Graph filters, defined as polynomial functions of a graph-shift operator (GSO), play a key role in signal processing over graphs. In this work, we are interested in the adaptive and distributed estimation of graph filter coefficients from streaming graph signals. To this end, diffusion LMS strategies can be employed. However, most popular GSOs such as those based on the graph Laplacian matrix or the adjacency matrix are not energy preserving. This may result in a large eigenvalue spread and a slow convergence of the graph diffusion LMS. To address this issue and improve the transient performance, we introduce a graph diffusion LMS-Newton algorithm. We also propose a computationally efficient preconditioned diffusion strategy and we study its performance.