mlsanityData to 7 Oct 2026

Discrete Diffusion Probabilistic Models for Symbolic Music Generation

arXiv 2305.09489 ↗First posted 16 May 2023cs.SD cs.AI eess.AScited by 16

On the map: Diffusion models → Audio, speech and music

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.

Key facts. Cited by 16 papers in the map (data through 7 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.

Builds on

18 of 31 references.

Closest ancestors · 3

Same direction, newest first

  1. 2022Multi-instrument Music Synthesis with Spectrogram Diffusion11 Jun
  2. 2021Symbolic Music Generation with Diffusion Models30 Mar
  3. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesis21 Sep

Other references · 15

  1. 2018BERT: Pre-training of Deep Bidirectional Transformers for Language Understandingcited by 40,204
  2. 2020Language Models are Few-Shot Learnerscited by 32,199
  3. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  4. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  5. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  6. 2022Generative Adversarial Networkscited by 5,603
  7. 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,665
  8. 2021Argmax Flows and Multinomial Diffusion: Learning Categorical Distributionscited by 566
  9. 2020Reliable Fidelity and Diversity Metrics for Generative Modelscited by 425
  10. 2018A Hierarchical Latent Vector Model for Learning Long-Term Structure in Musiccited by 131
  11. 2021Compound Word Transformer: Learning to Compose Full-Song Music over Dynamic Directed Hypergraphscited by 109
  12. 2021MusicBERT: Symbolic Music Understanding with Large-Scale Pre-Trainingcited by 89
3 more
  1. 2017MidiNet: A Convolutional Generative Adversarial Network for Symbolic-domain Music Generationcited by 72
  2. 2021Unleashing Transformers: Parallel Token Prediction with Discrete Absorbing Diffusion for Fast High-Resolution Image Generation from Vector-Quantized Codescited by 71
  3. 2021BERT-like Pre-training for Symbolic Piano Music Classification Taskscited by 12

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 3; 2025: 6; 2026: 6.

16 papers.

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  1. 2025Absorb and Converge: Provable Convergence Guarantee for Absorbing Discrete Diffusion Modelscited by 20
  2. 2024DExter: Learning and Controlling Performance Expression with Diffusion Modelscited by 11
  3. 2023Structured Multi-Track Accompaniment Arrangement via Style Prior Modellingcited by 9
  4. 2025ItDPDM: Information-Theoretic Discrete Poisson Diffusion Modelcited by 4
  5. 2024SYMPLEX: Controllable Symbolic Music Generation using Simplex Diffusion with Vocabulary Priorscited by 2
  6. 2024Why Perturbing Symbolic Music is Necessary: Fitting the Distribution of Never-used Notes through a Joint Probabilistic Diffusion Modelcited by 2
  7. 2025Diffusion-based Symbolic Music Generation with Structured State Space Modelscited by 2
  8. 2025ProGress: Structured Music Generation via Graph Diffusion and Hierarchical Music Analysiscited by 1
  9. 2025Amadeus: Autoregressive Model with Bidirectional Attribute Modelling for Symbolic Musiccited by 0
  10. 2025Conditional Diffusion as Latent Constraints for Controllable Symbolic Music Generationcited by 0
  11. 2026Pay (Cross) Attention to the Melody: Curriculum Masking for Single-Encoder Melodic Harmonizationcited by 0
  12. 2026D3PIA: A Discrete Denoising Diffusion Model for Piano Accompaniment Generation From Lead sheetcited by 0
4 more
  1. 2026Efficient Long-Sequence Diffusion Modeling for Symbolic Music Generationcited by 0
  2. 2026Anchored Cyclic Generation: A Novel Paradigm for Long-Sequence Symbolic Music Generationcited by 0
  3. 2026ChartGenEval: Corruption-Tested Multi-Dimensional Feedback for Rhythm-Game Chart Generationcited by 0
  4. 2026DDSynth-RL: Audio Synthesizer Inversion via Discrete Diffusion with Reinforcement Learningcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2023Composer Style-specific Symbolic Music Generation Using Vector Quantized Discrete Diffusion Models
  2. 2023Generating symbolic music using diffusion models
  3. 2026Diff-Symbo: Text-Controlled Long-Duration Symbolic Music Generation Using Autoregressive Latent Diffusion Model
  4. 2025Mamba-Diffusion Model with Learnable Wavelet for Controllable Symbolic Music Generation
  5. 2023GETMusic: Generating Any Music Tracks with a Unified Representation and Diffusion Framework
  6. 2024Efficient Fine-Grained Guidance for Diffusion Model Based Symbolic Music Generation
  7. 2022Realistic Gramophone Noise Synthesis using a Diffusion Model
  8. 2025PhraseVAE and PhraseLDM: Latent Diffusion for Full-Song Multitrack Symbolic Music Generation