# Diffusion Scattering Transforms on Graphs

arXiv: https://arxiv.org/abs/1806.08829 · HTML: https://mlsanity.com/paper/1806.08829/

## Key facts

- Cited by 44 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jun 2018.

## Built on by (most cited first, 30 of 44)

- [Rethinking Graph Neural Networks for Anomaly Detection](https://mlsanity.com/paper/2205.15508/) (2022)
- [Equivariant and Stable Positional Encoding for More Powerful Graph Neural Networks](https://mlsanity.com/paper/2203.00199/) (2022)
- [Unlearning Graph Classifiers with Limited Data Resources](https://mlsanity.com/paper/2211.03216/) (2022)
- [Skeleton-Parted Graph Scattering Networks for 3D Human Motion Prediction](https://mlsanity.com/paper/2208.00368/) (2022)
- [Can Hybrid Geometric Scattering Networks Help Solve the Maximum Clique Problem?](https://mlsanity.com/paper/2206.01506/) (2022)
- [Understanding Non-linearity in Graph Neural Networks from the Bayesian-Inference Perspective](https://mlsanity.com/paper/2207.11311/) (2022)
- [Scattering Networks on the Sphere for Scalable and Rotationally Equivariant Spherical CNNs](https://mlsanity.com/paper/2102.02828/) (2021)
- [Stability of Graph Convolutional Neural Networks to Stochastic Perturbations](https://mlsanity.com/paper/2106.10526/) (2021)
- [Overcoming Oversmoothness in Graph Convolutional Networks via Hybrid Scattering Networks](https://mlsanity.com/paper/2201.08932/) (2022)
- [Geometric Scattering on Measure Spaces](https://mlsanity.com/paper/2208.08561/) (2022)
- [Approximately Equivariant Graph Networks](https://mlsanity.com/paper/2308.10436/) (2023)
- [A Survey of Graph Unlearning](https://mlsanity.com/paper/2310.02164/) (2023)
- [Adaptive Gaussian Processes on Graphs via Spectral Graph Wavelets](https://mlsanity.com/paper/2110.12752/) (2021)
- [From Local to Global: Spectral-Inspired Graph Neural Networks](https://mlsanity.com/paper/2209.12054/) (2022)
- [The Manifold Scattering Transform for High-Dimensional Point Cloud Data](https://mlsanity.com/paper/2206.10078/) (2022)
- [Learnable Filters for Geometric Scattering Modules](https://mlsanity.com/paper/2208.07458/) (2022)
- [Convolutional Filtering and Neural Networks with Non Commutative Algebras](https://mlsanity.com/paper/2108.09923/) (2021)
- [Molecular Graph Generation via Geometric Scattering](https://mlsanity.com/paper/2110.06241/) (2021)
- [Graph Neural Networks With Lifting-based Adaptive Graph Wavelets](https://mlsanity.com/paper/2108.01660/) (2021)
- [A General Graph Spectral Wavelet Convolution via Chebyshev Order Decomposition](https://mlsanity.com/paper/2405.13806/) (2024)
- [Contrastive Learning for Non-Local Graphs with Multi-Resolution Structural Views](https://mlsanity.com/paper/2308.10077/) (2023)
- [DYMAG: Rethinking Message Passing Using Dynamical-systems-based Waveforms](https://mlsanity.com/paper/2309.09924/) (2023)
- [BLIS-Net: Classifying and Analyzing Signals on Graphs](https://mlsanity.com/paper/2310.17579/) (2023)
- [WaveletDiff: Multilevel Wavelet Diffusion For Time Series Generation](https://mlsanity.com/paper/2510.11839/) (2025)
- [Graph Scattering beyond Wavelet Shackles](https://mlsanity.com/paper/2301.11456/) (2023)
- [Manifold Filter-Combine Networks](https://mlsanity.com/paper/2307.04056/) (2023)
- [Directed Scattering for Knowledge Graph-based Cellular Signaling Analysis](https://mlsanity.com/paper/2309.07813/) (2023)
- [On the Trade-Off between Stability and Representational Capacity in Graph Neural Networks](https://mlsanity.com/paper/2312.02372/) (2023)
- [HiPoNet: A Multi-View Simplicial Complex Network for High Dimensional Point-Cloud and Single-Cell Data](https://mlsanity.com/paper/2502.07746/) (2025)
- [ViDa: Visualizing DNA hybridization trajectories with biophysics-informed deep graph embeddings](https://mlsanity.com/paper/2311.03411/) (2023)

## Abstract (arXiv)

Stability is a key aspect of data analysis. In many applications, the natural notion of stability is geometric, as illustrated for example in computer vision. Scattering transforms construct deep convolutional representations which are certified stable to input deformations. This stability to deformations can be interpreted as stability with respect to changes in the metric structure of the domain. In this work, we show that scattering transforms can be generalized to non-Euclidean domains using diffusion wavelets, while preserving a notion of stability with respect to metric changes in the domain, measured with diffusion maps. The resulting representation is stable to metric perturbations of the domain while being able to capture "high-frequency" information, akin to the Euclidean Scattering.