This work develops a variation of diffusion learning by incorporating an adaptive construction for the combination weights through local fusion steps. This leads to an implementation with enhanced convergence rate and mean-square-error performance while maintaining the same level of complexity as standard implementations. The approach is based on formulating optimal or close-to-optimal learning and fusion steps using a proximity function rationale within neighborhoods. The first version of the algorithm employs exact fusion in the least-squares sense using inverses of uncertainty matrices. The second version replaces these matrices by diagonal approximations with reduced complexity. The result is an LMS-complexity scheme with improved performance for distributed learning over networks.