# SYMPLEX: Controllable Symbolic Music Generation using Simplex Diffusion with Vocabulary Priors

arXiv: https://arxiv.org/abs/2405.12666 · HTML: https://mlsanity.com/paper/2405.12666/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 18 references that are in the map.
- First posted on arXiv 21 May 2024.

## Builds on (most cited first, 12 of 12)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Lumiere: A Space-Time Diffusion Model for Video Generation](https://mlsanity.com/paper/2401.12945/) (2024)
- [SSD-LM: Semi-autoregressive Simplex-based Diffusion Language Model for Text Generation and Modular Control](https://mlsanity.com/paper/2210.17432/) (2022)
- [Symbolic Music Generation with Diffusion Models](https://mlsanity.com/paper/2103.16091/) (2021)
- [TESS: Text-to-Text Self-Conditioned Simplex Diffusion](https://mlsanity.com/paper/2305.08379/) (2023)
- [Symbolic Music Generation with Non-Differentiable Rule Guided Diffusion](https://mlsanity.com/paper/2402.14285/) (2024)
- [CRASH: Raw Audio Score-based Generative Modeling for Controllable High-resolution Drum Sound Synthesis](https://mlsanity.com/paper/2106.07431/) (2021)
- [Polyffusion: A Diffusion Model for Polyphonic Score Generation with Internal and External Controls](https://mlsanity.com/paper/2307.10304/) (2023)
- [Discrete Diffusion Probabilistic Models for Symbolic Music Generation](https://mlsanity.com/paper/2305.09489/) (2023)
- [Symbolic Music Loop Generation with Neural Discrete Representations](https://mlsanity.com/paper/2208.05605/) (2022)
- [LooperGP: A Loopable Sequence Model for Live Coding Performance using GuitarPro Tablature](https://mlsanity.com/paper/2303.01665/) (2023)

## Built on by (most cited first, 2 of 2)

- [ProGress: Structured Music Generation via Graph Diffusion and Hierarchical Music Analysis](https://mlsanity.com/paper/2510.10249/) (2025)
- [Pay (Cross) Attention to the Melody: Curriculum Masking for Single-Encoder Melodic Harmonization](https://mlsanity.com/paper/2601.16150/) (2026)

## Abstract (arXiv)

We present a new approach for fast and controllable generation of symbolic music based on the simplex diffusion, which is essentially a diffusion process operating on probabilities rather than the signal space. This objective has been applied in domains such as natural language processing but here we apply it to generating 4-bar multi-instrument music loops using an orderless representation. We show that our model can be steered with vocabulary priors, which affords a considerable level control over the music generation process, for instance, infilling in time and pitch and choice of instrumentation -- all without task-specific model adaptation or applying extrinsic control.