# TumorFlow: Physics-Guided Longitudinal MRI Synthesis of Glioblastoma Growth

arXiv: https://arxiv.org/abs/2603.04058 · HTML: https://mlsanity.com/paper/2603.04058/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 26 references that are in the map.
- First posted on arXiv 4 Mar 2026.

## Builds on (most cited first, 17 of 17)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [The RSNA-ASNR-MICCAI BraTS 2021 Benchmark on Brain Tumor Segmentation and Radiogenomic Classification](https://mlsanity.com/paper/2107.02314/) (2021)
- [MAISI: Medical AI for Synthetic Imaging](https://mlsanity.com/paper/2409.11169/) (2024)
- [Conditional Diffusion Models for Semantic 3D Brain MRI Synthesis](https://mlsanity.com/paper/2305.18453/) (2023)
- [CoLa-Diff: Conditional Latent Diffusion Model for Multi-Modal MRI Synthesis](https://mlsanity.com/paper/2303.14081/) (2023)
- [The University of California San Francisco Preoperative Diffuse Glioma MRI (UCSF-PDGM) Dataset](https://mlsanity.com/paper/2109.00356/) (2021)
- [3D MedDiffusion: A 3D Medical Latent Diffusion Model for Controllable and High-quality Medical Image Generation](https://mlsanity.com/paper/2412.13059/) (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)
- [Beware of diffusion models for synthesizing medical images -- A comparison with GANs in terms of memorizing brain MRI and chest x-ray images](https://mlsanity.com/paper/2305.07644/) (2023)
- [Learn-Morph-Infer: a new way of solving the inverse problem for brain tumor modeling](https://mlsanity.com/paper/2111.04090/) (2021)
- [Brain tumor segmentation using synthetic MR images -- A comparison of GANs and diffusion models](https://mlsanity.com/paper/2306.02986/) (2023)
- [A Learnable Prior Improves Inverse Tumor Growth Modeling](https://mlsanity.com/paper/2403.04500/) (2024)
- [BraTS orchestrator : Democratizing and Disseminating state-of-the-art brain tumor image analysis](https://mlsanity.com/paper/2506.13807/) (2025)
- [3D MRI Synthesis with Slice-Based Latent Diffusion Models: Improving Tumor Segmentation Tasks in Data-Scarce Regimes](https://mlsanity.com/paper/2406.05421/) (2024)
- [Mechanistic Learning with Guided Diffusion Models to Predict Spatio-Temporal Brain Tumor Growth](https://mlsanity.com/paper/2509.09610/) (2025)

## Built on by (most cited first, 2 of 2)

- [Observation-Anchored Selective Assimilation for Longitudinal Tumor-State Proxy Forecasting in Post-Treatment Glioma](https://mlsanity.com/paper/2609.12435/) (2026)
- [What Makes a Good Medical Image Tokenizer? Rethinking Reconstruction and Generation in Medical Image Tokenization](https://mlsanity.com/paper/2609.24691/) (2026)

## Abstract (arXiv)

Glioblastoma exhibits diverse, infiltrative, and patient-specific growth patterns that are only partially visible on routine MRI, making it difficult to reliably assess true tumor extent and personalize treatment planning and follow-up. We present a biophysically-conditioned generative framework that synthesizes biologically realistic 3D brain MRI volumes from estimated, spatially continuous tumor-concentration fields. Our approach combines a generative model with tumor-infiltration maps that can be propagated through time using a biophysical growth model, enabling fine-grained control over tumor shape and growth while preserving patient anatomy. This enables us to synthesize consistent tumor growth trajectories directly in the space of real patients, providing interpretable, controllable estimation of tumor infiltration and progression beyond what is explicitly observed in imaging. We evaluate the framework on longitudinal glioblastoma cases and demonstrate that it can generate temporally coherent sequences with realistic changes in tumor appearance and surrounding tissue response. These results suggest that integrating mechanistic tumor growth priors with modern generative modeling can provide a practical tool for patient-specific progression visualization and for generating controlled synthetic data to support downstream neuro-oncology workflows. In longitudinal extrapolation, we achieve a consistent 75% Dice overlap with the biophysical model while maintaining a constant PSNR of 25 in the surrounding tissue. Our code is available at: https://github.com/valentin-biller/lgm.git