# CardiacFlow: 3D+t Four-Chamber Cardiac Shape Completion and Generation via Flow Matching

arXiv: https://arxiv.org/abs/2509.05754 · HTML: https://mlsanity.com/paper/2509.05754/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 19 of its 40 references that are in the map.
- First posted on arXiv 6 Sep 2025.

## Placed in

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

## Builds on (most cited first, 19 of 19)

- [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)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Swin UNETR: Swin Transformers for Semantic Segmentation of Brain Tumors in MRI Images](https://mlsanity.com/paper/2201.01266/) (2022)
- [Patch Diffusion: Faster and More Data-Efficient Training of Diffusion Models](https://mlsanity.com/paper/2304.12526/) (2023)
- [Improving the Training of Rectified Flows](https://mlsanity.com/paper/2405.20320/) (2024)
- [Evaluation of Algorithms for Multi-Modality Whole Heart Segmentation: An Open-Access Grand Challenge](https://mlsanity.com/paper/1902.07880/) (2019)
- [Beta Sampling is All You Need: Efficient Image Generation Strategy for Diffusion Models using Stepwise Spectral Analysis](https://mlsanity.com/paper/2407.12173/) (2024)
- [SDF4CHD: Generative Modeling of Cardiac Anatomies with Congenital Heart Defects](https://mlsanity.com/paper/2311.00332/) (2023)
- [DeepMesh: Mesh-based Cardiac Motion Tracking using Deep Learning](https://mlsanity.com/paper/2309.14306/) (2023)
- [CHeart: A Conditional Spatio-Temporal Generative Model for Cardiac Anatomy](https://mlsanity.com/paper/2301.13098/) (2023)
- [Improved 3D Whole Heart Geometry from Sparse CMR Slices](https://mlsanity.com/paper/2408.07532/) (2024)
- [Spatio-temporal neural distance fields for conditional generative modeling of the heart](https://mlsanity.com/paper/2407.10663/) (2024)
- [High-Resolution Maps of Left Atrial Displacements and Strains Estimated with 3D Cine MRI using Online Learning Neural Networks](https://mlsanity.com/paper/2312.09387/) (2023)

## Built on by (most cited first, 9 of 9)

- [VecHeart: Holistic Four-Chamber Cardiac Anatomy Modeling via Hybrid VecSets](https://mlsanity.com/paper/2604.19403/) (2026)
- [Personalized 4D Whole-Heart Mesh Reconstruction from Cine MRI via Multi-Scale Temporal Modeling and Differentiable Contour Rendering](https://mlsanity.com/paper/2607.01952/) (2026)
- [Chain of Flow: ECG-Conditioned 4D Cardiac Cine Generation from Patient-Specific Anatomical Anchor](https://mlsanity.com/paper/2602.22919/) (2026)
- [Flow Matching-enabled Test-Time Refinement for Unsupervised Cardiac MR Registration](https://mlsanity.com/paper/2603.01073/) (2026)
- [Conditional Latent Diffusion Model with Fourier-based Motion Modelling for Virtual Population Synthesis](https://mlsanity.com/paper/2606.03827/) (2026)
- [A Strong Linear Baseline for Whole-Heart Cardiac Shape Completion on CT, with an Open Eleven-Structure Statistical Shape Model](https://mlsanity.com/paper/2608.19932/) (2026)
- [Latent-to-Latent Flow for Volumetric Stochastic Segmentation](https://mlsanity.com/paper/2609.07460/) (2026)
- [Anatomy-Aligned Surface Field Learning for Myocardial Reconstruction from Sparse Short-Axis Cine MRI](https://mlsanity.com/paper/2609.29825/) (2026)
- [Focus, Align, and Diffuse: Time-Series-Aware Keyframe Diffusion for Cardiac Dynamic Synthesis from Sparse Observations](https://mlsanity.com/paper/2610.19050/) (2026)

## Abstract (arXiv)

Learning 3D+t shape completion and generation from multi-view cardiac magnetic resonance (CMR) images requires a large amount of high-resolution 3D whole-heart segmentations (WHS) to capture shape priors. In this work, we leverage flow matching techniques to learn deep generative flows for augmentation, completion, and generation of 3D+t shapes of four cardiac chambers represented implicitly by segmentations. Firstly, we introduce a latent rectified flow to generate 3D cardiac shapes for data augmentation, learnt from a limited number of 3D WHS data. Then, a label completion network is trained on both real and synthetic data to reconstruct 3D+t shapes from sparse multi-view CMR segmentations. Lastly, we propose CardiacFlow, a novel one-step generative flow model for efficient 3D+t four-chamber cardiac shape generation, conditioned on the periodic Gaussian kernel encoding of time frames. The experiments on the WHS datasets demonstrate that flow-based data augmentation reduces geometric errors by 16% in 3D shape completion. The evaluation on the UK Biobank dataset validates that CardiacFlow achieves superior generation quality and periodic consistency compared to existing baselines.