  In recent studies, diffusion models have shown promise as priors for solving
audio inverse problems. These models allow us to sample from the posterior
distribution of a target signal given an observed signal by manipulating the
diffusion process. However, when separating audio sources of the same type,
such as duet singing voices, the prior learned by the diffusion process may not
be sufficient to maintain the consistency of the source identity in the
separated audio. For example, the singer may change from one to another
occasionally. Tackling this problem will be useful for separating sources in a
choir, or a mixture of multiple instruments with similar timbre, without
acquiring large amounts of paired data. In this paper, we examine this problem
in the context of duet singing voices separation, and propose a method to
enforce the coherency of singer identity by splitting the mixture into
overlapping segments and performing posterior sampling in an auto-regressive
manner, conditioning on the previous segment. We evaluate the proposed method
on the MedleyVox dataset and show that the proposed method outperforms the
naive posterior sampling baseline. Our source code and the pre-trained model
are publicly available at https://github.com/yoyololicon/duet-svs-diffusion.
