# ProGress: Structured Music Generation via Graph Diffusion and Hierarchical Music Analysis

arXiv: https://arxiv.org/abs/2510.10249 · HTML: https://mlsanity.com/paper/2510.10249/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Audio, speech and music, one of 14 directions in Diffusion models.
- Builds on 24 of its 41 references that are in the map.
- First posted on arXiv 11 Oct 2025.

## Placed in

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

## Builds on (most cited first, 24 of 24)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [WaveGrad: Estimating Gradients for Waveform Generation](https://mlsanity.com/paper/2009.00713/) (2020)
- [Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions](https://mlsanity.com/paper/2102.05379/) (2021)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [Simple and Controllable Music Generation](https://mlsanity.com/paper/2306.05284/) (2023)
- [Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations](https://mlsanity.com/paper/2202.02514/) (2022)
- [Permutation Invariant Graph Generation via Score-Based Generative Modeling](https://mlsanity.com/paper/2003.00638/) (2020)
- [Diffsound: Discrete Diffusion Model for Text-to-sound Generation](https://mlsanity.com/paper/2207.09983/) (2022)
- [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)
- [DeepBach: a Steerable Model for Bach Chorales Generation](https://mlsanity.com/paper/1612.01010/) (2016)
- [Symbolic Music Generation with Non-Differentiable Rule Guided Diffusion](https://mlsanity.com/paper/2402.14285/) (2024)
- [NotaGen: Advancing Musicality in Symbolic Music Generation with Large Language Model Training Paradigms](https://mlsanity.com/paper/2502.18008/) (2025)
- [Beyond In-Place Corruption: Insertion and Deletion In Denoising Probabilistic Models](https://mlsanity.com/paper/2107.07675/) (2021)
- [Discrete Diffusion Probabilistic Models for Symbolic Music Generation](https://mlsanity.com/paper/2305.09489/) (2023)
- [A Hierarchical Recurrent Neural Network for Symbolic Melody Generation](https://mlsanity.com/paper/1712.05274/) (2017)
- [Improving Polyphonic Music Models with Feature-Rich Encoding](https://mlsanity.com/paper/1911.11775/) (2019)
- [SYMPLEX: Controllable Symbolic Music Generation using Simplex Diffusion with Vocabulary Priors](https://mlsanity.com/paper/2405.12666/) (2024)
- [BandCondiNet: Parallel Transformers-based Conditional Popular Music Generation with Multi-View Features](https://mlsanity.com/paper/2407.10462/) (2024)
- [A New Dataset, Notation Software, and Representation for Computational Schenkerian Analysis](https://mlsanity.com/paper/2408.07184/) (2024)

## Built on by (most cited first, 1 of 1)

- [Getting Motif-ated: Controllable AI Compositions from Injected Motif Prompts](https://mlsanity.com/paper/2609.32788/) (2026)

## Abstract (arXiv)

Artificial Intelligence (AI) for music generation is undergoing rapid developments, with recent symbolic models leveraging sophisticated deep learning and diffusion model algorithms. One drawback with existing models is that they lack structural cohesion, particularly on harmonic-melodic structure. Furthermore, such existing models are largely "black-box" in nature and are not musically interpretable. This paper addresses these limitations via a novel generative music framework that incorporates concepts of Schenkerian analysis (SchA) in concert with a diffusion modeling framework. This framework, which we call ProGress (Prolongation-enhanced DiGress), adapts state-of-the-art deep models for discrete diffusion (in particular, the DiGress model of Vignac et al., 2023) for interpretable and structured music generation. Concretely, our contributions include 1) novel adaptations of the DiGress model for music generation, 2) a novel SchA-inspired phrase fusion methodology, and 3) a framework allowing users to control various aspects of the generation process to create coherent musical compositions. Results from human experiments suggest superior performance to existing state-of-the-art methods.