  Emerging Denoising Diffusion Probabilistic Models (DDPM) have become
increasingly utilised because of promising results they have achieved in
diverse generative tasks with continuous data, such as image and sound
synthesis. Nonetheless, the success of diffusion models has not been fully
extended to discrete symbolic music. We propose to combine a vector quantized
variational autoencoder (VQ-VAE) and discrete diffusion models for the
generation of symbolic music with desired composer styles. The trained VQ-VAE
can represent symbolic music as a sequence of indexes that correspond to
specific entries in a learned codebook. Subsequently, a discrete diffusion
model is used to model the VQ-VAE's discrete latent space. The diffusion model
is trained to generate intermediate music sequences consisting of codebook
indexes, which are then decoded to symbolic music using the VQ-VAE's decoder.
The results demonstrate our model can generate symbolic music with target
composer styles that meet the given conditions with a high accuracy of 72.36%.
