# Why Perturbing Symbolic Music is Necessary: Fitting the Distribution of Never-used Notes through a Joint Probabilistic Diffusion Model

arXiv: https://arxiv.org/abs/2408.01950 · HTML: https://mlsanity.com/paper/2408.01950/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Audio, speech and music, one of 14 directions in Diffusion models.
- Builds on 23 of its 36 references that are in the map.
- First posted on arXiv 4 Aug 2024.

## Placed in

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

## Builds on (most cited first, 23 of 23)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [RWKV: Reinventing RNNs for the Transformer Era](https://mlsanity.com/paper/2305.13048/) (2023)
- [DiffuSeq: Sequence to Sequence Text Generation with Diffusion Models](https://mlsanity.com/paper/2210.08933/) (2022)
- [Noise2Music: Text-conditioned Music Generation with Diffusion Models](https://mlsanity.com/paper/2302.03917/) (2023)
- [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)
- [An Attention Free Transformer](https://mlsanity.com/paper/2105.14103/) (2021)
- [Compound Word Transformer: Learning to Compose Full-Song Music over Dynamic Directed Hypergraphs](https://mlsanity.com/paper/2101.02402/) (2021)
- [Mousai: Text-to-Music Generation with Long-Context Latent Diffusion](https://mlsanity.com/paper/2301.11757/) (2023)
- [Multi-Source Diffusion Models for Simultaneous Music Generation and Separation](https://mlsanity.com/paper/2302.02257/) (2023)
- [The Jazz Transformer on the Front Line: Exploring the Shortcomings of AI-composed Music through Quantitative Measures](https://mlsanity.com/paper/2008.01307/) (2020)
- [Discrete Contrastive Diffusion for Cross-Modal Music and Image Generation](https://mlsanity.com/paper/2206.07771/) (2022)
- [Multi-instrument Music Synthesis with Spectrogram Diffusion](https://mlsanity.com/paper/2206.05408/) (2022)
- [Multitrack Music Transformer](https://mlsanity.com/paper/2207.06983/) (2022)
- [A Domain-Knowledge-Inspired Music Embedding Space and a Novel Attention Mechanism for Symbolic Music Modeling](https://mlsanity.com/paper/2212.00973/) (2022)
- [Discrete Diffusion Probabilistic Models for Symbolic Music Generation](https://mlsanity.com/paper/2305.09489/) (2023)
- [ERNIE-Music: Text-to-Waveform Music Generation with Diffusion Models](https://mlsanity.com/paper/2302.04456/) (2023)
- [DiffRoll: Diffusion-based Generative Music Transcription with Unsupervised Pretraining Capability](https://mlsanity.com/paper/2210.05148/) (2022)
- [Unsupervised Learning of Deep Features for Music Segmentation](https://mlsanity.com/paper/2108.12955/) (2021)
- [Music Style Transfer with Time-Varying Inversion of Diffusion Models](https://mlsanity.com/paper/2402.13763/) (2024)
- [The Power of Fragmentation: A Hierarchical Transformer Model for Structural Segmentation in Symbolic Music Generation](https://mlsanity.com/paper/2205.08579/) (2022)

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

- [A Survey of RWKV](https://mlsanity.com/paper/2412.14847/) (2024)
- [Efficient Long-Sequence Diffusion Modeling for Symbolic Music Generation](https://mlsanity.com/paper/2603.00576/) (2026)

## Abstract (arXiv)

Existing music generation models are mostly language-based, neglecting the frequency continuity property of notes, resulting in inadequate fitting of rare or never-used notes and thus reducing the diversity of generated samples. We argue that the distribution of notes can be modeled by translational invariance and periodicity, especially using diffusion models to generalize notes by injecting frequency-domain Gaussian noise. However, due to the low-density nature of music symbols, estimating the distribution of notes latent in the high-density solution space poses significant challenges. To address this problem, we introduce the Music-Diff architecture, which fits a joint distribution of notes and accompanying semantic information to generate symbolic music conditionally. We first enhance the fragmentation module for extracting semantics by using event-based notations and the structural similarity index, thereby preventing boundary blurring. As a prerequisite for multivariate perturbation, we introduce a joint pre-training method to construct the progressions between notes and musical semantics while avoiding direct modeling of low-density notes. Finally, we recover the perturbed notes by a multi-branch denoiser that fits multiple noise objectives via Pareto optimization. Our experiments suggest that in contrast to language models, joint probability diffusion models perturbing at both note and semantic levels can provide more sample diversity and compositional regularity. The case study highlights the rhythmic advantages of our model over language- and DDPMs-based models by analyzing the hierarchical structure expressed in the self-similarity metrics.