A challenging problem in cognitive neuroscience is to relate the structural connectivity (SC) to the functional connectivity (FC) to better understand how large-scale network dynamics underlying human cognition emerges from the relatively fixed SC architecture. Recent modeling attempts point to the possibility of a single diffusion kernel giving a good estimate of the FC. We highlight the shortcomings of the single-diffusion-kernel model (SDK) and propose a multi-scale diffusion scheme. Our multi-scale model is formulated as a reaction-diffusion system giving rise to spatio-temporal patterns on a fixed topology. We hypothesize the presence of inter-regional co-activations (latent parameters) that combine diffusion kernels at multiple scales to characterize how FC could arise from SC. We formulated a multiple kernel learning (MKL) scheme to estimate the latent parameters from training data. Our model is analytically tractable and complex enough to capture the details of the underlying biological phenomena. The parameters learned by the MKL model lead to highly accurate predictions of subject-specific FCs from test datasets at a rate of 71%, surpassing the performance of the existing linear and non-linear models. We provide an example of how these latent parameters could be used to characterize age-specific reorganization in the brain structure and function.