# Mamba-Diffusion Model with Learnable Wavelet for Controllable Symbolic Music Generation

arXiv: https://arxiv.org/abs/2505.03314 · HTML: https://mlsanity.com/paper/2505.03314/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Audio, speech and music, one of 14 directions in Diffusion models.
- Builds on 25 of its 28 references that are in the map.
- First posted on arXiv 6 May 2025.

## Placed in

- Diffusion models / [Audio, speech and music](https://mlsanity.com/diffusion/audio-speech-and-music/)
- State-space sequence models (S4, Mamba) / [Video, motion and generative Mamba models](https://mlsanity.com/ssm/video-motion-and-generative-mamba-models/)

## Builds on (most cited first, 25 of 25)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Simple Baselines for Image Restoration](https://mlsanity.com/paper/2204.04676/) (2022)
- [Simple and Controllable Music Generation](https://mlsanity.com/paper/2306.05284/) (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)
- [Wavelet Diffusion Models are fast and scalable Image Generators](https://mlsanity.com/paper/2211.16152/) (2022)
- [POP909: A Pop-song Dataset for Music Arrangement Generation](https://mlsanity.com/paper/2008.07142/) (2020)
- [Symbolic Music Generation with Non-Differentiable Rule Guided Diffusion](https://mlsanity.com/paper/2402.14285/) (2024)
- [Learning Interpretable Representation for Controllable Polyphonic Music Generation](https://mlsanity.com/paper/2008.07122/) (2020)
- [Encoding Musical Style with Transformer Autoencoders](https://mlsanity.com/paper/1912.05537/) (2019)
- [Polyffusion: A Diffusion Model for Polyphonic Score Generation with Internal and External Controls](https://mlsanity.com/paper/2307.10304/) (2023)
- [Music SketchNet: Controllable Music Generation via Factorized Representations of Pitch and Rhythm](https://mlsanity.com/paper/2008.01291/) (2020)
- [Whole-Song Hierarchical Generation of Symbolic Music Using Cascaded Diffusion Models](https://mlsanity.com/paper/2405.09901/) (2024)
- [Efficient Multi-scale Network with Learnable Discrete Wavelet Transform for Blind Motion Deblurring](https://mlsanity.com/paper/2401.00027/) (2023)
- [TeleMelody: Lyric-to-Melody Generation with a Template-Based Two-Stage Method](https://mlsanity.com/paper/2109.09617/) (2021)
- [MusIAC: An extensible generative framework for Music Infilling Applications with multi-level Control](https://mlsanity.com/paper/2202.05528/) (2022)
- [Composer Style-specific Symbolic Music Generation Using Vector Quantized Discrete Diffusion Models](https://mlsanity.com/paper/2310.14044/) (2023)
- [Generating symbolic music using diffusion models](https://mlsanity.com/paper/2303.08385/) (2023)
- [WaveDH: Wavelet Sub-bands Guided ConvNet for Efficient Image Dehazing](https://mlsanity.com/paper/2404.01604/) (2024)

## Built on by (most cited first, 4 of 4)

- [Efficient Long-Sequence Diffusion Modeling for Symbolic Music Generation](https://mlsanity.com/paper/2603.00576/) (2026)
- [Training-Efficient Text-to-Music Generation with State-Space Modeling](https://mlsanity.com/paper/2601.14786/) (2026)
- [Pay (Cross) Attention to the Melody: Curriculum Masking for Single-Encoder Melodic Harmonization](https://mlsanity.com/paper/2601.16150/) (2026)
- [Self-Representation Alignment in Diffusion Models for Video Background Music Generation](https://mlsanity.com/paper/2610.15575/) (2026)

## Abstract (arXiv)

The recent surge in the popularity of diffusion models for image synthesis has attracted new attention to their potential for generation tasks in other domains. However, their applications to symbolic music generation remain largely under-explored because symbolic music is typically represented as sequences of discrete events and standard diffusion models are not well-suited for discrete data. We represent symbolic music as image-like pianorolls, facilitating the use of diffusion models for the generation of symbolic music. Moreover, this study introduces a novel diffusion model that incorporates our proposed Transformer-Mamba block and learnable wavelet transform. Classifier-free guidance is utilised to generate symbolic music with target chords. Our evaluation shows that our method achieves compelling results in terms of music quality and controllability, outperforming the strong baseline in pianoroll generation. Our code is available at https://github.com/jinchengzhanggg/proffusion.