Diffusion wavelets extract information from graph signals at different scales of resolution by utilizing graph diffusion operators raised to various powers, known as diffusion scales. Traditionally, these scales are chosen to be dyadic integers, $2^j$. Here, we propose a novel, unsupervised method for selecting the diffusion scales based on ideas from information theory. We then show that our method can be incorporated into wavelet-based GNNs, which are modeled after the geometric scattering transform, via graph classification experiments.