# Complexity-aware Large Scale Origin-Destination Network Generation via Diffusion Model arXiv: https://arxiv.org/abs/2306.04873 ยท HTML: https://mlsanity.com/paper/2306.04873/ ## Key facts - Cited by 9 papers in the map (data through 14 Oct 2026). - Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models. - Builds on 23 of its 45 references that are in the map. - First posted on arXiv 8 Jun 2023. ## Placed in - Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/) ## Builds on (most cited first, 23 of 23) - [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014) - [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020) - [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020) - [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017) - [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022) - [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022) - [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022) - [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018) - [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019) - [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021) - [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021) - [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020) - [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018) - [A Generalization of Transformer Networks to Graphs](https://mlsanity.com/paper/2012.09699/) (2020) - [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021) - [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022) - [Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations](https://mlsanity.com/paper/2202.02514/) (2022) - [Permutation Invariant Graph Generation via Score-Based Generative Modeling](https://mlsanity.com/paper/2003.00638/) (2020) - [NetGAN: Generating Graphs via Random Walks](https://mlsanity.com/paper/1803.00816/) (2018) - [Diffusion Models for Graphs Benefit From Discrete State Spaces](https://mlsanity.com/paper/2210.01549/) (2022) - [Deep Gravity: enhancing mobility flows generation with deep neural networks and geographic information](https://mlsanity.com/paper/2012.00489/) (2020) - [Learning Geo-Contextual Embeddings for Commuting Flow Prediction](https://mlsanity.com/paper/2005.01690/) (2020) - [A Machine Learning Approach to Modeling Human Migration](https://mlsanity.com/paper/1711.05462/) (2017) ## Built on by (most cited first, 9 of 9) - [Urban Generative Intelligence (UGI): A Foundational Platform for Agents in Embodied City Environment](https://mlsanity.com/paper/2312.11813/) (2023) - [Harnessing LLMs for Cross-City OD Flow Prediction](https://mlsanity.com/paper/2409.03937/) (2024) - [A Survey of Generative AI for Intelligent Transportation Systems: Road Transportation Perspective](https://mlsanity.com/paper/2312.08248/) (2023) - [OpFlow: Learning Opportunity-Conditioned Choice Potentials for Robust OD Flow Prediction](https://mlsanity.com/paper/2607.03200/) (2026) - [Sat2Flow: A Structure-Aware Diffusion Framework for Human Flow Generation from Satellite Imagery](https://mlsanity.com/paper/2508.19499/) (2025) - [A Comprehensive Evaluation Framework for Synthetic Trip Data Generation in Public Transport](https://mlsanity.com/paper/2510.24375/) (2025) - [Fusing Urban Structure and Semantics: A Conditional Diffusion Model for Cross-City OD Matrix Generation](https://mlsanity.com/paper/2605.00938/) (2026) - [SalAngaBhava: A Sinhala Market Dataset for Aspect-based Sentiment Analysis](https://mlsanity.com/paper/2607.05259/) (2026) - [Do Satellites See Commuters? A Critical Benchmark of Vision Foundation Models](https://mlsanity.com/paper/2609.00661/) (2026) ## Abstract (arXiv) The Origin-Destination~(OD) networks provide an estimation of the flow of people from every region to others in the city, which is an important research topic in transportation, urban simulation, etc. Given structural regional urban features, generating the OD network has become increasingly appealing to many researchers from diverse domains. However, existing works are limited in independent generation of each OD pair, i.e., flow of people from one region to another, overlooking the relations within the overall network. In this paper, we instead propose to generate the OD network, and design a graph denoising diffusion method to learn the conditional joint probability distribution of the nodes and edges within the OD network given city characteristics at region level. To overcome the learning difficulty of the OD networks covering over thousands of regions, we decompose the original one-shot generative modeling of the diffusion model into two cascaded stages, corresponding to the generation of network topology and the weights of edges, respectively. To further reproduce important network properties contained in the city-wide OD network, we design an elaborated graph denoising network structure including a node property augmentation module and a graph transformer backbone. Empirical experiments on data collected in three large US cities have verified that our method can generate OD matrices for new cities with network statistics remarkably similar with the ground truth, further achieving superior outperformance over competitive baselines in terms of the generation realism.