Here researchers via novel potential energy surface global exploration, report seven types low energy intermediate structures at the atomic level that are key to the kinetics of graphite to diamond solid phase transition. On the basis of quantitative kinetics data, they show that hexagonal diamond has a facile initial nucleation mechanism inside graphite matrix and faster propagation kinetics owing to the presence of three coherent graphite/hexagonal diamond interfaces, forming coherent nuclei in graphite matrix. By contrast, for the lack of coherent nucleus core, the growth of cubic diamond is at least 40 times slower and its growth is inevitably mixing with that of hexagonal diamond.