# Mechanistic Learning with Guided Diffusion Models to Predict Spatio-Temporal Brain Tumor Growth

arXiv: https://arxiv.org/abs/2509.09610 · HTML: https://mlsanity.com/paper/2509.09610/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 13 of its 25 references that are in the map.
- First posted on arXiv 11 Sep 2025.

## Placed in

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

## Builds on (most cited first, 13 of 13)

- [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)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Brain Imaging Generation with Latent Diffusion Models](https://mlsanity.com/paper/2209.07162/) (2022)
- [Anatomically-Controllable Medical Image Generation with Segmentation-Guided Diffusion Models](https://mlsanity.com/paper/2402.05210/) (2024)
- [Personalized Radiotherapy Design for Glioblastoma: Integrating Mathematical Tumor Models, Multimodal Scans and Bayesian Inference](https://mlsanity.com/paper/1807.00499/) (2018)
- [The Swiss Army Knife for Image-to-Image Translation: Multi-Task Diffusion Models](https://mlsanity.com/paper/2204.02641/) (2022)
- [TADM: Temporally-Aware Diffusion Model for Neurodegenerative Progression on Brain MRI](https://mlsanity.com/paper/2406.12411/) (2024)
- [Neural parameters estimation for brain tumor growth modeling](https://mlsanity.com/paper/1907.00973/) (2019)
- [BraTS-PEDs: Results of the Multi-Consortium International Pediatric Brain Tumor Segmentation Challenge 2023](https://mlsanity.com/paper/2407.08855/) (2024)

## Built on by (most cited first, 3 of 3)

- [TumorFlow: Physics-Guided Longitudinal MRI Synthesis of Glioblastoma Growth](https://mlsanity.com/paper/2603.04058/) (2026)
- [Integrating Mechanistic and Data-Driven Models for Neurological Disorders through Differentiable Programming](https://mlsanity.com/paper/2606.06094/) (2026)
- [Physics-Informed Diffusion for Biomechanically Plausible 3D Sign Language Generation](https://mlsanity.com/paper/2607.14836/) (2026)

## Abstract (arXiv)

Predicting the spatio-temporal progression of brain tumors is essential for guiding clinical decisions in neuro-oncology. We propose a hybrid mechanistic learning framework that combines a mathematical tumor growth model with a guided denoising diffusion implicit model (DDIM) to synthesize anatomically feasible future MRIs from preceding scans. The mechanistic model, formulated as a system of ordinary differential equations, captures temporal tumor dynamics including radiotherapy effects and estimates future tumor burden. These estimates condition a gradient-guided DDIM, enabling image synthesis that aligns with both predicted growth and patient anatomy. We train our model on the BraTS adult and pediatric glioma datasets and evaluate on 60 axial slices of in-house longitudinal pediatric diffuse midline glioma (DMG) cases. Our framework generates realistic follow-up scans based on spatial similarity metrics. It also introduces tumor growth probability maps, which capture both clinically relevant extent and directionality of tumor growth as shown by 95th percentile Hausdorff Distance. The method enables biologically informed image generation in data-limited scenarios, offering generative-space-time predictions that account for mechanistic priors.