# Anatomica: Localized Control over Geometric and Topological Properties for Anatomical Diffusion Models

arXiv: https://arxiv.org/abs/2511.20587 · HTML: https://mlsanity.com/paper/2511.20587/

## 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 30 of its 49 references that are in the map.
- First posted on arXiv 25 Nov 2025.

## Placed in

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

## Builds on (most cited first, 30 of 30)

- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [TotalSegmentator: robust segmentation of 104 anatomical structures in CT images](https://mlsanity.com/paper/2208.05868/) (2022)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [Diffusion Self-Guidance for Controllable Image Generation](https://mlsanity.com/paper/2306.00986/) (2023)
- [SynthSeg: Segmentation of brain MRI scans of any contrast and resolution without retraining](https://mlsanity.com/paper/2107.09559/) (2021)
- [A Topological Loss Function for Deep-Learning based Image Segmentation using Persistent Homology](https://mlsanity.com/paper/1910.01877/) (2019)
- [Generative models improve fairness of medical classifiers under distribution shifts](https://mlsanity.com/paper/2304.09218/) (2023)
- [A Topology Layer for Machine Learning](https://mlsanity.com/paper/1905.12200/) (2019)
- [SALAD: Part-Level Latent Diffusion for 3D Shape Generation and Manipulation](https://mlsanity.com/paper/2303.12236/) (2023)
- [CTSpine1K: A Large-Scale Dataset for Spinal Vertebrae Segmentation in Computed Tomography](https://mlsanity.com/paper/2105.14711/) (2021)
- [Fast Auto-Differentiable Digitally Reconstructed Radiographs for Solving Inverse Problems in Intraoperative Imaging](https://mlsanity.com/paper/2208.12737/) (2022)
- [Compositional Text-to-Image Generation with Dense Blob Representations](https://mlsanity.com/paper/2405.08246/) (2024)
- [Learning General-Purpose Biomedical Volume Representations using Randomized Synthesis](https://mlsanity.com/paper/2411.02372/) (2024)
- [Intraoperative 2D/3D Image Registration via Differentiable X-ray Rendering](https://mlsanity.com/paper/2312.06358/) (2023)
- [Cubical Ripser: Software for computing persistent homology of image and volume data](https://mlsanity.com/paper/2005.12692/) (2020)
- [A persistent homology-based topological loss for CNN-based multi-class segmentation of CMR](https://mlsanity.com/paper/2107.12689/) (2021)
- [A personalized time-resolved 3D mesh generative model for unveiling normal heart dynamics](https://mlsanity.com/paper/2409.13825/) (2024)
- [SDF4CHD: Generative Modeling of Cardiac Anatomies with Congenital Heart Defects](https://mlsanity.com/paper/2311.00332/) (2023)
- [BlobGEN-Vid: Compositional Text-to-Video Generation with Blob Video Representations](https://mlsanity.com/paper/2501.07647/) (2025)
- [Topology-Aware Latent Diffusion for 3D Shape Generation](https://mlsanity.com/paper/2401.17603/) (2024)
- [TopoDiffusionNet: A Topology-aware Diffusion Model](https://mlsanity.com/paper/2410.16646/) (2024)
- [Improving Performance, Robustness, and Fairness of Radiographic AI Models with Finely-Controllable Synthetic Data](https://mlsanity.com/paper/2508.16783/) (2025)
- [Probing the Limits and Capabilities of Diffusion Models for the Anatomic Editing of Digital Twins](https://mlsanity.com/paper/2401.00247/) (2023)
- [Steerable Anatomical Shape Synthesis with Implicit Neural Representations](https://mlsanity.com/paper/2504.03313/) (2025)
- [A Diffusion Model for Simulation Ready Coronary Anatomy with Morpho-skeletal Control](https://mlsanity.com/paper/2407.15631/) (2024)
- [Morphology-based non-rigid registration of coronary computed tomography and intravascular images through virtual catheter path optimization](https://mlsanity.com/paper/2301.00060/) (2022)
- [CardioComposer: Leveraging Differentiable Geometry for Compositional Control of Anatomical Diffusion Models](https://mlsanity.com/paper/2509.08015/) (2025)

## Abstract (arXiv)

We present Anatomica: an inference-time framework for generating multi-class anatomical voxel maps with localized geo-topological control. During generation, we use cuboidal control domains of varying dimensionality, location, and shape to slice out relevant substructures. These local substructures are used to compute differentiable penalty functions that steer the sample towards target constraints. We control geometric features such as size, shape, and position through voxel-wise moments, while topological features such as connected components, loops, and voids are enforced through persistent homology. Lastly, we implement Anatomica for latent diffusion models, where neural field decoders partially extract substructures, enabling the efficient control of anatomical properties. Anatomica applies flexibly across diverse anatomical systems, composing constraints to control complex structures over arbitrary dimensions and coordinate systems, thereby enabling the rational design of synthetic datasets for virtual trials or machine learning workflows.