Resting state functional magnetic resonance imaging (rsfMRI) data exhibits complex but structured patterns. However, the underlying origins are unclear and entangled in rsfMRI data. Here we establish a variational auto-encoder, as a generative model trainable with unsupervised learning, to disentangle the unknown sources of rsfMRI activity. After being trained with large data from the Human Connectome Project, the model has learned to represent and generate patterns of cortical activity and connectivity using latent variables. The latent representation and its trajectory represent the spatiotemporal characteristics of rsfMRI activity. The latent variables reflect the principal gradients of the latent trajectory and drive activity changes in cortical networks. Representational geometry captured as covariance or correlation between latent variables, rather than cortical connectivity, can be used as a more reliable feature to accurately identify subjects from a large group, even if only a short period of data is available in each subject. Our results demonstrate that VAE is a valuable addition to existing tools, particularly suited for unsupervised representation learning of resting state fMRI activity.