  In this work, we define a diffusion-based generative model capable of both
music synthesis and source separation by learning the score of the joint
probability density of sources sharing a context. Alongside the classic total
inference tasks (i.e., generating a mixture, separating the sources), we also
introduce and experiment on the partial generation task of source imputation,
where we generate a subset of the sources given the others (e.g., play a piano
track that goes well with the drums). Additionally, we introduce a novel
inference method for the separation task based on Dirac likelihood functions.
We train our model on Slakh2100, a standard dataset for musical source
separation, provide qualitative results in the generation settings, and
showcase competitive quantitative results in the source separation setting. Our
method is the first example of a single model that can handle both generation
and separation tasks, thus representing a step toward general audio models.
