Driven by the need to solve increasingly complex optimization problems in\nsignal processing and machine learning, there has been increasing interest in\nunderstanding the behavior of gradient-descent algorithms in non-convex\nenvironments. Most available works on distributed non-convex optimization\nproblems focus on the deterministic setting where exact gradients are available\nat each agent. In this work and its Part II, we consider stochastic cost\nfunctions, where exact gradients are replaced by stochastic approximations and\nthe resulting gradient noise persistently seeps into the dynamics of the\nalgorithm. We establish that the diffusion learning strategy continues to yield\nmeaningful estimates non-convex scenarios in the sense that the iterates by the\nindividual agents will cluster in a small region around the network centroid.\nWe use this insight to motivate a short-term model for network evolution over a\nfinite-horizon. In Part II [2] of this work, we leverage this model to\nestablish descent of the diffusion strategy through saddle points in O(1/$\\mu$)\nsteps and the return of approximately second-order stationary points in a\npolynomial number of iterations.\n