The experimental study of the CO_{2} phase diagram is hampered by strong kinetic effects leading to wide regions of metastability and to large uncertainties in the location of some phase boundaries. Here, we determine CO_{2}'s thermodynamic phase boundaries by means of ab initio calculations of the Gibbs free energy of several solid phases of CO_{2} up to 50 Gigapascals. Temperature effects are included in the quasiharmonic approximation. Contrary to previous suggestions, we find that the boundary between molecular forms and the nonmolecular phase V has, indeed, a positive slope and starts at 21.5 GPa at T=0 K. A triple point between phase IV, V, and the liquid phase is found at 35 GPa and 1600 K, indicating a broader region of stability for the nonmolecular form than previously thought. The experimentally determined boundary line between CO_{2}-II and CO_{2}-IV phases is reproduced by our calculations, indicating that kinetic effects do not play a major role in that particular transition. Our results also show that CO_{2}-III is stabilized at high temperature and its stability region coincides with the P-T conditions where phase VII has been reported experimentally; instead, phase II is the most stable molecular phase at low temperatures, extending its region of stability to every P-T condition where phase III is reported experimentally.