The document proposes an improved method for audio signal separation using supervised nonnegative matrix factorization (NMF) with time-variant basis deformation. The key contributions are: 1. Classifying supervised bases into time-variant attack and sustain parts and applying different all-pole model-based deformations to each. 2. Introducing discriminative training to avoid overfitting the interference signal and better separate the target. 3. An iterative approximated algorithm is presented that searches for deformation matrices representing the target signal while being constrained to also fit the mixture signal. 4. Experimental results on instrument mixtures show the proposed method achieves better signal-to-distortion ratio performance than previous supervised NMF techniques.