  Supervised deep learning approaches to underdetermined audio source
separation achieve state-of-the-art performance but require a dataset of
mixtures along with their corresponding isolated source signals. Such datasets
can be extremely costly to obtain for musical mixtures. This raises a need for
unsupervised methods. We propose a novel unsupervised model-based deep learning
approach to musical source separation. Each source is modelled with a
differentiable parametric source-filter model. A neural network is trained to
reconstruct the observed mixture as a sum of the sources by estimating the
source models' parameters given their fundamental frequencies. At test time,
soft masks are obtained from the synthesized source signals. The experimental
evaluation on a vocal ensemble separation task shows that the proposed method
outperforms learning-free methods based on nonnegative matrix factorization and
a supervised deep learning baseline. Integrating domain knowledge in the form
of source models into a data-driven method leads to high data efficiency: the
proposed approach achieves good separation quality even when trained on less
than three minutes of audio. This work makes powerful deep learning based
separation usable in scenarios where training data with ground truth is
expensive or nonexistent.
