The diffusion strategy for distributed learning from streaming data employs local stochastic gradient updates along with exchange of iterates over neighborhoods. In this work we establish that agents cluster around a network centroid in the mean-fourth sense and proceeded to study the dynamics of this point. We establish expected descent in non-convex environments in the large-gradient regime and introduce a short-term model to examine the dynamics over finitetime horizons. Using this model, we establish that the diffusion strategy is able to escape from strict saddle-points in O(1/mu) iterations, where mu denotes the step-size; it is also able to return approximately second-order stationary points in a polynomial number of iterations. Relative to prior works on the polynomial escape from saddle-points, most of which focus on centralized perturbed or stochastic gradient descent, our approach requires less restrictive conditions on the gradient noise process.