  Denoising Diffusion Probabilistic Models (DDPMs) have made great strides in
generating high-quality samples in both discrete and continuous domains.
However, Discrete DDPMs (D3PMs) have yet to be applied to the domain of
Symbolic Music. This work presents the direct generation of Polyphonic Symbolic
Music using D3PMs. Our model exhibits state-of-the-art sample quality,
according to current quantitative evaluation metrics, and allows for flexible
infilling at the note level. We further show, that our models are accessible to
post-hoc classifier guidance, widening the scope of possible applications.
However, we also cast a critical view on quantitative evaluation of music
sample quality via statistical metrics, and present a simple algorithm that can
confound our metrics with completely spurious, non-musical samples.
