Cardiac Mesh Flow: One-Step Generation of 3D+t Cardiac Four-Chamber Meshes via Flow Matching

Spatio-temporal (3D+t) generative modelling of cardiac shape and motion is crucial for understanding heart structure and function at population scale. Existing generative models for cardiac shape synthesis either adopt volumetric shape representations that lack anatomical correspondence across different time points and subjects, or rely on VAE-based frameworks that suffer from a trade-off between reconstruction fidelity and generative diversity. In this work, we propose Cardiac Mesh Flow, a novel generative flow model for 3D+t cardiac four-chamber mesh generation with anatomical correspondence, temporal coherence, and periodic consistency. Leveraging the flow matching technique, Cardiac Mesh Flow performs efficient one-step generation of multi-scale free-form deformation fields, which warp a template mesh to generate cardiac four-chamber meshes across a cardiac cycle. Furthermore, Cardiac Mesh Flow enables controllable generation conditioned on cardiac chamber volumes, allowing precise control of the synthetic heart. Experimental results demonstrate that Cardiac Mesh Flow achieves high fidelity and diversity on both unconditional and conditional generation, compared to state-of-the-art 3D+t cardiac mesh generation methods.