Introduction: Despite advances in catheter ablation and pulmonary vein isolation (PVI), recurrence rates remain high, particularly in persistent atrial fibrillation (AF), underscoring the need for patient-specific computational models. Digital twins and in silico models have emerged as promising tools using statistical shape models, however, are often limited by the simplistic generative capabilities. In this study, we propose a self-supervised learning framework based on a β-variational autoencoder (β-VAE) to represent left atrial morphology from 3D point clouds derived from electroanatomical mapping data. The model aims to capture inter-patient anatomical variability within a compact latent space to create a morphological signature that is computationally efficient for downstream predictive tasks. Materials and Methods: We used a dataset of 340 left atrial meshes from patients with persistent AF (65.6±10.1 years, 33.3% female) acquired using the CARTO3 system. The meshes were preprocessed into a unit cube and centered downsampled point clouds of 2048 points, each described by 10 geometric features. Our proposed architecture includes a graph-based encoder integrating sequentially PointNet layers and dynamic edge convolutions, coupled with a hierarchical folding-based decoder to enable coarse-to-dense reconstruction of arterial geometry. The loss function combines Chamfer distance for reconstruction error and Kullback–Leibler divergence, weighted via a β-annealing strategy to encourage a structured latent representation. Results: The model achieved accurate reconstruction of atrial point clouds, with a Chamfer Distance of 0.1181±0.018 and a Hausdorff Distance of 0.28±0.059. These results show that the latent space preserves both global structure and local morphological details, in regions such as the atrial wall. Additionally, latent space interpolation shows smooth anatomical transitions between patients. Conclusion: These results demonstrate the potential of β-VAE-based point cloud models to capture atrial morphological variability and generate anatomically plausible shapes. The learned latent space can be incorporated into in silico cardiovascular frameworks or in dimensionality reduction representation predictive tasks.