The flow in a diffuser is unsteady in the range of optimum pressure recovery; diffusers can therefore be a major source of noise in pipework systems. A theory is developed to predict the frequency of this noise and good agreement with experimental results, for both conical and rectangular diffusers, is demonstrated. The acoustics of the duct to which a diffuser is connected are found to have a crucial effect on the unsteady flow within the diffuser, a point which has been overlooked previously in the literature. Once this is recognized, it is possible to reconcile experimental results for air and water diffusers.