The long standing problem of the α-γ phase transition in cerium metal is approached by treating all electrons at the same quantum mechanical level, using both hybrid functionals (PBE0 and HSE06) and exact exchange plus correlation in the random-phase approximation (EX+cRPA). The exact-exchange contribution in PBE0 and HSE06 is crucial to produce two distinct solutions that can be associated with the α and γ phases. An analysis of the band structure and the electron density reveals a localization and delocalization behavior of the f electrons in the γ and α phases, respectively. However, a quantitative agreement with the extrapolated phase diagram to zero temperature is achieved only with EX+cRPA, based on the hybrid functional starting point. We predict that a pressure induced phase transition should exist at or close to T=0K. By adding entropic contributions we determine the pressure-temperature phase diagram, which is in reasonable agreement with experiment.