This paper presents an efficient adaptive combination strategy for the distributed estimation problem over diffusion networks in order to improve robustness against the spatial variation of signal and noise statistics over the network. The concept of minimum variance unbiased estimation is used to derive the proposed adaptive combiner in a systematic way. The mean, mean-square, and steady-state performance analyses of the diffusion least-mean squares (LMS) algorithms with adaptive combiners are included and the stability of convex combination rules is proved. Simulation results show (i) that the diffusion LMS algorithm with the proposed adaptive combiners outperforms those with existing static combiners and the incremental LMS algorithm, and (ii) that the theoretical analysis provides a good approximation of practical performance.