Virtual cohorts of cardiac anatomies that reflect real anatomical variability are essential for model personalization within cardiac digital twins, and in silico trials of medical devices. Conditional generative models construct such cohorts by learning the distribution of anatomies conditioned on patient characteristics. Such models can yield personalized anatomical priors against which pathological deviations can be quantified. Most existing deep learning-based generative models of cardiac anatomy rely on variational autoencoders (VAEs) or generative adversarial networks (GANs). However, these approaches impose Gaussian constraints on shape representations or require adversarial training, potentially leading to restricted representational capacity, mode collapse, or unstable training. Here we propose a novel conditional generative framework based on normalizing flows, for generation of biventricular anatomies conditioned on demographic and anthropometric characteristics, including age, sex, and body mass index. To circumvent the aforementioned limitations, we derive reduced-dimensional anatomical representations by leveraging diffeomorphisms and an autoencoder whose latent space is not constrained to any predefined distribution. To sample from this latent space, we develop a normalizing flow that learns a characteristics-informed mapping from Gaussian noise to anatomical representations. We train our model on a healthy subset (2274 individuals) of the UK Biobank imaging cohort, and compare its performance with baseline VAEs and GANs trained on the same dataset. We evaluate each model’s ability to reproduce the distributions of clinical biomarkers of the real cohort, including myocardial mass and ventricular volume, and assess anatomical variability using principal component analysis. Our findings reveal that formulating the anatomical generation as a normalizing flow in an unconstrained latent space yields expressive latent representations, and synthetic cohorts that resemble real cohort heterogeneity significantly better than VAEs and GANs. Additionally, the proposed approach offers improved interpretability through the computation of exact conditional likelihoods, enabling quantification of deviations from expected anatomy, and stable performance across different neural architectures.