<p>With the development of wireless sensor networks, diffusion distributed networks have received widespread attention. In order to improve the robustness of existing diffusion subband algorithm in distributed networks against impulsive noise, the median absolute deviation (MAD) theorem is applied to the error boundary selection, and the robust set-membership diffusion normalization subband adaptive filtering algorithms is proposed in this paper. It is also analyzed for theoretical performance and computational complexity. Simulation results show that the algorithm has good robustness to impulsive noise in a distributed network with different nodes; in addition, it also exhibits good convergence performance in the face of generalized Gaussian noise.</p>