We give a criterion to differentiate between dissipative and diffusive quantum operations. It is based on the classical idea that dissipative processes contract volumes in phase space. We define a quantity that can be regarded as quantum phase space contraction rate and which is related to a fundamental property of quantum channels: nonunitality. We relate it to other properties of the channel and also show a simple example of dissipative noise composed with a chaotic map. The emergence of attractor-like structures is displayed.