Evaluating and Calibrating Diffusion Model-derived Uncertainty for Quantitative MRI Mapping
Authors: Shishuai Wang, Stefan Klein, Juan A. Hernandez-Tamames, Dirk H. J. Poot
Organizations: Department of Radiology and Nuclear Medicine, Erasmus MC, Rotterdam, The Netherlands · Department of Imaging Physics, TU Delft, Delft, The Netherlands
Abstract
Quantitative MRI (qMRI) provides standardised tissue parameter maps, but the reliability of deep learning-based qMRI mapping methods is often not explicitly characterised. In this work we systematically evaluate uncertainty maps for quantitative MRI derived from multiple inferences of a data-consistent diffusion model-based qMRI framework. Evaluation on synthetic test data assessed error-awareness, high-error detection, selective prediction, and Gaussian interval calibration. Diffusion model-derived uncertainty was positively associated with the mapping error, while risk-coverage analysis showed that excluding high-uncertainty voxels reduced the retained error. However, the raw uncertainty was poorly calibrated for quantitative interval interpretation. Calibration was substantially improved using a post-hoc procedure combining prediction-value-dependent bias correction with scalar uncertainty scaling. Qualitative evaluation on a healthy volunteer showed spatially meaningful uncertainty patterns. These results indicate that diffusion model-derived uncertainty is informative for reliability assessment and selective prediction, but requires calibration for quantitative interval interpretation.
Parallel imaging techniques reduce magnetic resonance imaging (MRI) scan time but image quality degrades as the acceleration factor increases. In clinical practice, conservative acceleration factors are chosen because no mechanism exists to automatically assess the diagnostic quality of undersampled reconstructions. This work introduces a general framework for pixel-wise uncertainty quantification in parallel MRI reconstructions, enabling automatic identification of unreliable regions without access to any ground-truth reference image. Our method integrates conformal quantile regression with image reconstruction methods to estimate statistically rigorous pixel-wise uncertainty intervals. We trained and evaluated our model on Cartesian undersampled brain and knee data obtained from the fastMRI dataset using acceleration factors ranging from 2 to 10. An end-to-end Variational Network was used for image reconstruction. Quantitative experiments demonstrate strong agreement between predicted uncertainty maps and true reconstruction error. Using our method, the corresponding Pearson correlation coefficient was higher than 90% at acceleration levels at and above four-fold; whereas it dropped to less than 70% when the uncertainty was computed using a simpler a heuristic notion (magnitude of the residual). Qualitative examples further show the uncertainty maps based on quantile regression capture the magnitude and spatial distribution of reconstruction errors across acceleration factors, with regions of elevated uncertainty aligning with pathologies and artifacts. The proposed framework enables evaluation of reconstruction quality without access to fully-sampled ground-truth reference images. It represents a step toward adaptive MRI acquisition protocols that may be able to dynamically balance scan time and diagnostic reliability.
Ilias I. Giannakopoulos, Lokesh B Gautham Muthukumar, Yvonne W. Lui +1
Understanding the human brain requires access to its microscopic tissue architecture. Diffusion magnetic resonance imaging (MRI) provides the only noninvasive window into whole-brain microstructure in vivo, yet reliable quantitative mapping remains confined to specialized research settings requiring dense sampling and optimized acquisition protocols. To address this gap, we present a physics-informed generative microstructure network (PIGMENT) that learns a universal generative prior of human brain microstructure and adapts it zero-shot to each participant's measured data to recover subject-specific maps. Trained on 11375 scans spanning multiple sites, vendors, and field strengths, PIGMENT enabled reliable quantitative mapping for tensor, kurtosis, and NODDI models across external datasets from five independent centers. It remains effective where conventional fitting becomes unreliable, recovering meaningful maps from extremely sparse acquisitions while supporting downstream tractography and structural connectivity mapping. PIGMENT estimates demonstrated strong biological validity, preserving submillimeter cortical microarchitectural patterns and early-childhood white matter developmental trajectories from 10-fold accelerated scans. Furthermore, PIGMENT enables reliable quantitative tensor mapping on cost-efficient low-field systems and the extraction of tumor-related biomarkers using ultra-fast clinical protocols. Together, these results establish PIGMENT as a physics-informed foundation model that extends quantitative diffusion MRI into regimes traditionally too sparse, heterogeneous, or clinically constrained for reliable analysis.
Diffusion models have seen wide adoption for 3D molecular generation, yet they offer no principled signal of when a generated molecule is likely to be of low quality. We propose a post-hoc method for estimating per-sample uncertainty in pretrained molecular diffusion models. Building on a Laplace approximation of the denoising network, we measure the variability of the noise prediction across the generation trajectory. Empirically, we show that the resulting uncertainty score is informative of sample quality, exhibiting a negative correlation with established sample-level quality metrics. We further study how the proposed uncertainty score can be used to filter generated samples, improving model performance via test-time scaling.
Paul Seij, Christian A. Naesseth, Stephan Mandt +1