Brain states are frequently represented using a unidimensional scale measuring the richness of subjective experience (level of consciousness). This description assumes a mapping between the high-dimensional space of whole-brain configurations and the trajectories of brain states associated with changes in consciousness, yet this mapping and its properties remain unclear. We combine whole-brain modeling, data augmentation, and deep learning for dimensionality reduction to determine a mapping representing states of consciousness in a low-dimensional space, where distances parallel similarities between states. An orderly trajectory from wakefulness to patients with brain injury is revealed in a latent space whose coordinates represent metrics related to functional modularity and structure-function coupling, increasing alongside loss of consciousness. Finally, we investigate the effects of model perturbations, providing geometrical interpretation for the stability and reversibility of states. We conclude that conscious awareness depends on functional patterns encoded as a low-dimensional trajectory within the vast space of brain configurations.