We determined the phase diagram involving diamond, graphite, and liquid carbon using a recently developed semiempirical potential. Using accurate free-energy calculations, we computed the solid-solid and solid-liquid phase boundaries for pressures and temperatures up to 400 GPa and 12 000 K, respectively. The graphite-diamond transition line that we computed is in good agreement with experimental data, confirming the accuracy of the employed empirical potential. On the basis of the computed slope of the graphite melting line, we rule out the hotly debated liquid-liquid phase transition of carbon. Our simulations allow us to give accurate estimates of the location of the diamond melting curve and of the graphite-diamond-liquid triple point.