Achieving nuanced and accurate emulation of human voice has been a longstanding goal in artificial intelligence. Although significant progress has been made in recent years, the mainstream of speech synthesis models still relies on supervised speaker modeling and explicit reference utterances. However, there are many aspects of human voice, such as emotion, intonation, and speaking style, for which it is hard to obtain accurate labels. In this paper, we propose VoxGenesis, a novel unsupervised speech synthesis framework that can discover a latent speaker manifold and meaningful voice editing directions without supervision. VoxGenesis is conceptually simple. Instead of mapping speech features to waveforms deterministically, VoxGenesis transforms a Gaussian distribution into speech distributions conditioned and aligned by semantic tokens. This forces the model to learn a speaker distribution disentangled from the semantic content. During the inference, sampling from the Gaussian distribution enables the creation of novel speakers with distinct characteristics. More importantly, the exploration of latent space uncovers human-interpretable directions associated with specific speaker characteristics such as gender attributes, pitch, tone, and emotion, allowing for voice editing by manipulating the latent codes along these identified directions. We conduct extensive experiments to evaluate the proposed VoxGenesis using both subjective and objective metrics, finding that it produces significantly more diverse and realistic speakers with distinct characteristics than the previous approaches. We also show that latent space manipulation produces consistent and human-identifiable effects that are not detrimental to the speech quality, which was not possible with previous approaches. Audio samples of VoxGenesis can be found at: \url{https://bit.ly/VoxGenesis}.