# Colored Graph Signal Diffusion Models

arXiv: https://arxiv.org/abs/2610.17282 · HTML: https://mlsanity.com/paper/2610.17282/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 21 of its 26 references that are in the map.
- First posted on arXiv 12 Oct 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 21 of 21)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Understanding Diffusion Objectives as the ELBO with Simple Data Augmentation](https://mlsanity.com/paper/2303.00848/) (2023)
- [Generative Modelling With Inverse Heat Dissipation](https://mlsanity.com/paper/2206.13397/) (2022)
- [Soft Diffusion: Score Matching for General Corruptions](https://mlsanity.com/paper/2209.05442/) (2022)
- [Blurring Diffusion Models](https://mlsanity.com/paper/2209.05557/) (2022)
- [PriorGrad: Improving Conditional Denoising Diffusion Models with Data-Dependent Adaptive Prior](https://mlsanity.com/paper/2106.06406/) (2021)
- [A Fourier Space Perspective on Diffusion Models](https://mlsanity.com/paper/2505.11278/) (2025)
- [Stationary Graph Processes and Spectral Estimation](https://mlsanity.com/paper/1603.04667/) (2016)
- [Stationary signal processing on graphs](https://mlsanity.com/paper/1601.02522/) (2016)
- [coVariance Neural Networks](https://mlsanity.com/paper/2205.15856/) (2022)
- [Spectral Analysis of Diffusion Models with Application to Schedule Design](https://mlsanity.com/paper/2502.00180/) (2025)
- [Graph-Aware Diffusion for Signal Generation](https://mlsanity.com/paper/2510.05036/) (2025)
- [S-Diff: An Anisotropic Diffusion Model for Collaborative Filtering in Spectral Domain](https://mlsanity.com/paper/2501.00384/) (2024)
- [Graph Signal Diffusion Models for Wireless Resource Allocation](https://mlsanity.com/paper/2604.05175/) (2026)
- [Generative Diffusion Models of Stochastic Graph Signals](https://mlsanity.com/paper/2607.06833/) (2026)
- [Stability of Flow Models for Graph Signals](https://mlsanity.com/paper/2607.07510/) (2026)

## Abstract (arXiv)

Standard diffusion processes with isotropic noise corruption are not spectrally neutral. They inherit a coarse-to-fine generation hierarchy from the nonuniform data spectrum, because each frequency band loses signal-to-noise ratio (SNR) at its own rate. For signals on a graph, the relevant spectrum is that of the graph shift operator (GSO). A natural construction, therefore, builds both the diffusion dynamics and the denoiser from graph filters of the GSO, and any such design also takes a position on this hierarchy. We expose this hierarchy as a tunable axis through a family of colored score-based diffusions. Fixing the terminal prior to a Gaussian colored by the GSO couples the drift and diffusion through a positive spectral rate, which acts as a clock for each graph-frequency band. The clock sets when a band loses and recovers information, and the forward processes of standard and certain graph-aware diffusions appear as members of this family. A GSO-valued EDM preconditioning splits the denoiser into an analytic Wiener head that carries the Gaussian second-order structure and a graph neural network (GNN) that learns the remaining non-Gaussian dependencies. Numerical experiments show that colored diffusions reach a given generation quality in far fewer sampling steps than standard diffusion.