# Source Localization of Graph Diffusion via Variational Autoencoders for Graph Inverse Problems

arXiv: https://arxiv.org/abs/2206.12327 · HTML: https://mlsanity.com/paper/2206.12327/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 65 references that are in the map.
- First posted on arXiv 24 Jun 2022.

## Builds on (most cited first, 22 of 22)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [Generative Image Inpainting with Contextual Attention](https://mlsanity.com/paper/1801.07892/) (2018)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Fairness in Criminal Justice Risk Assessments: The State of the Art](https://mlsanity.com/paper/1703.09207/) (2017)
- [Say No to the Discrimination: Learning Fair Graph Neural Networks with Limited Sensitive Attribute Information](https://mlsanity.com/paper/2009.01454/) (2020)
- [Cost Sensitive Learning of Deep Feature Representations from Imbalanced Data](https://mlsanity.com/paper/1508.03422/) (2015)
- [A Systematic Survey on Deep Generative Models for Graph Generation](https://mlsanity.com/paper/2007.06686/) (2020)
- [VERSE: Versatile Graph Embeddings from Similarity Measures](https://mlsanity.com/paper/1803.04742/) (2018)
- [Estimating Mixed Memberships with Sharp Eigenvector Deviations](https://mlsanity.com/paper/1709.00407/) (2017)
- [Catch'Em All: Locating Multiple Diffusion Sources in Networks with Partial Observations](https://mlsanity.com/paper/1611.06963/) (2016)
- [An Invertible Graph Diffusion Neural Network for Source Localization](https://mlsanity.com/paper/2206.09214/) (2022)
- [Algorithmic Aspects of Inverse Problems Using Generative Models](https://mlsanity.com/paper/1810.03587/) (2018)
- [Lower Bounds for Compressed Sensing with Generative Models](https://mlsanity.com/paper/1912.02938/) (2019)
- [Debiasing Community Detection: The Importance of Lowly-Connected Nodes](https://mlsanity.com/paper/1903.08136/) (2019)
- [Information Diffusion in Social Networks in Two Phases](https://mlsanity.com/paper/1706.07739/) (2017)
- [NesTPP: Modeling Thread Dynamics in Online Discussion Forums](https://mlsanity.com/paper/2003.06051/) (2020)

## Built on by (most cited first, 18 of 18)

- [Uncertainty Quantification for In-Context Learning of Large Language Models](https://mlsanity.com/paper/2402.10189/) (2024)
- [Deep Graph Representation Learning and Optimization for Influence Maximization](https://mlsanity.com/paper/2305.02200/) (2023)
- [Reconstructing Graph Diffusion History from a Single Snapshot](https://mlsanity.com/paper/2306.00488/) (2023)
- [Curriculum Learning for Graph Neural Networks: Which Edges Should We Learn First](https://mlsanity.com/paper/2310.18735/) (2023)
- [GIN-SD: Source Detection in Graphs with Incomplete Nodes via Positional Encoding and Attentive Fusion](https://mlsanity.com/paper/2403.00014/) (2024)
- [Staleness-Alleviated Distributed GNN Training via Online Dynamic-Embedding Prediction](https://mlsanity.com/paper/2308.13466/) (2023)
- [Robust Node Representation Learning via Graph Variational Diffusion Networks](https://mlsanity.com/paper/2312.10903/) (2023)
- [Two-stage Denoising Diffusion Model for Source Localization in Graph Inverse Problems](https://mlsanity.com/paper/2304.08841/) (2023)
- [Sequential Attention Source Identification Based on Feature Representation](https://mlsanity.com/paper/2306.15886/) (2023)
- [Identifying Super Spreaders in Multilayer Networks](https://mlsanity.com/paper/2505.20980/) (2025)
- [MIM-Reasoner: Learning with Theoretical Guarantees for Multiplex Influence Maximization](https://mlsanity.com/paper/2402.16898/) (2024)
- [GraphSL: An Open-Source Library for Graph Source Localization Approaches and Benchmark Datasets](https://mlsanity.com/paper/2405.03724/) (2024)
- [Deep Demixing: Reconstructing the Evolution of Network Epidemics](https://mlsanity.com/paper/2306.07938/) (2023)
- [Structure-prior Informed Diffusion Model for Graph Source Localization with Limited Data](https://mlsanity.com/paper/2502.17928/) (2025)
- [HyperDet: Source Detection in Hypergraphs via Interactive Relationship Construction and Feature-rich Attention Fusion](https://mlsanity.com/paper/2505.12894/) (2025)
- [SourceDetMamba: A Graph-aware State Space Model for Source Detection in Sequential Hypergraphs](https://mlsanity.com/paper/2505.12910/) (2025)
- [Graph Neural Networks for Source Detection: A Review and Benchmark Study](https://mlsanity.com/paper/2512.20657/) (2025)
- [Network World Models as Environments for Algorithm Design on Complex Systems](https://mlsanity.com/paper/2610.01048/) (2026)

## Abstract (arXiv)

Graph diffusion problems such as the propagation of rumors, computer viruses, or smart grid failures are ubiquitous and societal. Hence it is usually crucial to identify diffusion sources according to the current graph diffusion observations. Despite its tremendous necessity and significance in practice, source localization, as the inverse problem of graph diffusion, is extremely challenging as it is ill-posed: different sources may lead to the same graph diffusion patterns. Different from most traditional source localization methods, this paper focuses on a probabilistic manner to account for the uncertainty of different candidate sources. Such endeavors require overcoming challenges including 1) the uncertainty in graph diffusion source localization is hard to be quantified; 2) the complex patterns of the graph diffusion sources are difficult to be probabilistically characterized; 3) the generalization under any underlying diffusion patterns is hard to be imposed. To solve the above challenges, this paper presents a generic framework: Source Localization Variational AutoEncoder (SL-VAE) for locating the diffusion sources under arbitrary diffusion patterns. Particularly, we propose a probabilistic model that leverages the forward diffusion estimation model along with deep generative models to approximate the diffusion source distribution for quantifying the uncertainty. SL-VAE further utilizes prior knowledge of the source-observation pairs to characterize the complex patterns of diffusion sources by a learned generative prior. Lastly, a unified objective that integrates the forward diffusion estimation model is derived to enforce the model to generalize under arbitrary diffusion patterns. Extensive experiments are conducted on 7 real-world datasets to demonstrate the superiority of SL-VAE in reconstructing the diffusion sources by excelling other methods on average 20% in AUC score.