We propose a novel unsupervised approach for sleep dynamics exploration and automatic annotation by combining modern harmonic analysis tools. Specifically, we apply diffusion-based algorithms, diffusion map (DM), and alternating diffusion (AD) algorithms, to reconstruct the intrinsic geometry of sleep dynamics by reorganizing the spectral information of an electroencephalogram (EEG) extracted from a nonlinear-type time frequency analysis tool, the synchrosqueezing transform (SST). The visualization is achieved by the nonlinear dimension reduction properties of DM and AD. Moreover, the reconstructed nonlinear geometric structure of the sleep dynamics allows us to achieve the automatic annotation purpose. The hidden Markov model is trained to predict the sleep stage. The prediction performance is validated on a publicly available benchmark database, Physionet Sleep-EDF [extended] SC∗ and ST∗, with the leave-one-subject-out cross-validation. The overall accuracy and macro F1 achieve 82.57% and 76% in Sleep-EDF SC∗ and 77.01% and 71.53% in Sleep-EDF ST∗, which is compatible with the state-of-the-art results by supervised learning-based algorithms. The results suggest the potential of the proposed algorithm for clinical applications.