# Discrete Diffusion Probabilistic Models for Symbolic Music Generation

arXiv: https://arxiv.org/abs/2305.09489 · HTML: https://mlsanity.com/paper/2305.09489/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Placed in Audio, speech and music, one of 14 directions in Diffusion models.
- Builds on 18 of its 31 references that are in the map.
- First posted on arXiv 16 May 2023.

## Placed in

- Diffusion models / [Audio, speech and music](https://mlsanity.com/diffusion/audio-speech-and-music/)

## Builds on (most cited first, 18 of 18)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions](https://mlsanity.com/paper/2102.05379/) (2021)
- [Reliable Fidelity and Diversity Metrics for Generative Models](https://mlsanity.com/paper/2002.09797/) (2020)
- [Symbolic Music Generation with Diffusion Models](https://mlsanity.com/paper/2103.16091/) (2021)
- [A Hierarchical Latent Vector Model for Learning Long-Term Structure in Music](https://mlsanity.com/paper/1803.05428/) (2018)
- [Compound Word Transformer: Learning to Compose Full-Song Music over Dynamic Directed Hypergraphs](https://mlsanity.com/paper/2101.02402/) (2021)
- [MusicBERT: Symbolic Music Understanding with Large-Scale Pre-Training](https://mlsanity.com/paper/2106.05630/) (2021)
- [MidiNet: A Convolutional Generative Adversarial Network for Symbolic-domain Music Generation](https://mlsanity.com/paper/1703.10847/) (2017)
- [Unleashing Transformers: Parallel Token Prediction with Discrete Absorbing Diffusion for Fast High-Resolution Image Generation from Vector-Quantized Codes](https://mlsanity.com/paper/2111.12701/) (2021)
- [Multi-instrument Music Synthesis with Spectrogram Diffusion](https://mlsanity.com/paper/2206.05408/) (2022)
- [BERT-like Pre-training for Symbolic Piano Music Classification Tasks](https://mlsanity.com/paper/2107.05223/) (2021)

## Built on by (most cited first, 16 of 16)

- [Absorb and Converge: Provable Convergence Guarantee for Absorbing Discrete Diffusion Models](https://mlsanity.com/paper/2506.02318/) (2025)
- [DExter: Learning and Controlling Performance Expression with Diffusion Models](https://mlsanity.com/paper/2406.14850/) (2024)
- [Structured Multi-Track Accompaniment Arrangement via Style Prior Modelling](https://mlsanity.com/paper/2310.16334/) (2023)
- [ItDPDM: Information-Theoretic Discrete Poisson Diffusion Model](https://mlsanity.com/paper/2505.05082/) (2025)
- [SYMPLEX: Controllable Symbolic Music Generation using Simplex Diffusion with Vocabulary Priors](https://mlsanity.com/paper/2405.12666/) (2024)
- [Why Perturbing Symbolic Music is Necessary: Fitting the Distribution of Never-used Notes through a Joint Probabilistic Diffusion Model](https://mlsanity.com/paper/2408.01950/) (2024)
- [Diffusion-based Symbolic Music Generation with Structured State Space Models](https://mlsanity.com/paper/2507.20128/) (2025)
- [ProGress: Structured Music Generation via Graph Diffusion and Hierarchical Music Analysis](https://mlsanity.com/paper/2510.10249/) (2025)
- [Efficient Long-Sequence Diffusion Modeling for Symbolic Music Generation](https://mlsanity.com/paper/2603.00576/) (2026)
- [Amadeus: Autoregressive Model with Bidirectional Attribute Modelling for Symbolic Music](https://mlsanity.com/paper/2508.20665/) (2025)
- [Conditional Diffusion as Latent Constraints for Controllable Symbolic Music Generation](https://mlsanity.com/paper/2511.07156/) (2025)
- [Pay (Cross) Attention to the Melody: Curriculum Masking for Single-Encoder Melodic Harmonization](https://mlsanity.com/paper/2601.16150/) (2026)
- [D3PIA: A Discrete Denoising Diffusion Model for Piano Accompaniment Generation From Lead sheet](https://mlsanity.com/paper/2602.03523/) (2026)
- [Anchored Cyclic Generation: A Novel Paradigm for Long-Sequence Symbolic Music Generation](https://mlsanity.com/paper/2604.05343/) (2026)
- [ChartGenEval: Corruption-Tested Multi-Dimensional Feedback for Rhythm-Game Chart Generation](https://mlsanity.com/paper/2607.12857/) (2026)
- [DDSynth-RL: Audio Synthesizer Inversion via Discrete Diffusion with Reinforcement Learning](https://mlsanity.com/paper/2608.03032/) (2026)

## Abstract (arXiv)

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.