Two new cellular-automata models of the diffusion process are pro- posed. They are based on integer states of cells instead of Boolean ones in the known models: asynchronous naive diffusion by Toffolli and block-synchronous Margolus diffusion. Computing experiments have been carried out with these models; they demonstrate a good correlation with this physical phenomenon. A dependence of a maximum state value of the multi-particle model on the averaging radius of the Boolean one with equal automaton noise level is obtained. The main advantages of the proposed models are (i) low automata noise and (ii) variable diffusion rate.