Abstract: In complex environments with variable errors and non-Gaussian interference， traditional diffusion-based adaptive filtering algorithms based on second-order statistics suffer from estimation bias and are highly sensitive to outliers and heavy-tailed noise， leading to a significant deterioration in distributed network performance. Accordingly， this study proposes an information-theoretic robust filtering method， i.e.， a diffusion minimum total error entropy with fiducial points （DMTEF） algorithm. This algorithm introduces the minimum error entropy criterion with fiducial points into the diffusion network， thereby significantly improving its robustness under non-Gaussian noise. To adapt to resource-constrained distributed networks， this study further proposes an improved method with low communication overhead， i.e.， a partial-diffusion DMTEF （DPMTEF） algorithm. This method reduces the single communication load per link from $M$ to $L$ coefficients by sharing pseudo-random coordinate selection rules and performing partial information exchange only in the combination phase. A quantitative analysis of the communication cost is also provided. Simulation results under typical non-Gaussian scenarios， such as mixed Gaussian noise， impulse noise， and $\alpha$-stable noise， demonstrate the highest filtering accuracy of the proposed DMTEF algorithm among the compared methods. Furthermore， the DPMTEF algorithm， while significantly reducing communication overhead， still achieves a filtering performance similar to that of the DMTEF algorithm， thus realizing an effective trade-off between communication efficiency and estimation accuracy.