arXiv:2610.29119v1 Announce Type: new Abstract: Target speech extraction (TSE) isolates a speaker's voice given an enrollment utterance, but existing work is validated almost exclusively without music. Discriminative methods are content-faithful yet masking-bounded; generative methods improve naturalness but may hallucinate, drift in identity, and require many steps. We present MuseFlow-TSE, a discriminative deletion, generative insertion framework for music-bearing scenes. Stage-1 is a music-aware cross-source band-split extractor that estimates target, interfering speakers, music, and noise under conservation and music-leakage constraints. Stage-2 is a data-to-data flow refiner initialized by the discriminative estimate, negatively conditioned on interference stems, and run for 1--4 difficulty-adaptive Euler steps with an end-to-end fidelity objective.