and

We provide an explicit rigorous derivation of a diffusion limit – a stochas-tic differential equation with additive noise – from a deterministic skew-product flow. This flow is assumed to exhibit time-scale separation and has the form of a slowly evolving system driven by a fast chaotic flow. Under mild assumptions on the fast flow, we prove convergence to a stochastic dif-ferential equation as the time-scale separation grows. In contrast to existing work, we do not require the flow to have good mixing properties. As a con-sequence, our results incorporate a large class of fast flows, including the classical Lorenz equations.