The diffusion neural network can be cfficiently applied to the Gaussian processing. For example, a difference of two Gaussians(DOG) is performed by this network with ease. In this paper, we model a neural network to perform the function /t(.del.${Delta}^{2}$G) by using the diffusion neural network. This model is used to detect the edges of moving target in image. By this model not only moving target is separated from stationary background but also their trajectories are obtained using accumulated past information in the diffusion neural network. Furthermore this model needs a small number of connections per cell and the connection weights are fixed-valued. Therefore its hardware can be easily implemented with simple structure.