# An Invertible Graph Diffusion Neural Network for Source Localization arXiv: https://arxiv.org/abs/2206.09214 ยท HTML: https://mlsanity.com/paper/2206.09214/ ## Key facts - Cited by 14 papers in the map (data through 14 Oct 2026). - Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. - Builds on 17 of its 74 references that are in the map. - First posted on arXiv 18 Jun 2022. ## Placed in - Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/) ## Builds on (most cited first, 17 of 17) - [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014) - [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016) - [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018) - [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017) - [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018) - [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018) - [i-RevNet: Deep Invertible Networks](https://mlsanity.com/paper/1802.07088/) (2018) - [DeepInf: Social Influence Prediction with Deep Learning](https://mlsanity.com/paper/1807.05560/) (2018) - [Reversible Architectures for Arbitrarily Deep Residual Neural Networks](https://mlsanity.com/paper/1709.03698/) (2017) - [GEMSEC: Graph Embedding with Self Clustering](https://mlsanity.com/paper/1802.03997/) (2018) - [Popularity Prediction on Social Platforms with Coupled Graph Neural Networks](https://mlsanity.com/paper/1906.09032/) (2019) - [A Survey of Information Cascade Analysis: Models, Predictions, and Recent Advances](https://mlsanity.com/paper/2005.11041/) (2020) - [Topological Recurrent Neural Network for Diffusion Prediction](https://mlsanity.com/paper/1711.10162/) (2017) - [Event Prediction in the Big Data Era: A Systematic Survey](https://mlsanity.com/paper/2007.09815/) (2020) - [Modeling and Predicting Popularity Dynamics of Microblogs using Self-Excited Hawkes Processes](https://mlsanity.com/paper/1503.02754/) (2015) - [Network Diffusions via Neural Mean-Field Dynamics](https://mlsanity.com/paper/2006.09449/) (2020) - [Multi-instance Domain Adaptation for Vaccine Adverse Event Detection](https://mlsanity.com/paper/2009.04901/) (2020) ## Built on by (most cited first, 14 of 14) - [Deep Graph Representation Learning and Optimization for Influence Maximization](https://mlsanity.com/paper/2305.02200/) (2023) - [Source Localization of Graph Diffusion via Variational Autoencoders for Graph Inverse Problems](https://mlsanity.com/paper/2206.12327/) (2022) - [Multi-conditioned Graph Diffusion for Neural Architecture Search](https://mlsanity.com/paper/2403.06020/) (2024) - [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) - [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) - [GraphSL: An Open-Source Library for Graph Source Localization Approaches and Benchmark Datasets](https://mlsanity.com/paper/2405.03724/) (2024) - [Representation Learning of Geometric Trees](https://mlsanity.com/paper/2408.08799/) (2024) - [Non-Euclidean Spatial Graph Neural Network](https://mlsanity.com/paper/2312.10808/) (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) ## Abstract (arXiv) Localizing the source of graph diffusion phenomena, such as misinformation propagation, is an important yet extremely challenging task. Existing source localization models typically are heavily dependent on the hand-crafted rules. Unfortunately, a large portion of the graph diffusion process for many applications is still unknown to human beings so it is important to have expressive models for learning such underlying rules automatically. This paper aims to establish a generic framework of invertible graph diffusion models for source localization on graphs, namely Invertible Validity-aware Graph Diffusion (IVGD), to handle major challenges including 1) Difficulty to leverage knowledge in graph diffusion models for modeling their inverse processes in an end-to-end fashion, 2) Difficulty to ensure the validity of the inferred sources, and 3) Efficiency and scalability in source inference. Specifically, first, to inversely infer sources of graph diffusion, we propose a graph residual scenario to make existing graph diffusion models invertible with theoretical guarantees; second, we develop a novel error compensation mechanism that learns to offset the errors of the inferred sources. Finally, to ensure the validity of the inferred sources, a new set of validity-aware layers have been devised to project inferred sources to feasible regions by flexibly encoding constraints with unrolled optimization techniques. A linearization technique is proposed to strengthen the efficiency of our proposed layers. The convergence of the proposed IVGD is proven theoretically. Extensive experiments on nine real-world datasets demonstrate that our proposed IVGD outperforms state-of-the-art comparison methods significantly. We have released our code at https://github.com/xianggebenben/IVGD.