Outliers and noises are unavoidable factors that cause performance of the distributed learning algorithms to be severely reduced. Developing a robust algorithm is vital in applications such as system identification and forecasting stock market, in which noise on the desired signals may intensely divert the solutions. In this paper, we propose a Robust Diffusion Stochastic Gradient Descent (RDSGD) algorithm based on the pseudo-Huber loss function which can significantly suppress the effect of Gaussian and non-Gaussian noises on estimation performances in the adaptive networks. Performance and convergence behavior of RDSGD are assessed in presence of the ????-stable and Mixed-Gaussian noises in the stationary and non-stationary environments. Simulation results show that the proposed algorithm can achieve both higher convergence rate and lower steady-state misadjustment than the conventional diffusion algorithms and several robust algorithms.

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