We explore how a few-layer graphene can undergo phase transformation into thin diamond film under reduced or no pressure, if the process is facilitated by hydrogenation of the surfaces. Such a "chemically induced phase transition" is inherently nanoscale phenomenon, when the surface conditions directly affect thermodynamics, and the transition pressure depends greatly on film thickness. For the first time we obtain, by ab initio computations of the Gibbs free energy, a phase diagram (P, T, h) of quasi-two-dimensional carbon-diamond film versus multilayered graphene. It describes accurately the role of film thickness h and shows the feasibility of creating novel quasi-two-dimensional materials. Further, the role of finite diameter of graphene flakes and possible formation of the diamond films with the (110) surface are described as well.