Brain states are conventionally divided into wake, slow wave sleep (SWS) and rapid eye movement (REM) sleep based on distinct patterns of neural activity and muscle tone. However, recently available large-scale recordings indicate that this conventional division of brain states is insufficient to account for rich heterogeneity of neural dynamics on the global scale. During sleep, neural activity in some brain regions can exhibit awake signatures and vice versa [1,2]. While brain states provide the backdrop for any activity underlying behavioral functions, the spatiotemporal structure of multi-regional brain states remains unexplored. We simultaneously recorded electromyogram (EMG) and local field potentials (LFP) at 14 sites across the mouse cortex during the natural variation of sleep and wake cycles continuously over multiple days. To characterize the heterogeneity of brain states in these multi-regional recordings, we developed an approach to uncover a low- dimensional manifold on which these states evolve. We use unsupervised dimensionality reduction based on a variational autoencoder (VAE) that predicts the next point in time. We trained the model on activity from an individual channel to uncover a local characterization of brain states. For single channels, the inferred manifold revealed three major clusters corresponding with human-expert labels of the basic wake, SWS, and REM states. Classical frequency bands, such as alpha, beta, and gamma, contributed nonlinearly to the inferred manifold. Applying the model to other electrodes, we found profound differences in the expression of states across cortical areas, particularly, the lack of REM-like activity in the lateral somatosensory cortex. We found that heterogeneity of states largely appears during transition periods between primary states, suggesting a more continuous global manifold. Our work provides a framework for quantifying heterogeneous brains states and shows that the regional co-existence of wake and sleep states is a common feature of global brain activity.