified corrupted and out-of-distribution input image data using some of the widely used image deblurring and super-resolution neural networks as testbeds. The blind testing of our method outperformed other models in identifying unseen input data corruption and distribution shifts. This work provides a simple-to-implement and rapid uncertainty quantification method that can be universally applied to various neural networks used for solving inverse problems.