# DiffTraj: Generating GPS Trajectory with Diffusion Probabilistic Model

arXiv: https://arxiv.org/abs/2304.11582 · HTML: https://mlsanity.com/paper/2304.11582/

## Key facts

- Cited by 65 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 22 of its 43 references that are in the map.
- First posted on arXiv 23 Apr 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, 22 of 22)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [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)
- [Blended Diffusion for Text-driven Editing of Natural Images](https://mlsanity.com/paper/2111.14818/) (2021)
- [Wide & Deep Learning for Recommender Systems](https://mlsanity.com/paper/1606.07792/) (2016)
- [A Survey on Deep Learning for Human Mobility](https://mlsanity.com/paper/2012.02825/) (2020)
- [DiffSTG: Probabilistic Spatio-Temporal Graph Forecasting with Denoising Diffusion Models](https://mlsanity.com/paper/2301.13629/) (2023)
- [DL-Traff: Survey and Benchmark of Deep Learning Models for Urban Traffic Prediction](https://mlsanity.com/paper/2108.09091/) (2021)
- [LDPTrace: Locally Differentially Private Trajectory Synthesis](https://mlsanity.com/paper/2302.06180/) (2023)
- [AutoSTL: Automated Spatio-Temporal Multi-Task Learning](https://mlsanity.com/paper/2304.09174/) (2023)
- [Privacy-preserving Travel Time Prediction with Uncertainty Using GPS Trace Data](https://mlsanity.com/paper/2101.00310/) (2021)

## Built on by (most cited first, 30 of 65)

- [Foundation Models for Time Series Analysis: A Tutorial and Survey](https://mlsanity.com/paper/2403.14735/) (2024)
- [Large Language Models as Urban Residents: An LLM Agent Framework for Personal Mobility Generation](https://mlsanity.com/paper/2402.14744/) (2024)
- [A Survey on Diffusion Models for Time Series and Spatio-Temporal Data](https://mlsanity.com/paper/2404.18886/) (2024)
- [G3: An Effective and Adaptive Framework for Worldwide Geolocalization Using Large Multi-Modality Models](https://mlsanity.com/paper/2405.14702/) (2024)
- [Simulating Human-like Daily Activities with Desire-driven Autonomy](https://mlsanity.com/paper/2412.06435/) (2024)
- [Diff-RNTraj: A Structure-aware Diffusion Model for Road Network-constrained Trajectory Generation](https://mlsanity.com/paper/2402.07369/) (2024)
- [Towards Urban General Intelligence: A Review and Outlook of Urban Foundation Models](https://mlsanity.com/paper/2402.01749/) (2024)
- [Trajectory Data Management and Mining: A Survey from Deep Learning to the LLM Era](https://mlsanity.com/paper/2403.14151/) (2024)
- [Be More Real: Travel Diary Generation Using LLM Agents and Individual Profiles](https://mlsanity.com/paper/2407.18932/) (2024)
- [Parsimony or Capability? Decomposition Delivers Both in Long-term Time Series Forecasting](https://mlsanity.com/paper/2401.11929/) (2024)
- [Chain-of-Planned-Behaviour Workflow Elicits Few-Shot Mobility Generation in LLMs](https://mlsanity.com/paper/2402.09836/) (2024)
- [A Survey of Generative Techniques for Spatial-Temporal Data Mining](https://mlsanity.com/paper/2405.09592/) (2024)
- [MM-Path: Multi-modal, Multi-granularity Path Representation Learning -- Extended Version](https://mlsanity.com/paper/2411.18428/) (2024)
- [Trajectory Prediction for Autonomous Driving: Progress, Limitations, and Future Directions](https://mlsanity.com/paper/2503.03262/) (2025)
- [GRE Suite: Geo-localization Inference via Fine-Tuned Vision-Language Models and Enhanced Reasoning Chains](https://mlsanity.com/paper/2505.18700/) (2025)
- [MobilityGPT: Enhanced Human Mobility Modeling with a GPT model](https://mlsanity.com/paper/2402.03264/) (2024)
- [Diffusion Transformers as Open-World Spatiotemporal Foundation Models](https://mlsanity.com/paper/2411.12164/) (2024)
- [Unraveling Spatio-Temporal Foundation Models via the Pipeline Lens: A Comprehensive Review](https://mlsanity.com/paper/2506.01364/) (2025)
- [C2F-TP: A Coarse-to-Fine Denoising Framework for Uncertainty-Aware Trajectory Prediction](https://mlsanity.com/paper/2412.13231/) (2024)
- [Taming the Long Tail in Human Mobility Prediction](https://mlsanity.com/paper/2410.14970/) (2024)
- [Noise Matters: Diffusion Model-based Urban Mobility Generation with Collaborative Noise Priors](https://mlsanity.com/paper/2412.05000/) (2024)
- [Geo-Llama: Leveraging LLMs for Human Mobility Trajectory Generation with Spatiotemporal Constraints](https://mlsanity.com/paper/2408.13918/) (2024)
- [Modeling Human Gaze Behavior with Diffusion Models for Unified Scanpath Prediction](https://mlsanity.com/paper/2507.23021/) (2025)
- [Certified Human Trajectory Prediction](https://mlsanity.com/paper/2403.13778/) (2024)
- [Learning Universal Human Mobility Patterns with a Foundation Model for Cross-domain Data Fusion](https://mlsanity.com/paper/2503.15779/) (2025)
- [TrajFlow: Nation-wide Pseudo GPS Trajectory Generation with Flow Matching Models](https://mlsanity.com/paper/2603.15009/) (2026)
- [A Gentle Introduction and Tutorial on Deep Generative Models in Transportation Research](https://mlsanity.com/paper/2410.07066/) (2024)
- [Large Vision Model-Enhanced Digital Twin with Deep Reinforcement Learning for User Association and Load Balancing in Dynamic Wireless Networks](https://mlsanity.com/paper/2410.07611/) (2024)
- [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)

## Abstract (arXiv)

Pervasive integration of GPS-enabled devices and data acquisition technologies has led to an exponential increase in GPS trajectory data, fostering advancements in spatial-temporal data mining research. Nonetheless, GPS trajectories contain personal geolocation information, rendering serious privacy concerns when working with raw data. A promising approach to address this issue is trajectory generation, which involves replacing original data with generated, privacy-free alternatives. Despite the potential of trajectory generation, the complex nature of human behavior and its inherent stochastic characteristics pose challenges in generating high-quality trajectories. In this work, we propose a spatial-temporal diffusion probabilistic model for trajectory generation (DiffTraj). This model effectively combines the generative abilities of diffusion models with the spatial-temporal features derived from real trajectories. The core idea is to reconstruct and synthesize geographic trajectories from white noise through a reverse trajectory denoising process. Furthermore, we propose a Trajectory UNet (Traj-UNet) deep neural network to embed conditional information and accurately estimate noise levels during the reverse process. Experiments on two real-world datasets show that DiffTraj can be intuitively applied to generate high-fidelity trajectories while retaining the original distributions. Moreover, the generated results can support downstream trajectory analysis tasks and significantly outperform other methods in terms of geo-distribution evaluations.