Natural conversations are spontaneous exchanges involving two or more people speaking in an intermittent manner. Therefore one expects such conversation to have intervals where some of the speakers are silent. Yet, most (multichannel) audio source separation (MASS) methods consider the sound sources to be continuously emitting on the total duration of the processed mixture. In this paper we propose a probabilistic model for MASS where the sources may have pauses. The activity of the sources is modeled as a hidden state, the diarization state, enabling us to activate/de-activate the sound sources at time frame resolution. We plug the diarization model within the spatial covariance matrix model proposed for MASS, and obtain an improvement in performance over the state of the art when separating mixtures with intermittent speakers.