We present the first derivation of the phase field equations using a coarse-graining procedure on a microscopic master equation. The procedure leads to a mesoscopic nonlinear Fokker-Planck equation equivalent to a Cahn-Hilliard equation supplemented with a noise, but with specific prescriptions for the mobilities and the noise term. All the ingredients (chemical potentials, mobilities, stiffness coefficient) depend on the coarse-graining size. Finally, we show the ability of the phase field equations to describe a precipitation kinetics involving a nucleation and growth mechanism.