# Multiparameter Uncertainty Mapping in Quantitative Molecular MRI using a Physics-Structured Variational Autoencoder (PS-VAE)

arXiv: https://arxiv.org/abs/2602.03317 · HTML: https://mlsanity.com/paper/2602.03317/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 77 references that are in the map.
- First posted on arXiv 3 Feb 2026.

## Builds on (most cited first, 18 of 18)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)
- [Bayesian parameter estimation using conditional variational autoencoders for gravitational-wave astronomy](https://mlsanity.com/paper/1909.06296/) (2019)
- [Solving Bayesian Inverse Problems via Variational Autoencoders](https://mlsanity.com/paper/1912.04212/) (2019)
- [MR fingerprinting Deep RecOnstruction NEtwork (DRONE)](https://mlsanity.com/paper/1710.05267/) (2017)
- [Uncertainty-Aware Self-supervised Neural Network for Liver T1ρ Mapping with Relaxation Constraint](https://mlsanity.com/paper/2207.03105/) (2022)
- [Phi-DVAE: Physics-Informed Dynamical Variational Autoencoders for Unstructured Data Assimilation](https://mlsanity.com/paper/2209.15609/) (2022)
- [SSL-QALAS: Self-Supervised Learning for Rapid Multiparameter Estimation in Quantitative MRI Using 3D-QALAS](https://mlsanity.com/paper/2302.14240/) (2023)
- [Stochastic Variational Bayesian Inference for a Nonlinear Forward Model](https://mlsanity.com/paper/2007.01675/) (2020)
- [Compressed Sensing MRI Reconstruction Regularized by VAEs with Structured Image Covariance](https://mlsanity.com/paper/2210.14586/) (2022)
- [Dynamic and Rapid Deep Synthesis of Molecular MRI Signals](https://mlsanity.com/paper/2305.19413/) (2023)
- [Multi-Parameter Molecular MRI Quantification using Physics-Informed Self-Supervised Learning](https://mlsanity.com/paper/2411.06447/) (2024)
- [Posterior Estimation for Dynamic PET imaging using Conditional Variational Inference](https://mlsanity.com/paper/2310.15850/) (2023)
- [Decoding the human brain tissue response to radiofrequency excitation using a biophysical-model-free deep MRI on a chip framework](https://mlsanity.com/paper/2408.08376/) (2024)
- [Quantitative multi-metabolite imaging of Parkinson's disease using AI boosted molecular MRI](https://mlsanity.com/paper/2507.11329/) (2025)

## Abstract (arXiv)

Quantitative imaging methods, such as magnetic resonance fingerprinting (MRF), aim to extract interpretable pathology biomarkers by estimating biophysical tissue parameters from signal evolutions. However, the pattern-matching algorithms or neural networks used in such inverse problems often lack principled uncertainty quantification, which limits the trustworthiness and transparency, required for clinical acceptance. Here, we describe a physics-structured variational autoencoder (PS-VAE) designed for rapid extraction of voxelwise multi-parameter posterior distributions. Our approach integrates a differentiable spin physics simulator with self-supervised learning, and provides a full covariance that captures the inter-parameter correlations of the latent biophysical space. The method was validated in a multi-proton pool chemical exchange saturation transfer (CEST) and semisolid magnetization transfer (MT) molecular MRF study, across in-vitro phantoms, tumor-bearing mice, healthy human volunteers, and a subject with glioblastoma. The resulting multi-parametric posteriors are in good agreement with those calculated using a brute-force Bayesian analysis, while providing an orders-of-magnitude acceleration in whole brain quantification. In addition, we demonstrate how monitoring the multi-parameter posterior dynamics across progressively acquired signals provides practical insights for protocol optimization and may facilitate real-time adaptive acquisition.