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Abstract
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 nearly-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.
Links to Paper and Supplementary Materials
Main Paper (Open Access Version): https://papers.miccai.org/miccai-2026/paper/1472_paper.pdf
SharedIt Link: Not yet available
SpringerLink (DOI): Not yet available
Supplementary Material: Not Submitted
Link to the Code Repository
N/A
Link to the Dataset(s)
N/A
BibTex
@InProceedings{LanSha_Conditional_MICCAI2026,
author = { Lan, Shaokun AND Dou, Haoran AND Huang, Jinghan AND Zakeri, Arezoo AND Lin, Fengming AND Zhou, Zherui AND Duan, Jinming AND Frangi, Alejandro F.},
title = { { Conditional Latent Diffusion Model with Fourier-Based Motion Modelling for Virtual Population Synthesis } },
booktitle = {Medical Image Computing and Computer Assisted Intervention -- MICCAI 2026},
year = {2026},
publisher = {Springer Nature Switzerland},
volume = {LNCS 16890},
month = {September},
page = {pending}
}
Reviews
Review #1
- Please describe the contribution of the paper
This is a well-written paper on a conditional 3D+t full-cardiac-cycle heart mesh synthesis framework. The proposed pipeline uses a mesh VAE to encode phase-wise meshes into latent codes, then fits a truncated Fourier representation to the latent trajectory so that periodic motion is enforced by construction. A Transformer-based DDPM is then used to model the resulting Fourier coefficient tokens under clinical covariates. The paper demonstrates strong generation fidelity and near-zero cycle-closure error, and the unconditioned and conditioned generation results are overall convincing for full-cycle heart-model synthesis.
- Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
3D+t heart-model generation is a critical and difficult problem. It is important because clinically relevant functional indices such as EDV, ESV, and EF are derived from the full cardiac cycle and are meaningful for downstream clinical assessment and in-silico studies. It is also difficult because the method must model both anatomical variability and temporally coherent cardiac motion.
The intuition of the paper is strong and important for the field. The methodological design is elegant, especially in the way the authors introduce truncated Fourier fitting in latent space. The method separates a time-invariant coefficient representation from the phase sampling basis and cycle duration. The representation is clearly interpretable and well motivated, and it supports robust full-cycle mesh synthesis with exact periodicity by construction.
In terms of experiments, the use of 5,000 UK Biobank subjects gives a solid empirical basis. The selected evaluation metrics cover both generation quality and temporal or clinical behaviour, which reflects good scientific judgment. The comparisons against the baselines show clear advantages for 4D F-MeshLDM in anatomical fidelity, coverage, and cycle consistency, and the results make a convincing case for clinically relevant virtual-population synthesis.
- Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.
I do not identify a major conceptual weakness in this work. My concerns are mainly minor points of presentation and explanation rather than substantive weaknesses in the proposed framework.
- Please rate the clarity and organization of this paper
Good
- Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.
The submission does not mention open access to source code or data, but provides a clear and detailed description of the algorithm to ensure reproducibility.
- Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?
N/A
- Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2026/en/REVIEWER-GUIDELINES.html
First, the overview of 4D F-MeshLDM in Fig. 1 is not as well organised as the mechanism described in Section 2.2.The figure contains the right components, but the flow of reconstruction of the latent trajectory and generation of the final sequence is harder to follow visually than in the text. It would be easier for readers if the steps and directional flow were presented more clearly.
Second, Table 2 requires clearer explanation. The downward arrow for EF is appropriate because the reported quantity is EF MAE, so smaller is better. However, the table can still be confusing because 4D CardioSynth has smaller EDV and ESV MAEs in some entries, while 4D F-MeshLDM achieves the lowest EF MAE. This is not necessarily contradictory, since EF is derived from EDV and ESV and the error relationship is not linear, but the paper should explain this more explicitly.
Third, also in Table 2, the interpretation of volume smoothness and mesh smoothness could be stated more carefully. The downward arrows are consistent with the metric definitions, but these quantities still reflect a trade-off between smooth temporal evolution and faithfulness to the true dynamic behaviour.
- Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.
(5) Accept — should be accepted, independent of rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
This assessment is mainly driven by the paper’s clear and coherent presentation, the strong intuition behind the proposed idea, the elegant methodological development, and the convincing empirical results. The work is further strengthened by a careful and scientifically sensible choice of experiments and evaluation metrics, and it shows clear promise for clinically relevant applications.
- Reviewer confidence
Very confident (4)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
N/A
- [Post rebuttal] Please justify your final decision from above.
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Review #2
- Please describe the contribution of the paper
The paper incorporates a Fourier-series prior into a conditional latent diffusion model for periodicity-enhanced 3D+t cardiac mesh sequence generation. The major contributions are Fourier series fitting and the utilization of Fourier tokens for the conditional diffusion model. The experiments demonstrate that the proposed model outperforms previous approaches and achieves exceptional periodicity preservation.
- Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
1) The utilization of the Fourier series to keep periodicity has a good mathematical intuition and leads to effective implementation, and the paper clearly illustrates the motivation and implementation of this idea. 2) The constructed pipeline of the conditional latent diffusion model is straightforward to understand. There are no unclear or potentially meaningless designs. The employed diffusion transformer architecture is suitable for the task, as the diffused quantities are the fitted tokens. 3) The experiments are comprehensive, where qualitative and quantitative results are both presented. Ablation studies are carried out to verify the choice of K, a crucial hyperparameter of the approach. Both morphological metrics, such as the Sequence Root Mean Square error, and physiological metrics, such as ejection fraction, are employed in the experiments, enhancing the convincingness of the results.
- Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.
1) When measuring the geometric distances between two meshes, the paper computes the distances between corresponding vertices of the meshes. Since the mesh vertices are a consequence of the discretization of continuous surfaces, the vertices do not necessarily correspond in the same order. A more reasonable approach is to define such correspondence based on nearest neighbors, that is, the corresponding point in the point set B with respect to a given point a in the point set A is the point in B that is closest to a, just as how Chamfer Distance is computed. This problem might not strongly affect the experimental results, but could decrease their solidity. 2) In Table 2, 4D CardioSynth consistently predicts more accurate EDV and ESV than the proposed model, but the proposed method achieves a better EF prediction. It is questionable if this better EF prediction can support that the model preserves global pump function well, given that its predicted EDV and ESV are relatively less accurate.
- Please rate the clarity and organization of this paper
Good
- Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.
The submission does not mention open access to source code or data, but provides a clear and detailed description of the algorithm to ensure reproducibility.
- Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?
N/A
- Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2026/en/REVIEWER-GUIDELINES.html
N/A
- Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.
(5) Accept — should be accepted, independent of rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
The proposed method has a solid basis and reasonable implementation. The important details of it are well illustrated and explained. The experiments are comprehensive to support the arguments of the approach.
- Reviewer confidence
Confident but not absolutely certain (3)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
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- [Post rebuttal] Please justify your final decision from above.
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Review #3
- Please describe the contribution of the paper
The paper introduces 4D F-MeshLDM, a conditional latent diffusion framework for generating 3D+t cardiac meshes. The key technical idea is to enforce mathematically exact cycle periodicity by representing each subject’s latent trajectory as a truncated Fourier series and model the fourier series “tokens” with a DDPM conditioned on clinical covariates (age and gender). The authors report improvements over several baselines on a UK Biobank dataset of 5,000 time-resolved biventricular meshes.
- Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
- The paper is well written and easy to read and understand.
- The method is well described and the need for generation of cycle-consistent cardiac anatomies are well argued.
- Modelling the motion as a periodic fourier series is a novel addition enforcing periodicity into a conditional generative framework.
- The method is well evaluated and sufficiently compared to relevant SOTA methods, showing the benefit of the method.
- Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.
- The authors claim that the method can dynamically adjust to different cycle durations, but only use sequences with a set length. While I recognise the need for using a set sequence length for comparing to baselines, there is no support on how well the target cycle prediction mapping works.
- The clinical covariates are limited to only age and sex. The solution space of possible generated anatomies with these two covariates is very large. How is this taken into account in the evaluation?
- The ablation study is somewhat narrow and could be extended to i.e. meshVAE architectures, conditioning mechanisms and many more, but cannot be expected in a conference proceeding with limited space. The authors perspective on using latent-diffusion vs. direct mesh/voxel-space diffusion could however be an interesting addition.
- Th reproducibility is limited - while the paper has a section on implementation details that theoretically allow for some level of reproducibility I strongly encourage releasing the code for full reproducibility.
- Please rate the clarity and organization of this paper
Good
- Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.
The submission does not mention open access to source code or data, but provides a clear and detailed description of the algorithm to ensure reproducibility.
- Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?
N/A
- Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2026/en/REVIEWER-GUIDELINES.html
N/A
- Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.
(5) Accept — should be accepted, independent of rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
The method is interesting, well-described and proves good generative abilities.
- Reviewer confidence
Confident but not absolutely certain (3)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
N/A
- [Post rebuttal] Please justify your final decision from above.
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Author Feedback
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Meta-Review
Meta-review #1
- Your recommendation
Provisional Accept
- Please justify your decision. In case you deviate from the reviewers’ recommendations, explain in detail the reasons why. In case of an invitation for rebuttal, clarify which points are important to address in the rebuttal.
This paper proposes a conditional latent diffusion framework for 3D+t cardiac mesh generation, with the key idea of modeling latent motion trajectories using a truncated Fourier representation to enforce exact cycle periodicity. Reviewers agreed that this is a well-motivated and elegant methodological contribution to an important problem in virtual population synthesis and cardiac motion modeling.
The paper was consistently viewed as clearly written, technically sound, and well evaluated. In particular, reviewers appreciated the mathematical intuition and practical effectiveness of the Fourier-based motion representation, as well as the strong experimental validation on a large UK Biobank cohort with both anatomical and clinically relevant metrics. The comparisons to existing methods were considered appropriate and convincing.
The main weaknesses raised were relatively minor, including the need for clearer discussion of some evaluation metrics, more support for claims regarding varying cycle duration, and broader discussion of conditioning and reproducibility. These concerns do not outweigh the overall strength of the submission.