This paper introduces a constrained source/filter model for semi-supervised speech separation based on non-negative matrix factor-ization (NMF). The objective is to inform NMF with prior knowledge about speech, providing a physically meaningful speech separation. To do so, a source/filter model (indicated as Instantaneous Mixture Model or IMM) is integrated in the NMF. Furthermore , constraints are added to the IMM-NMF, in order to control the NMF behaviour during separation, and to enforce its physical meaning. In particular, a speech specific constraint-based on the source/filter coherence of speech-and a method for the automatic adaptation of constraints' weights during separation are presented. Also, the proposed source/filter model is semi-supervised: during training, one filter basis is estimated for each phoneme of a speaker; during separation, the estimated filter bases are then used in the constrained source/filter model. An experimental evaluation for speech separation was conducted on the TIMIT speakers database mixed with various environmental background noises from the QUT-NOISE database. This evaluation showed that the use of adap-tive constraints increases the performance of the source/filter model for speaker-dependent speech separation, and compares favorably to fully-supervised speech separation. Index Terms: speech separation, non-negative matrix factorization, source/filter model, constraints.