  We study the problem of symbolic music generation (e.g., generating piano
rolls), with a technical focus on non-differentiable rule guidance. Musical
rules are often expressed in symbolic form on note characteristics, such as
note density or chord progression, many of which are non-differentiable which
pose a challenge when using them for guided diffusion. We propose \oursfull
(\ours), a novel guidance method that only requires forward evaluation of rule
functions that can work with pre-trained diffusion models in a plug-and-play
way, thus achieving training-free guidance for non-differentiable rules for the
first time. Additionally, we introduce a latent diffusion architecture for
symbolic music generation with high time resolution, which can be composed with
SCG in a plug-and-play fashion. Compared to standard strong baselines in
symbolic music generation, this framework demonstrates marked advancements in
music quality and rule-based controllability, outperforming current
state-of-the-art generators in a variety of settings. For detailed
demonstrations, code and model checkpoints, please visit our project website:
https://scg-rule-guided-music.github.io/.
