# CardioComposer: Leveraging Differentiable Geometry for Compositional Control of Anatomical Diffusion Models

arXiv: https://arxiv.org/abs/2509.08015 · HTML: https://mlsanity.com/paper/2509.08015/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 31 of its 59 references that are in the map.
- First posted on arXiv 8 Sep 2025.

## Placed in

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

## Builds on (most cited first, 30 of 31)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [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)
- [Universal Guidance for Diffusion Models](https://mlsanity.com/paper/2302.07121/) (2023)
- [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)
- [Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMC](https://mlsanity.com/paper/2302.11552/) (2023)
- [A-SDF: Learning Disentangled Signed Distance Functions for Articulated Shape Representation](https://mlsanity.com/paper/2104.07645/) (2021)
- [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)
- [Can segmentation models be trained with fully synthetically generated data?](https://mlsanity.com/paper/2209.08256/) (2022)
- [DeepSSM: A Deep Learning Framework for Statistical Shape Modeling from Raw Images](https://mlsanity.com/paper/1810.00111/) (2018)
- [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)
- [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)
- [ORBIT-Surgical: An Open-Simulation Framework for Learning Surgical Augmented Dexterity](https://mlsanity.com/paper/2404.16027/) (2024)
- [BlobGEN-Vid: Compositional Text-to-Video Generation with Blob Video Representations](https://mlsanity.com/paper/2501.07647/) (2025)
- [Probing the Limits and Capabilities of Diffusion Models for the Anatomic Editing of Digital Twins](https://mlsanity.com/paper/2401.00247/) (2023)
- [A Generative Shape Compositional Framework to Synthesise Populations of Virtual Chimaeras](https://mlsanity.com/paper/2210.01607/) (2022)
- [svMorph: Interactive geometry-editing tools for virtual patient-specific vascular anatomies](https://mlsanity.com/paper/2210.07087/) (2022)
- [Steerable Anatomical Shape Synthesis with Implicit Neural Representations](https://mlsanity.com/paper/2504.03313/) (2025)
- [HUG-VAS: A Hierarchical NURBS-Based Generative Model for Aortic Geometry Synthesis and Controllable Editing](https://mlsanity.com/paper/2507.11474/) (2025)
- [Fully automated construction of three-dimensional finite element simulations from Optical Coherence Tomography](https://mlsanity.com/paper/2405.13643/) (2024)

## Built on by (most cited first, 1 of 1)

- [Anatomica: Localized Control over Geometric and Topological Properties for Anatomical Diffusion Models](https://mlsanity.com/paper/2511.20587/) (2025)

## Abstract (arXiv)

Generative models of 3D cardiovascular anatomy can synthesize informative structures for clinical research and medical device evaluation, but face a trade-off between geometric controllability and realism. We propose CardioComposer: a programmable, inference-time framework for generating multi-class anatomical label maps from interpretable ellipsoidal primitives. These primitives represent geometric attributes such as the size, shape, and position of discrete substructures. We specifically develop differentiable measurement functions based on voxel-wise geometric moments, enabling loss-based gradient guidance during diffusion model sampling. We demonstrate that these losses can constrain individual geometric attributes in a disentangled manner and provide compositional control over multiple substructures. Finally, we show that our method is compatible with a broad range of anatomical systems containing non-convex substructures, spanning cardiac, vascular, and skeletal organs. We release our code at https://github.com/kkadry/CardioComposer.