The influence of diffusive nonlinearity on mobility of photovoltaic lattice solitons is demonstrated. The dynamical evolution of collision between photovoltaic lattice solitons and nonlinear lattices are simulated numerically. The results show the lattice solitons with a transverse velocity have complicated behaviors and will not propagate with an oblique trajectory. When considering the diffusive nonlinearity, we find that diffusive nonlinearity can introduce a nonlinear chirped phase to lattice soliton and the lattice soliton with a special incident angle can become a "tilted soliton".