Dynamic virtual populations are critical for realistic in-silico cardiovascular trials, yet current approaches primarily generate static anatomies, limiting their clinical and computational value. In this study, we present 4D CardioSynth, a generative framework for constructing dynamic 3D virtual populations of cardiovascular structures that change over time (3D+t). To model the complex interplay between cardiac structure and motion, we develop a factorised variational approach that disentangles spatial and temporal information in latent space, enabling independent control over anatomical variations and motion patterns. We demonstrate 4D CardioSynth’s performance using a diverse dataset of bi-ventricle shapes acquired from 6,500 patients across complete cardiac cycles. Our results illustrate the superiority of 4D CardioSynth over state-of-the-art methods with respect to anatomical specificity, diversity, and generalisability, as well as motion plausibility. This approach enables more accurate virtual trials for cardiovascular interventions.