# Physics-Grounded Disentangled Flow Modeling for Brain Disease Progression Trajectory

arXiv: https://arxiv.org/abs/2606.28630 · HTML: https://mlsanity.com/paper/2606.28630/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 26 of its 50 references that are in the map.
- First posted on arXiv 26 Jun 2026.

## Placed in

- Diffusion models / [Medical imaging and segmentation](https://mlsanity.com/diffusion/medical-imaging-and-segmentation/)

## Builds on (most cited first, 26 of 26)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Scalable Gradients for Stochastic Differential Equations](https://mlsanity.com/paper/2001.01328/) (2020)
- [I2SB: Image-to-Image Schr"odinger Bridge](https://mlsanity.com/paper/2302.05872/) (2023)
- [Learn-Morph-Infer: a new way of solving the inverse problem for brain tumor modeling](https://mlsanity.com/paper/2111.04090/) (2021)
- [Learning Spatio-Temporal Model of Disease Progression with NeuralODEs from Longitudinal Volumetric Data](https://mlsanity.com/paper/2211.04234/) (2022)
- [ImageFlowNet: Forecasting Multiscale Image-Level Trajectories of Disease Progression with Irregularly-Sampled Longitudinal Medical Images](https://mlsanity.com/paper/2406.14794/) (2024)
- [Brain Latent Progression: Individual-based Spatiotemporal Disease Progression on 3D Brain MRIs via Latent Diffusion](https://mlsanity.com/paper/2502.08560/) (2025)
- [Clinically-Inspired Multi-Agent Transformers for Disease Trajectory Forecasting from Multimodal Data](https://mlsanity.com/paper/2210.13889/) (2022)
- [Comprehensive Evaluation of Multimodal AI Models in Medical Imaging Diagnosis: From Data Augmentation to Preference-Based Comparison](https://mlsanity.com/paper/2412.05536/) (2024)
- [A Learnable Prior Improves Inverse Tumor Growth Modeling](https://mlsanity.com/paper/2403.04500/) (2024)
- [Physics-Regularized Multi-Modal Image Assimilation for Brain Tumor Localization](https://mlsanity.com/paper/2409.20409/) (2024)
- [Learning Patient-Specific Disease Dynamics with Latent Flow Matching for Longitudinal Imaging Generation](https://mlsanity.com/paper/2512.09185/) (2025)
- [Multiatlas Calibration of Biophysical Brain Tumor Growth Models with Mass Effect](https://mlsanity.com/paper/2006.09932/) (2020)
- [Personalized Prediction of Future Lesion Activity and Treatment Effect in Multiple Sclerosis from Baseline MRI](https://mlsanity.com/paper/2204.01702/) (2022)
- [Longitudinal Flow Matching for Trajectory Modeling](https://mlsanity.com/paper/2510.03569/) (2025)
- [NODER: Image Sequence Regression Based on Neural Ordinary Differential Equations](https://mlsanity.com/paper/2407.13241/) (2024)
- [PDE-constrained optimization in medical image analysis](https://mlsanity.com/paper/1803.00058/) (2018)
- [Image-Driven Biophysical Tumor Growth Model Calibration](https://mlsanity.com/paper/1907.07774/) (2019)
- [Deep Learning for Reaction-Diffusion Glioma Growth Modelling: Towards a Fully Personalised Model?](https://mlsanity.com/paper/2111.13404/) (2021)
- [TimeFlow: Temporal Conditioning for Longitudinal Brain MRI Registration and Aging Analysis](https://mlsanity.com/paper/2501.08667/) (2025)
- [USB: Unified Synthetic Brain Framework for Bidirectional Pathology-Healthy Generation and Editing](https://mlsanity.com/paper/2512.00269/) (2025)

## Abstract (arXiv)

Forecasting longitudinal brain lesion evolution is critical for disease monitoring and treatment planning. Existing approaches typically learn a direct mapping from a baseline image to a future observation, without explicitly modeling the physical mechanisms underlying the lesion progression. Such an entangled modeling of structural deformation and image intensity variation limits physical plausibility, model generalization, and interpretability. To address this, we propose PDF, a Physics-grounded Disentangled Flow matching framework for longitudinal brain disease forecasting. We explicitly decompose the longitudinal modeling of lesion growth into two processes, each learned by a dedicated flow matching network: morphology evolution, which captures lesion growth and structural deformation; and intensity evolution, which models signal changes driven by variations in lesion concentration. To enforce physics-grounded constraints, we introduce a PDE-regularized loss based on lesion growth dynamics, that enforces a diffusion-reaction-advection formulation for morphological evolution. Experiments on three public longitudinal datasets spanning diverse brain diseases demonstrate state-of-the-art performance, validating the effectiveness of the disentangled modeling framework and physics-grounded learning design. Code is publicly available at https://github.com/jhuldr/PDF.