# Anatomy-DT: A Cross-Diffusion Digital Twin for Anatomical Evolution

arXiv: https://arxiv.org/abs/2509.25280 · HTML: https://mlsanity.com/paper/2509.25280/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 57 references that are in the map.
- First posted on arXiv 29 Sep 2025.

## 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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Uni-ControlNet: All-in-One Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2305.16322/) (2023)
- [Unsupervised Medical Image Translation with Adversarial Diffusion Models](https://mlsanity.com/paper/2207.08208/) (2022)
- [MedGAN: Medical Image Translation using GANs](https://mlsanity.com/paper/1806.06397/) (2018)
- [A Topological Loss Function for Deep-Learning based Image Segmentation using Persistent Homology](https://mlsanity.com/paper/1910.01877/) (2019)
- [Adaptive Latent Diffusion Model for 3D Medical Image to Image Translation: Multi-modal Magnetic Resonance Imaging Study](https://mlsanity.com/paper/2311.00265/) (2023)
- [Unsupervised Deformable Registration for Multi-Modal Images via Disentangled Representations](https://mlsanity.com/paper/1903.09331/) (2019)
- [Connectivity-Optimized Representation Learning via Persistent Homology](https://mlsanity.com/paper/1906.09003/) (2019)
- [Centerline Boundary Dice Loss for Vascular Segmentation](https://mlsanity.com/paper/2407.01517/) (2024)
- [Local Spatiotemporal Representation Learning for Longitudinally-consistent Neuroimage Analysis](https://mlsanity.com/paper/2206.04281/) (2022)
- [Learning Spatio-Temporal Model of Disease Progression with NeuralODEs from Longitudinal Volumetric Data](https://mlsanity.com/paper/2211.04234/) (2022)
- [Treatment-aware Diffusion Probabilistic Model for Longitudinal MRI Generation and Diffuse Glioma Growth Prediction](https://mlsanity.com/paper/2309.05406/) (2023)
- [TopoCellGen: Generating Histopathology Cell Topology with a Diffusion Model](https://mlsanity.com/paper/2412.06011/) (2024)
- [Predictive Digital Twin for Optimizing Patient-Specific Radiotherapy Regimens under Uncertainty in High-Grade Gliomas](https://mlsanity.com/paper/2308.12429/) (2023)
- [TopoDiffusionNet: A Topology-aware Diffusion Model](https://mlsanity.com/paper/2410.16646/) (2024)
- [Med-Real2Sim: Non-Invasive Medical Digital Twins using Physics-Informed Self-Supervised Learning](https://mlsanity.com/paper/2403.00177/) (2024)
- [Deep Learning for Reaction-Diffusion Glioma Growth Modelling: Towards a Fully Personalised Model?](https://mlsanity.com/paper/2111.13404/) (2021)
- [BrainMRDiff: A Diffusion Model for Anatomically Consistent Brain MRI Synthesis](https://mlsanity.com/paper/2504.04532/) (2025)
- [ImmunoDiff: A Diffusion Model for Immunotherapy Response Prediction in Lung Cancer](https://mlsanity.com/paper/2505.23675/) (2025)

## Abstract (arXiv)

Accurately modeling the spatiotemporal evolution of tumor morphology from baseline imaging is a pre-requisite for developing digital twin frameworks that can simulate disease progression and treatment response. Most existing approaches primarily characterize tumor growth while neglecting the concomitant alterations in adjacent anatomical structures. In reality, tumor evolution is highly non-linear and heterogeneous, shaped not only by therapeutic interventions but also by its spatial context and interaction with neighboring tissues. Therefore, it is critical to model tumor progression in conjunction with surrounding anatomy to obtain a comprehensive and clinically relevant understanding of disease dynamics. We introduce a mathematically grounded framework that unites mechanistic partial differential equations with differentiable deep learning. Anatomy is represented as a multi-class probability field on the simplex and evolved by a cross-diffusion reaction-diffusion system that enforces inter-class competition and exclusivity. A differentiable implicit-explicit scheme treats stiff diffusion implicitly while handling nonlinear reaction and event terms explicitly, followed by projection back to the simplex. To further enhance global plausibility, we introduce a topology regularizer that simultaneously enforces centerline preservation and penalizes region overlaps. The approach is validated on synthetic datasets and a clinical dataset. On synthetic benchmarks, our method achieves state-of-the-art accuracy while preserving topology, and also demonstrates superior performance on the clinical dataset. By integrating PDE dynamics, topology-aware regularization, and differentiable solvers, this work establishes a principled path toward anatomy-to-anatomy generation for digital twins that are visually realistic, anatomically exclusive, and topologically consistent.