The diffusion property of wave functions in the non-periodic quantum walks is investigated in detail. The numerical results show that the multipath coherent superposition state can be precisely controlled by using position-dependent unitary evolution. Different evolutionary operations lead to the phenomenon of constructive or destructive interference and thus it affects the diffusion property. The diffusion speed of the walker can be changed by adjusting the evolution parameters of the system. The research on the diffusion speed of quantum walks is helpful to design new algorithms based on quantum walks.