The diffusion neural network forms a Gaussian distribution by transferring an excitation to the surround. A DOG(difference of two Gaussians) is obtained by the diffusion neural network. This type of the DOG, which can detect the intensity changes of an image, has the same shape as a LOG(Laplacian of a Gaussian:${Delta}^2$G) and narrow band pass characteristics. In this paper we show that another type of the DOG which has a very narrow Gaussian for the excitatory and a very wide Gaussian for the inhibitory, can be formed by the diffusion process of this network, This type of the DOG has a wide band width in spatial frequency domain and can be used efficiently in detecting special type of edges.