We have found a series of resonances associated with the bound state (polyexcitons, PE(N)s) of N excitons up to N=6 in the emission spectra of diamond under two-photon excitation at around 10 K. Time-resolved spectra show a stepwise formation of PE(N)s with smaller to larger N, as well as a successive decay from larger to smaller N. At higher excitation levels, the transformation of PE(N)s into a condensed phase of electron-hole droplets occurs. The binding energies of the PE(N)s, normalized to the exciton Rydberg energy, agree well with those of silicon, suggesting the universality of the phenomena.