# Stable Filters for Generative Modeling of Graph Signals

arXiv: https://arxiv.org/abs/2609.18759 · HTML: https://mlsanity.com/paper/2609.18759/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 27 references that are in the map.
- First posted on arXiv 16 Sep 2026.

## Builds on (most cited first, 20 of 20)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [A survey of the Schr"odinger problem and some of its connections with optimal transport](https://mlsanity.com/paper/1308.0215/) (2013)
- [Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theory](https://mlsanity.com/paper/2110.11291/) (2021)
- [Stability Properties of Graph Neural Networks](https://mlsanity.com/paper/1905.04497/) (2019)
- [Learning graphs from data: A signal representation perspective](https://mlsanity.com/paper/1806.00848/) (2018)
- [Convolutional Neural Network Architectures for Signals Supported on Graphs](https://mlsanity.com/paper/1805.00165/) (2018)
- [Graph Neural Networks: Architectures, Stability and Transferability](https://mlsanity.com/paper/2008.01767/) (2020)
- [Discrete Signal Processing on Graphs: Frequency Analysis](https://mlsanity.com/paper/1307.0468/) (2013)
- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Graph Signal Diffusion Model for Collaborative Filtering](https://mlsanity.com/paper/2311.08744/) (2023)
- [Graph-Aware Diffusion for Signal Generation](https://mlsanity.com/paper/2510.05036/) (2025)
- [Topological Flow Matching](https://mlsanity.com/paper/2606.15897/) (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)
- [Graph Contrastive Learning for Connectome Classification](https://mlsanity.com/paper/2502.05109/) (2025)

## Abstract (arXiv)

Generating signals on graphs requires permutation-equivariant models that exhibit stability with respect to relative structural perturbations. While recent graph-aware Schr"odinger bridge models incorporate topology information directly into their reference dynamics, it is unclear how perturbations of the graph propagate through these dynamics and affect the resulting generated distributions. In this paper, we analyze the structural stability of graph-aware continuous-time generative models whose drift combines a graph filter with a learned graph neural network. We derive explicit Wasserstein stability bounds that quantify the effect of relative graph perturbations on the generated distributions. Motivated by these bounds, we introduce a principled framework for designing stable graph filters that preserve the smoothing behavior of graph heat diffusion, while boosting structural stability. Experiments on synthetic and fMRI signals show our stable filters enhance structural robustness while matching or exceeding the generative quality of the heat equation baseline.