# Diff-RNTraj: A Structure-aware Diffusion Model for Road Network-constrained Trajectory Generation

arXiv: https://arxiv.org/abs/2402.07369 · HTML: https://mlsanity.com/paper/2402.07369/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 63 references that are in the map.
- First posted on arXiv 12 Feb 2024.

## Builds on (most cited first, 30 of 30)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Imagen Video: High Definition Video Generation with Diffusion Models](https://mlsanity.com/paper/2210.02303/) (2022)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1606.03476/) (2016)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Vector Quantized Diffusion Model for Text-to-Image Synthesis](https://mlsanity.com/paper/2111.14822/) (2021)
- [WaveGrad: Estimating Gradients for Waveform Generation](https://mlsanity.com/paper/2009.00713/) (2020)
- [AudioLDM: Text-to-Audio Generation with Latent Diffusion Models](https://mlsanity.com/paper/2301.12503/) (2023)
- [SeqGAN: Sequence Generative Adversarial Nets with Policy Gradient](https://mlsanity.com/paper/1609.05473/) (2016)
- [Analog Bits: Generating Discrete Data using Diffusion Models with Self-Conditioning](https://mlsanity.com/paper/2208.04202/) (2022)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [MCVD: Masked Conditional Video Diffusion for Prediction, Generation, and Interpolation](https://mlsanity.com/paper/2205.09853/) (2022)
- [Glow-TTS: A Generative Flow for Text-to-Speech via Monotonic Alignment Search](https://mlsanity.com/paper/2005.11129/) (2020)
- [A Survey on Generative Diffusion Model](https://mlsanity.com/paper/2209.02646/) (2022)
- [DiffusionBERT: Improving Generative Masked Language Models with Diffusion Models](https://mlsanity.com/paper/2211.15029/) (2022)
- [Diff-TTS: A Denoising Diffusion Model for Text-to-Speech](https://mlsanity.com/paper/2104.01409/) (2021)
- [DiffSinger: Singing Voice Synthesis via Shallow Diffusion Mechanism](https://mlsanity.com/paper/2105.02446/) (2021)
- [DiffTraj: Generating GPS Trajectory with Diffusion Probabilistic Model](https://mlsanity.com/paper/2304.11582/) (2023)
- [TrajGAIL: Generating Urban Vehicle Trajectories using Generative Adversarial Imitation Learning](https://mlsanity.com/paper/2007.14189/) (2020)
- [Global Context with Discrete Diffusion in Vector Quantised Modelling for Image Generation](https://mlsanity.com/paper/2112.01799/) (2021)
- [Continuous Trajectory Generation Based on Two-Stage GAN](https://mlsanity.com/paper/2301.07103/) (2023)

## Built on by (most cited first, 29 of 29)

- [A Survey on Diffusion Models for Time Series and Spatio-Temporal Data](https://mlsanity.com/paper/2404.18886/) (2024)
- [Trajectory Data Management and Mining: A Survey from Deep Learning to the LLM Era](https://mlsanity.com/paper/2403.14151/) (2024)
- [A Survey of Generative Techniques for Spatial-Temporal Data Mining](https://mlsanity.com/paper/2405.09592/) (2024)
- [DDAT: Diffusion Policies Enforcing Dynamically Admissible Robot Trajectories](https://mlsanity.com/paper/2502.15043/) (2025)
- [Modeling Human Gaze Behavior with Diffusion Models for Unified Scanpath Prediction](https://mlsanity.com/paper/2507.23021/) (2025)
- [TrajFlow: Nation-wide Pseudo GPS Trajectory Generation with Flow Matching Models](https://mlsanity.com/paper/2603.15009/) (2026)
- [TransferTraj: A Vehicle Trajectory Learning Model for Region and Task Transferability](https://mlsanity.com/paper/2505.12672/) (2025)
- [Leveraging the Spatial Hierarchy: Coarse-to-fine Trajectory Generation via Cascaded Hybrid Diffusion](https://mlsanity.com/paper/2507.13366/) (2025)
- [FollowGen: A Scaled Noise Conditional Diffusion Model for Car-Following Trajectory Prediction](https://mlsanity.com/paper/2411.16747/) (2024)
- [Bus-Conditioned Zero-Shot Trajectory Generation via Task Arithmetic](https://mlsanity.com/paper/2602.13071/) (2026)
- [TrajWeaver: Trajectory Recovery with State Propagation Diffusion Model](https://mlsanity.com/paper/2409.02124/) (2024)
- [PLMTrajRec: A Scalable and Generalizable Trajectory Recovery Method with Pre-trained Language Models](https://mlsanity.com/paper/2410.14281/) (2024)
- [DiffMOD: Progressive Diffusion Point Denoising for Moving Object Detection in Remote Sensing](https://mlsanity.com/paper/2504.10278/) (2025)
- [What is the Cost of Differential Privacy for Deep Learning-Based Trajectory Generation?](https://mlsanity.com/paper/2506.09312/) (2025)
- [Traj-Transformer: Diffusion Models with Transformer for GPS Trajectory Generation](https://mlsanity.com/paper/2510.06291/) (2025)
- [Dynamic Population Distribution Aware Human Trajectory Generation with Diffusion Model](https://mlsanity.com/paper/2511.01929/) (2025)
- [Learning to Land Anywhere: Transferable Generative Models for Aircraft Trajectories](https://mlsanity.com/paper/2511.04155/) (2025)
- [M-STAR: Multi-Scale Spatiotemporal Autoregression for Human Mobility Modeling](https://mlsanity.com/paper/2512.07314/) (2025)
- [TrajGPT-R: Generating Urban Mobility Trajectory with Reinforcement Learning-Enhanced Generative Pre-trained Transformer](https://mlsanity.com/paper/2602.20643/) (2026)
- [Learning Demographic-Conditioned Mobility Trajectories with Aggregate Supervision](https://mlsanity.com/paper/2603.03275/) (2026)
- [TRACE: Trajectory Recovery with State Propagation Diffusion for Urban Mobility](https://mlsanity.com/paper/2603.19474/) (2026)
- [InsTraj: Instructing Diffusion Models with Travel Intentions to Generate Real-world Trajectories](https://mlsanity.com/paper/2604.04106/) (2026)
- [Privacy Evaluation of Generative Models for Trajectory Generation](https://mlsanity.com/paper/2605.15246/) (2026)
- [CityTrajBench: A Unified Benchmark for City-Scale Vehicle Trajectory Generation](https://mlsanity.com/paper/2606.02287/) (2026)
- [TDDM-Melatt: A Decoupled Memory and Diffusion Framework for Generalizable Encrypted Traffic Classification](https://mlsanity.com/paper/2608.30745/) (2026)
- [Editable Map-Conditioned Trajectory Generation for Human Mobility Simulation](https://mlsanity.com/paper/2609.32360/) (2026)
- [Plan-to-Synthesis: Cross-City Human Mobility Generation via Semantic Latent Flow Matching](https://mlsanity.com/paper/2609.32732/) (2026)
- [Relative Transitions, Not Absolute Destinations: A Transfer-and-Ground Framework for Target-Trajectory-Free Human Mobility Generation](https://mlsanity.com/paper/2610.02033/) (2026)
- [Looking Ahead and Back: Anticipatory Generative Modeling for Road-Network Trajectories](https://mlsanity.com/paper/2610.13131/) (2026)

## Abstract (arXiv)

Trajectory data is essential for various applications as it records the movement of vehicles. However, publicly available trajectory datasets remain limited in scale due to privacy concerns, which hinders the development of trajectory data mining and trajectory-based applications. To address this issue, some methods for generating synthetic trajectories have been proposed to expand the scale of the dataset. However, all existing methods generate trajectories in the geographical coordinate system, which poses two limitations for their utilization in practical applications: 1) the inability to ensure that the generated trajectories are constrained on the road. 2) the lack of road-related information. In this paper, we propose a new problem to meet the practical application need, i.e., road network-constrained trajectory (RNTraj) generation, which can directly generate trajectories on the road network with road-related information. RNTraj is a hybrid type of data, in which each point is represented by a discrete road segment and a continuous moving rate. To generate RNTraj, we design a diffusion model called Diff-RNTraj. This model can effectively handle the hybrid RNTraj using a continuous diffusion framework by incorporating a pre-training strategy to embed hybrid RNTraj into continuous representations. During the sampling stage, a RNTraj decoder is designed to map the continuous representation generated by the diffusion model back to the hybrid RNTraj format. Furthermore, Diff-RNTraj introduces a novel loss function to enhance the spatial validity of the generated trajectories. Extensive experiments conducted on two real-world trajectory datasets demonstrate the effectiveness of the proposed model.