We propose a novel approach to improve adaptive decorrelation filtering- (ADF-) based speech source separation in diffuse noise. The effects of noise on system adaptation and separation outputs are handled separately. First, fast noise compensation (NC) is developed for adaptation of separation filters, forcing ADF to focus on source separation; next, output noises are suppressed by speech enhancement. By tracking noise components in output cross-correlation functions, the bias effect of noise on the system adaptation objective function is compensated, and by adaptively estimating output noise autocorrelations, the speech separation output is enhanced. For fast noise compensation, a blockwise fast ADF (FADF) is implemented. Experiments were conducted on real and simulated diffuse noises. Speech mixtures were generated by convolving TIMIT speech sources with acoustic path impulse responses measured in a real room with reverberation time second. The proposed techniques significantly improved separation performance and phone recognition accuracy of ADF outputs.