The motion energy model is the standard account of motion detection in animals from beetles to humans. Despite this common basis, we show here that a difference in the early stages of visual processing between mammals and insects leads this model to make radically different behavioural predictions. In insects, early filtering is spatially lowpass, which makes the surprising prediction that motion detection can be impaired by "invisible" noise, i.e. noise at a spatial frequency that elicits no response when presented on its own as a signal. We confirm this prediction using the optomotor response of praying mantis Sphodromantis lineola. This does not occur in mammals, where spatially bandpass early filtering means that linear systems techniques, such as deriving channel sensitivity from masking functions, remain approximately valid. Counter-intuitive effects such as masking by invisible noise may occur in neural circuits wherever a nonlinearity is followed by a difference operation.