Stochastic effects on convergence dynamics of reaction-diffusion Cohen-Grossberg neural networks (CGNNs) with delays are studied. By utilizing Poincaré inequality, constructing suitable Lyapunov functionals, and employing the method of stochastic analysis and nonnegative semimartingale convergence theorem, some sufficient conditions ensuring almost sure exponential stability and mean square exponential stability are derived. Diffusion term has played an important role in the sufficient conditions, which is a preeminent feature that distinguishes the present research from the previous. Two numerical examples and comparison are given to illustrate our results.