arXiv:2610.32870v1 Announce Type: cross Abstract: In speech enhancement, standard supervised training requires pairs of noisy and clean speech. Such pairs are typically created by artificially degrading clean speech, leading to a domain mismatch between synthetic training data and real recordings. Noisy target training (NyTT) mitigates this limitation by training an enhancement model to predict a noisy recording from a noisier version generated by adding extra noise. However, since the training target is noisy, NyTT might learn to leave residual noise in the enhanced output. In this paper, we address this issue in NyTT by incorporating a Sinkhorn drifting loss that matches the distribution of the enhanced speech to that of unpaired clean speech. The Sinkhorn drifting loss attracts enhanced speech toward high-density regions of the clean-speech distribution while repelling it from the current enhanced-speech distribution in latent space. This loss uses only unpaired clean speech rather than the clean counterpart of each degraded recording, preserving the weakly-supervised nature of NyTT. Experimental results on VoiceBank-DEMAND and CHiME-3 real recordings demonstrate the efficacy of the proposed combination.