# Conditional Latent Diffusion Model with Fourier-based Motion Modelling for Virtual Population Synthesis

arXiv: https://arxiv.org/abs/2606.03827 · HTML: https://mlsanity.com/paper/2606.03827/

## 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 12 of its 21 references that are in the map.
- First posted on arXiv 2 Jun 2026.

## Placed in

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

## Builds on (most cited first, 12 of 12)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Reliable Fidelity and Diversity Metrics for Generative Models](https://mlsanity.com/paper/2002.09797/) (2020)
- [Generating 3D faces using Convolutional Mesh Autoencoders](https://mlsanity.com/paper/1807.10267/) (2018)
- [A personalized time-resolved 3D mesh generative model for unveiling normal heart dynamics](https://mlsanity.com/paper/2409.13825/) (2024)
- [CHeart: A Conditional Spatio-Temporal Generative Model for Cardiac Anatomy](https://mlsanity.com/paper/2301.13098/) (2023)
- [CardiacFlow: 3D+t Four-Chamber Cardiac Shape Completion and Generation via Flow Matching](https://mlsanity.com/paper/2509.05754/) (2025)
- [Spatio-temporal neural distance fields for conditional generative modeling of the heart](https://mlsanity.com/paper/2407.10663/) (2024)
- [A Conditional Flow Variational Autoencoder for Controllable Synthesis of Virtual Populations of Anatomy](https://mlsanity.com/paper/2306.14680/) (2023)
- [A Generative Shape Compositional Framework to Synthesise Populations of Virtual Chimaeras](https://mlsanity.com/paper/2210.01607/) (2022)
- [Improve Myocardial Strain Estimation based on Deformable Groupwise Registration with a Locally Low-Rank Dissimilarity Metric](https://mlsanity.com/paper/2311.07348/) (2023)
- [3D Cardiac Anatomy Generation Using Mesh Latent Diffusion Models](https://mlsanity.com/paper/2508.14122/) (2025)

## Abstract (arXiv)

In-silico trials of medical devices require the generation of virtual populations of anatomies. In cardiovascular applications, virtual anatomy is typically represented as a 3D+t mesh sampled from a generative model. However, most existing mesh generators focus on static anatomy, while sequence models often lack explicit periodicity. To this end, we propose 4D F-MeshLDM, a conditional generative framework comprising a convolutional mesh VAE to encode meshes, a structural latent space that parameterises motion using a truncated Fourier series, and a diffusion prior that learns the latent distribution over Fourier coefficient tokens. By conditioning the diffusion process on clinical covariates via affine modulation, we enable controllable synthesis. Sampling tokens and performing inverse Fourier synthesis yield cycle-consistent latent trajectories, which can be decoded into 3D+t cardiac mesh sequences. Experiments on 5,000 UK Biobank subjects demonstrate that 4D F-MeshLDM outperforms state-of-the-art baselines in anatomical fidelity and achieves near-zero cycle closure error. Furthermore, the generated cohorts accurately preserve clinical functional indices, highlighting the potential of our framework for reliable in-silico cardiac trials.