We calculated the dynamics of photoinduced domain growth in two-dimensional models. When a single molecular cell is excited by a photon, vibronic interaction induces energy transfer to the vibration mode in the cell and subsequently the inter-cell interaction helps energy distribution to the adjacent cells. Since nonadiabtic transition between ground and the excited electronic states within a cell is important to consider the dynamics, we fully quantized the vibrational degree of freedom to solve the time-dependent Schrödinger equation numerically. We show that both the interaction between the relevant vibration modes and the electronic states of different cells is necessary to the domain growth in higher dimensional systems.