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

TL;DR

ProGress tackles the lack of structural coherence and interpretability in symbolic music generation by fusing Schenkerian analysis with a discrete graph diffusion framework (DiGress adaptation). It generates a library of phrases via diffusion over a graph of scale-degree nodes and relations, then applies SchA-guided phrase fusion and pivot-modulation to assemble coherent scores, with rhythmic sampling providing a robust backbone. Key contributions include (1) a novel DiGress adaptation for music, (2) a SchA-inspired phrase fusion mechanism, and (3) a controllable generation framework that uses orders of magnitude fewer parameters while delivering superior subjective quality in human experiments. The approach yields more cohesive harmonic-melodic structure and interpretability, with practical implications for data-efficient, style-transferable symbolic music generation. Overall, ProGress offers a principled, structure-aware alternative to purely data-driven generation with demonstrated human preferences. The diffusion operates over graphs with node classes $\mathcal{X}$ and edge classes $\mathcal{E}$ using forward transitions $\mathbf{Q}^t_{X}$ and $\mathbf{Q}^t_{E}$, and leverages rhythmic features $\mathbf{R}$ to condition the denoiser, enabling controllable, interpretable composition.

Abstract

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.

Figures (10)

• Figure 1: Example SchA of J.S. Bach's C$\sharp$ major fugue subject from Das Wohltemperierte Klavier I.
• Figure 2: Overview of the phrase generation process. On the left half, B phrases are generated via diffusion, and on the right, phrases are fused together according to music theoretical principles and structures. In the generation stage, starting with the yellow block, we sample a phrase from our dataset $D$ and extract rhythmic relationships to build a heterogeneous, discrete graph $G^T$. This discrete graph is iteratively passed through a denoising model $p_\theta$ to determine the notes for a novel piece of music. Finally, the inferred notes are mapped back to the rhythmic skeleton of the sampled phrase. This process is repeated $B$ times to generate $B$ phrases. For the fusion stage, phrases are first analyzed and organized based on harmonic and structural features. Based on user-defined rules, certain phrases are rejected. Phrases are then fused according to a sampled Schenkerian structure as described in Section \ref{['subsec:inference']}.
• Figure 3: Example phrase fusion via pivot chord modulation from C Major (CM) to G Major (GM). The light and dark blue represent foreground and background analysis, respectively. The antecedent is in CM, leading to GM in the consequent by reinterpreting the final antecedent "I" as "IV" in the new key.
• Figure 4: A common Schenkerian structure as three phrases of generated music. Green and red represent music in the home and dominant key, respectively. Here, the 2nd phrase was originally generated in the home key, but is transposed to the dominant via our fusion method in Section \ref{['subsec:inference']}.
• Figure 5: "Weird or bad" survey results.