# A Comprehensive Framework for Uncertainty Quantification of Voxel-wise Supervised Models in IVIM MRI

arXiv: https://arxiv.org/abs/2508.04588 · HTML: https://mlsanity.com/paper/2508.04588/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 55 references that are in the map.
- First posted on arXiv 6 Aug 2025.

## Builds on (most cited first, 14 of 14)

- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [Evaluating Scalable Bayesian Deep Learning Methods for Robust Computer Vision](https://mlsanity.com/paper/1906.01620/) (2019)
- [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)
- [Quality of Uncertainty Quantification for Bayesian Neural Network Inference](https://mlsanity.com/paper/1906.09686/) (2019)
- [A review of uncertainty quantification in medical image analysis: probabilistic and non-probabilistic methods](https://mlsanity.com/paper/2310.06873/) (2023)
- [Improved unsupervised physics-informed deep learning for intravoxel incoherent motion modeling and evaluation in pancreatic cancer patients](https://mlsanity.com/paper/2011.01689/) (2020)
- [How to Evaluate Uncertainty Estimates in Machine Learning for Regression?](https://mlsanity.com/paper/2106.03395/) (2021)
- [Uncertainty Quantification for Machine Learning in Healthcare: A Survey](https://mlsanity.com/paper/2505.02874/) (2025)
- [Implicit Modeling with Uncertainty Estimation for Intravoxel Incoherent Motion Imaging](https://mlsanity.com/paper/1810.10358/) (2018)
- [A Deep Learning Approach to Multi-Fiber Parameter Estimation and Uncertainty Quantification in Diffusion MRI](https://mlsanity.com/paper/2405.13655/) (2024)

## Abstract (arXiv)

Accurate estimation of intravoxel incoherent motion (IVIM) parameters from diffusion-weighted MRI remains challenging due to the ill-posed nature of the inverse problem and high sensitivity to noise, particularly in the perfusion compartment. In this work, we propose a probabilistic deep learning framework based on Deep Ensembles (DE) of Mixture Density Networks (MDNs), enabling estimation of total predictive uncertainty and decomposition into aleatoric (AU) and epistemic (EU) components. The method was benchmarked against non probabilistic neural networks, a Bayesian fitting approach and a probabilistic network with single Gaussian parametrization. Supervised training was performed on synthetic data, and evaluation was conducted on both simulated and an in vivo dataset. The reliability of the quantified uncertainties was assessed using calibration curves, output distribution sharpness, and the Continuous Ranked Probability Score (CRPS). MDNs produced more calibrated and sharper predictive distributions for the diffusion coefficient D and fraction f parameters, although slight overconfidence was observed in pseudo-diffusion coefficient D*. The Robust Coefficient of Variation (RCV) indicated smoother in vivo estimates for D* with MDNs compared to Gaussian model. Despite the training data covering the expected physiological range, elevated EU in vivo suggests a mismatch with real acquisition conditions, highlighting the importance of incorporating EU, which was allowed by DE. Overall, we present a comprehensive framework for IVIM fitting with uncertainty quantification, which enables the identification and interpretation of unreliable estimates. The proposed approach can also be adopted for fitting other physical models through appropriate architectural and simulation adjustments.