This paper presents a cooperative filtering scheme for online parameter identification of 2D diffusion processes using data collected by a mobile sensor network moving in the diffusion field. The diffusion equation is incorporated into the information dynamics associated with the trajectories of the mobile sensors. A cooperative Kalman filter is developed to provide estimates of field values, the gradient, and the temporal variations of the field values along the trajectories. This leads to a co-design scheme for state estimation and parameter identification for diffusion processes that is different from using static sensors. Utilizing the state estimates from the filters, a recursive least square (RLS) algorithm is designed to estimate the unknown diffusion coefficient of the field. A set of sufficient conditions is derived for the convergence of the cooperative Kalman filter. Simulation results show satisfactory performance of the proposed method.