# Uncertainty quantification in medical image segmentation with normalizing flows

arXiv: https://arxiv.org/abs/2006.02683 · HTML: https://mlsanity.com/paper/2006.02683/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jun 2020.

## Built on by (most cited first, 23 of 23)

- [Ambiguous Medical Image Segmentation using Diffusion Models](https://mlsanity.com/paper/2304.04745/) (2023)
- [Trustworthy clinical AI solutions: a unified review of uncertainty quantification in deep learning models for medical image analysis](https://mlsanity.com/paper/2210.03736/) (2022)
- [Stochastic Segmentation with Conditional Categorical Diffusion Models](https://mlsanity.com/paper/2303.08888/) (2023)
- [BerDiff: Conditional Bernoulli Diffusion Model for Medical Image Segmentation](https://mlsanity.com/paper/2304.04429/) (2023)
- [The Treasure Beneath Multiple Annotations: An Uncertainty-aware Edge Detector](https://mlsanity.com/paper/2303.11828/) (2023)
- [Data synthesis and adversarial networks: A review and meta-analysis in cancer imaging](https://mlsanity.com/paper/2107.09543/) (2021)
- [Improving Aleatoric Uncertainty Quantification in Multi-Annotated Medical Image Segmentation with Normalizing Flows](https://mlsanity.com/paper/2108.02155/) (2021)
- [That Label's Got Style: Handling Label Style Bias for Uncertain Image Segmentation](https://mlsanity.com/paper/2303.15850/) (2023)
- [Generalized Probabilistic U-Net for medical image segementation](https://mlsanity.com/paper/2207.12872/) (2022)
- [Laplacian Segmentation Networks Improve Epistemic Uncertainty Quantification](https://mlsanity.com/paper/2303.13123/) (2023)
- [Epistemic Uncertainty in Conformal Scores: A Unified Approach](https://mlsanity.com/paper/2502.06995/) (2025)
- [Effect of latent space distribution on the segmentation of images with multiple annotations](https://mlsanity.com/paper/2304.13476/) (2023)
- [A Review of Bayesian Uncertainty Quantification in Deep Probabilistic Image Segmentation](https://mlsanity.com/paper/2411.16370/) (2024)
- [Ambiguous Medical Image Segmentation Using Diffusion Schr"odinger Bridge](https://mlsanity.com/paper/2509.17187/) (2025)
- [Probabilistic 3D segmentation for aleatoric uncertainty quantification in full 3D medical data](https://mlsanity.com/paper/2305.00950/) (2023)
- [Conditional Pseudo-Reversible Normalizing Flow for Surrogate Modeling in Quantifying Uncertainty Propagation](https://mlsanity.com/paper/2404.00502/) (2024)
- [Flow Stochastic Segmentation Networks](https://mlsanity.com/paper/2507.18838/) (2025)
- [Deep Learning with Uncertainty Quantification for Predicting the Segmentation Dice Coefficient of Prostate Cancer Biopsy Images](https://mlsanity.com/paper/2109.00115/) (2021)
- [Investigating and Improving Latent Density Segmentation Models for Aleatoric Uncertainty Quantification in Medical Imaging](https://mlsanity.com/paper/2307.16694/) (2023)
- [Uncertainty Quantification for Deep Regression using Contextualised Normalizing Flows](https://mlsanity.com/paper/2512.00835/) (2025)
- [MSEG-VCUQ: Multimodal SEGmentation with Enhanced Vision Foundation Models, Convolutional Neural Networks, and Uncertainty Quantification for High-Speed Video Phase Detection Data](https://mlsanity.com/paper/2411.07463/) (2024)
- [UnGAP: Uncertainty-Guided Affine Prompting for Real-Time Crack Segmentation](https://mlsanity.com/paper/2605.02380/) (2026)
- [Neural Architecture Distributions: A New Paradigm for Stochastic Segmentation](https://mlsanity.com/paper/2606.21061/) (2026)

## Abstract (arXiv)

Medical image segmentation is inherently an ambiguous task due to factors such as partial volumes and variations in anatomical definitions. While in most cases the segmentation uncertainty is around the border of structures of interest, there can also be considerable inter-rater differences. The class of conditional variational autoencoders (cVAE) offers a principled approach to inferring distributions over plausible segmentations that are conditioned on input images. Segmentation uncertainty estimated from samples of such distributions can be more informative than using pixel level probability scores. In this work, we propose a novel conditional generative model that is based on conditional Normalizing Flow (cFlow). The basic idea is to increase the expressivity of the cVAE by introducing a cFlow transformation step after the encoder. This yields improved approximations of the latent posterior distribution, allowing the model to capture richer segmentation variations. With this we show that the quality and diversity of samples obtained from our conditional generative model is enhanced. Performance of our model, which we call cFlow Net, is evaluated on two medical imaging datasets demonstrating substantial improvements in both qualitative and quantitative measures when compared to a recent cVAE based model.