MeshLDM: 3D Cardiac Mesh Generation

• MeshLDM is a latent diffusion model for generating phase-specific 3D left ventricular meshes using a compact latent code from a mesh autoencoder.
• It employs a two-stage process that first encodes fixed-topology meshes with graph convolutions and then denoises latent vectors with a fully connected MLP.
• Evaluations using clinical and geometric metrics show low relative error in key cardiac measures, though the generated distribution exhibits reduced diversity.

Searching arXiv for MeshLDM and closely related mesh latent diffusion work to ground the article in current papers. MeshLDM is a latent diffusion framework for generating realistic 3D meshes of cardiac anatomy, introduced for human left ventricular anatomy reconstructed from cardiac MRI in post-myocardial-infarction cohorts. Its central design choice is to avoid diffusion over full mesh coordinate vectors and instead denoise a compact latent code learned by a mesh autoencoder, after which the decoder reconstructs the surface geometry. In the reported implementation, MeshLDM treats end-diastolic and end-systolic anatomy as separate unconditional generative tasks and targets anatomically meaningful virtual populations for data augmentation, computational cardiology, and in-silico studies (Mozyrska et al., 18 Aug 2025).

1. Clinical and geometric scope

MeshLDM was developed for direct generation of 3D left ventricular meshes rather than image volumes, point clouds, or rasterized geometry. The application domain is clinically specific: left ventricular anatomies from patients with acute myocardial infarction, including both ST-elevation myocardial infarction and non-ST-elevation myocardial infarction. The method models two cardiac phases separately, end-diastole and end-systole, corresponding respectively to the relaxed and contracted ventricle (Mozyrska et al., 18 Aug 2025).

The representation presumes a fixed-topology mesh setting. Every mesh has the same number of vertices, and the vertices are consistently ordered across samples. This supplies pointwise correspondence inherited from dataset construction and permits each mesh to be treated as a fixed-size vector of concatenated $(x,y,z)$ coordinates. The same assumption makes mesh-native latent learning feasible with graph-convolutional and pooling operators, but it also constrains applicability to registered populations rather than variable-topology anatomy (Mozyrska et al., 18 Aug 2025).

The scope is therefore narrower than generic 3D shape generation. MeshLDM is not a free-form topology generator, not a phase-conditioned cardiac-cycle model, and not a simulator of temporal mechanics. It is a phase-specific generator of anatomically plausible ventricular surfaces within a clinically delimited cohort.

2. Model architecture and latent diffusion formulation

The architecture has two stages: a mesh autoencoder derived from MeshVAE, followed by a latent-space denoising model. The autoencoder uses geometric deep learning layers, specifically graph convolutions and mesh pooling, to map an input mesh to a latent code of dimension $m=16$ and reconstruct the mesh from that code. The paper states that KL regularization is used and that the same $\beta$-VAE framework and parameters from earlier MeshVAE work are adopted. A faithful formulation of the setup is

$$z \sim q_\phi(z \mid x), \qquad \hat{x} = D_\theta(z),$$

with training objective of the form

$$\mathcal{L}_{\text{AE}} = \mathcal{L}_{\text{recon}}(x,\hat{x}) + \beta\, D_{\mathrm{KL}}\!\left(q_\phi(z\mid x)\,\|\,p(z)\right),$$

where the prior is typically $p(z)=\mathcal{N}(0,I)$. The paper does not restate the exact reconstruction term inherited from MeshVAE, so a more specific formula is not warranted (Mozyrska et al., 18 Aug 2025).

After the autoencoder is trained, all meshes are encoded into normalized latent vectors, and diffusion is performed in that 16-dimensional latent space. The denoiser is not a U-Net; it is a fully connected multilayer perceptron with 6 fully connected layers, each of input and output dimension 16, with the Swish-1 activation function applied between layers. The diffusion timestep $t$ is injected at each layer through a sinusoidal positional embedding following Ho et al.’s DDPM formulation. The scheduler is the standard DDPM scheduler as implemented in Hugging Face Diffusers, with 1000 diffusion steps and a linearly increasing noise variance schedule from $\beta_0=0.0001$ to $\beta_T=0.02$ (Mozyrska et al., 18 Aug 2025).

In standard DDPM notation consistent with the scheduler, the forward process is

$$q(z_t \mid z_{t-1}) = \mathcal{N}\!\left(z_t; \sqrt{1-\beta_t}\, z_{t-1}, \beta_t I\right),$$

or equivalently

$m=16$0

with

$m=16$1

Thus,

$m=16$2

The denoiser is trained with the standard noise-prediction objective

$m=16$3

At inference, the reverse process iteratively denoises an initial Gaussian latent and the decoder reconstructs a synthetic mesh,

$m=16$4

No conditioning variable is used in the reported MeshLDM implementation. Instead, separate unconditional models are trained for end-diastole and end-systole because the paper argues that naively mixing both phases in one unconditional model could yield anatomically implausible blends (Mozyrska et al., 18 Aug 2025).

3. Data representation, preprocessing, and training protocol

The dataset comprises 1034 left ventricular meshes at end-diastole and 1034 left ventricular meshes at end-systole, derived from cine MR images of post-myocardial-infarction patients. The cohort includes both STEMI and NSTEMI cases. The train/validation/test split is approximately 70% / 5% / 25%, and the reported test-set size is $m=16$5. The data are not public because of ethical and legal constraints, although generated virtual data can be requested (Mozyrska et al., 18 Aug 2025).

Before training, each mesh is standardized coordinate-wise: for each coordinate dimension, the training-set mean is subtracted and divided by the training-set standard deviation. The paper does not provide the explicit number of vertices or faces in the current text and does not restate remeshing-resolution details, so those details remain unspecified. What is explicit is the latent dimension, which is 16, and the requirement of consistent vertex ordering across all samples (Mozyrska et al., 18 Aug 2025).

Training is staged rather than joint. For each cardiac phase separately, the autoencoder is trained first using batch size 8, the Adam optimizer, learning rate 0.001, and 250 epochs. The denoising model is then trained on normalized latent vectors using batch size 64, the Adam optimizer, and an initial learning rate of 0.005 with a PyTorch LambdaLR scheduler. The diffusion scheduler uses 1000 steps with the linear $m=16$6 schedule from 0.0001 to 0.02. No classifier-free guidance, no conditioning, and no DDIM sampling are described (Mozyrska et al., 18 Aug 2025).

At generation time, 1000 random vectors are sampled from a normal distribution for each phase-specific model, passed through the reverse denoising process, rescaled by the latent standard deviation and shifted by the latent mean to undo normalization, and finally decoded to synthetic 3D meshes. Because the end-diastolic and end-systolic models are separate, the generated samples are not in correspondence across phases.

4. Evaluation methodology

MeshLDM is evaluated with both clinical metrics and geometric generative metrics. The clinical metrics are left ventricular endocardial volume and left ventricular myocardial mass. Myocardial mass is computed from myocardial volume times tissue density with

$m=16$7

These metrics assess whether the generated anatomies lie in a physiologically plausible range (Mozyrska et al., 18 Aug 2025).

For geometric evaluation, each mesh is converted to a point cloud by keeping only vertices and discarding faces and edges. The generated set and reference set are denoted $m=16$8 and $m=16$9, and 285 generated meshes are randomly selected from the 1000 synthesized samples so that both sets have equal size. The underlying distance is Chamfer distance,

$\beta$0

From this, the paper uses coverage,

$\beta$1

minimum matching distance,

$\beta$2

and 1-nearest-neighbor accuracy,

$\beta$3

A value of 1-NNA near 50% indicates that the generated and reference distributions are difficult to distinguish. The paper also computes these metrics between random training-set samples and the test set as an approximate upper bound on achievable distributional similarity (Mozyrska et al., 18 Aug 2025).

Because MeshLDM models end-diastole and end-systole separately rather than jointly, it does not support phase-paired evaluation such as ejection fraction. This is not a minor omission but a direct consequence of the formulation: the method generates anatomies at isolated phases rather than a temporally coherent cardiac cycle.

5. Empirical performance

Qualitatively, MeshLDM generates plausible end-diastolic and end-systolic left ventricular anatomies. The end-diastolic samples show the expected larger cavity volume and thinner myocardium, whereas the end-systolic samples are more contracted with thicker myocardium. The generated meshes also vary in clinically relevant shape attributes including apex pointedness, longitudinal curvature, overall heart size, mid-cavity diameter, myocardial thickness, basal plane tilt, and left ventricular elongation. The authors explicitly note, however, that diversity is somewhat lower than in the real test set (Mozyrska et al., 18 Aug 2025).

The principal quantitative headline is an average 2.4% difference in population mean across the reported clinical metrics relative to the gold-standard test data. At end-diastole, the gold-standard left ventricular cavity volume is $\beta$4 mL and MeshLDM generates $\beta$5 mL, corresponding to a relative error of 0.32%. End-diastolic left ventricular mass is $\beta$6 g in the test set versus $\beta$7 g for MeshLDM, a relative error of 0.08%. At end-systole, the gold-standard cavity volume is $\beta$8 mL while MeshLDM gives $\beta$9 mL, a 7.03% relative error. End-systolic left ventricular mass is $$z \sim q_\phi(z \mid x), \qquad \hat{x} = D_\theta(z),$$0 g in the test set versus $$z \sim q_\phi(z \mid x), \qquad \hat{x} = D_\theta(z),$$1 g for MeshLDM, a 2.09% relative error. In all cases, the MeshLDM standard deviations are lower than those in the test set, indicating under-dispersion (Mozyrska et al., 18 Aug 2025).

The geometric metrics show strong local fidelity but incomplete distributional coverage. For end-diastole, the training-vs-test upper-bound comparison gives 1-NNA $$z \sim q_\phi(z \mid x), \qquad \hat{x} = D_\theta(z),$$2, coverage $$z \sim q_\phi(z \mid x), \qquad \hat{x} = D_\theta(z),$$3, and MMD $$z \sim q_\phi(z \mid x), \qquad \hat{x} = D_\theta(z),$$4 mm. MeshLDM achieves 1-NNA $$z \sim q_\phi(z \mid x), \qquad \hat{x} = D_\theta(z),$$5, coverage $$z \sim q_\phi(z \mid x), \qquad \hat{x} = D_\theta(z),$$6, and MMD $$z \sim q_\phi(z \mid x), \qquad \hat{x} = D_\theta(z),$$7 mm. For end-systole, the training-vs-test comparison gives 1-NNA $$z \sim q_\phi(z \mid x), \qquad \hat{x} = D_\theta(z),$$8, coverage $$z \sim q_\phi(z \mid x), \qquad \hat{x} = D_\theta(z),$$9, and MMD $$\mathcal{L}_{\text{AE}} = \mathcal{L}_{\text{recon}}(x,\hat{x}) + \beta\, D_{\mathrm{KL}}\!\left(q_\phi(z\mid x)\,\|\,p(z)\right),$$0 mm, whereas MeshLDM gives 1-NNA $$\mathcal{L}_{\text{AE}} = \mathcal{L}_{\text{recon}}(x,\hat{x}) + \beta\, D_{\mathrm{KL}}\!\left(q_\phi(z\mid x)\,\|\,p(z)\right),$$1, coverage $$\mathcal{L}_{\text{AE}} = \mathcal{L}_{\text{recon}}(x,\hat{x}) + \beta\, D_{\mathrm{KL}}\!\left(q_\phi(z\mid x)\,\|\,p(z)\right),$$2, and MMD $$\mathcal{L}_{\text{AE}} = \mathcal{L}_{\text{recon}}(x,\hat{x}) + \beta\, D_{\mathrm{KL}}\!\left(q_\phi(z\mid x)\,\|\,p(z)\right),$$3 mm. The closeness of MMD to the training upper bound indicates that generated shapes are geometrically close to real examples, especially at end-diastole, but the elevated 1-NNA and reduced coverage indicate a narrower and more easily distinguishable generated distribution. The discrepancy is larger for end-systole, suggesting that end-systolic anatomy is harder for the model to capture (Mozyrska et al., 18 Aug 2025).

6. Limitations, misconceptions, and comparison with MeshVAE

MeshLDM is often best understood as a first latent-diffusion model for phase-specific cardiac mesh generation rather than as a general solution to cardiac anatomy synthesis. Its main limitations are explicit. The dataset is relatively small for diffusion modeling, with only 1034 meshes per phase. The model is unconditional and phase-specific, so it cannot jointly model end-diastole and end-systole or generate phase-paired anatomies. It assumes fixed mesh topology with consistent vertex ordering. The data are pathology-specific, coming from post-myocardial-infarction patients, and generalization to healthy cohorts or other disease populations is not demonstrated. The evaluation is clinically and geometrically informative but does not establish downstream benefit in simulation or disease-classification tasks (Mozyrska et al., 18 Aug 2025).

A common misconception is to treat MeshLDM as a temporal or motion model. It is not. The method produces static phase-specific anatomies, and the generated end-diastolic and end-systolic samples are not in correspondence. A second misconception is to regard it as a variable-topology 3D generator. It is not; the method relies on a registered fixed-topology mesh population. A third misconception is to equate latent diffusion with automatic improvement over earlier mesh VAEs. The reported comparison is more nuanced (Mozyrska et al., 18 Aug 2025).

Against MeshVAE, MeshLDM is better for end-diastolic clinical means and less favorable for end-systolic means. For example, in end-diastolic cavity volume, MeshLDM has 0.32% relative mean error versus 4.03% for MeshVAE, and in end-diastolic mass, 0.08% versus 5.37%. But in end-systolic cavity volume, MeshVAE is more accurate at 0.83% versus 7.03% for MeshLDM, and in end-systolic mass MeshVAE matches the gold-standard mean exactly while MeshLDM has 2.09% error. MeshVAE also better preserves diversity, as reflected in coverage and end-systolic distributional similarity. The paper therefore characterizes MeshLDM as a strong alternative rather than an across-the-board improvement (Mozyrska et al., 18 Aug 2025).

7. Relation to later and adjacent models

Subsequent work extends the underlying idea from static anatomy generation to full-cycle cardiac motion. A later variant, 4D F-MeshLDM, is a conditional latent diffusion framework for generating full-cycle $$\mathcal{L}_{\text{AE}} = \mathcal{L}_{\text{recon}}(x,\hat{x}) + \beta\, D_{\mathrm{KL}}\!\left(q_\phi(z\mid x)\,\|\,p(z)\right),$$4 cardiac meshes. It combines a convolutional mesh VAE, a structural latent-space motion model that fits latent trajectories with a truncated Fourier series, and a Transformer DDPM prior that generates Fourier coefficient tokens conditioned on clinical covariates. In that system, periodicity is enforced analytically rather than learned implicitly: inverse Fourier synthesis yields latent trajectories with exact latent-space cycle closure by construction. The reported implementation uses latent dimension $$\mathcal{L}_{\text{AE}} = \mathcal{L}_{\text{recon}}(x,\hat{x}) + \beta\, D_{\mathrm{KL}}\!\left(q_\phi(z\mid x)\,\|\,p(z)\right),$$5, Fourier order $$\mathcal{L}_{\text{AE}} = \mathcal{L}_{\text{recon}}(x,\hat{x}) + \beta\, D_{\mathrm{KL}}\!\left(q_\phi(z\mid x)\,\|\,p(z)\right),$$6, and therefore $$\mathcal{L}_{\text{AE}} = \mathcal{L}_{\text{recon}}(x,\hat{x}) + \beta\, D_{\mathrm{KL}}\!\left(q_\phi(z\mid x)\,\|\,p(z)\right),$$7 spectral tokens, and conditions on age and sex via Adaptive Layer Normalization. On 5,000 UK Biobank subjects with 4000/500/500 train/validation/test split, 4D F-MeshLDM is reported to outperform state-of-the-art baselines in anatomical fidelity and to achieve near-zero cycle closure error, including volume cycle consistency of $$\mathcal{L}_{\text{AE}} = \mathcal{L}_{\text{recon}}(x,\hat{x}) + \beta\, D_{\mathrm{KL}}\!\left(q_\phi(z\mid x)\,\|\,p(z)\right),$$8 and mesh cycle consistency of $$\mathcal{L}_{\text{AE}} = \mathcal{L}_{\text{recon}}(x,\hat{x}) + \beta\, D_{\mathrm{KL}}\!\left(q_\phi(z\mid x)\,\|\,p(z)\right),$$9 (Lan et al., 2 Jun 2026).

This suggests a clear trajectory in mesh-native cardiac generative modeling: the original MeshLDM formulation addresses static, phase-specific ventricular surfaces, whereas 4D F-MeshLDM moves temporal structure into a compact spectral motion descriptor and makes controllability explicit through covariate conditioning. The conceptual continuity lies in latent generative modeling on mesh-aligned representations; the principal difference is that the later framework generates motion descriptors rather than isolated phase anatomies (Lan et al., 2 Jun 2026).

The name “LDM” also creates a separate terminological ambiguity. “LDM: Large Tensorial SDF Model for Textured Mesh Generation” is a mesh-generation paper enabled by diffusion-generated views, but it is not a latent diffusion model over meshes or mesh latents. In that system, diffusion is used only as an upstream multi-view image synthesizer through MVDream or ImageDream, while the actual 3D generator is a feed-forward transformer that predicts a tensorial signed distance field and refines it with FlexiCubes to produce a textured triangular mesh. The title acronym “LDM” there is specific to that paper and should not be read as “latent diffusion model” in the MeshLDM sense (Xie et al., 2024).

A broader but still non-mesh-native neighboring line is latent diffusion for topology optimization, where diffusion operates on latent codes of rasterized $p(z)=\mathcal{N}(0,I)$0 material-layout fields rather than on irregular meshes. That literature is conceptually aligned with MeshLDM in its use of latent compression and conditional diffusion, but it is geometrically distinct because the generated objects are dense finite-element fields rather than surface meshes (Lutheran et al., 7 Aug 2025).