# ControlTraj: Controllable Trajectory Generation with Topology-Constrained Diffusion Model

arXiv: https://arxiv.org/abs/2404.15380 · HTML: https://mlsanity.com/paper/2404.15380/

## Key facts

- Cited by 49 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 65 references that are in the map.
- First posted on arXiv 23 Apr 2024.

## 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)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [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)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (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)
- [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)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [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)
- [Deep Gravity: enhancing mobility flows generation with deep neural networks and geographic information](https://mlsanity.com/paper/2012.00489/) (2020)
- [A Survey on Trajectory Data Management, Analytics, and Learning](https://mlsanity.com/paper/2003.11547/) (2020)
- [Trajectory Data Management and Mining: A Survey from Deep Learning to the LLM Era](https://mlsanity.com/paper/2403.14151/) (2024)
- [Towards Unifying Diffusion Models for Probabilistic Spatio-Temporal Graph Learning](https://mlsanity.com/paper/2310.17360/) (2023)
- [LDPTrace: Locally Differentially Private Trajectory Synthesis](https://mlsanity.com/paper/2302.06180/) (2023)
- [Learning to Route with Sparse Trajectory Sets---Extended Version](https://mlsanity.com/paper/1802.07980/) (2018)
- [Crime in Urban Areas: A Data Mining Perspective](https://mlsanity.com/paper/1804.08159/) (2018)

## Built on by (most cited first, 30 of 49)

- [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)
- [Geolocation with Real Human Gameplay Data: A Large-Scale Dataset and Human-Like Reasoning Framework](https://mlsanity.com/paper/2502.13759/) (2025)
- [Foundation Models for Spatio-Temporal Data Science: A Tutorial and Survey](https://mlsanity.com/paper/2503.13502/) (2025)
- [UniTraj: Learning a Universal Trajectory Foundation Model from Billion-Scale Worldwide Traces](https://mlsanity.com/paper/2411.03859/) (2024)
- [MM-Path: Multi-modal, Multi-granularity Path Representation Learning -- Extended Version](https://mlsanity.com/paper/2411.18428/) (2024)
- [GRE Suite: Geo-localization Inference via Fine-Tuned Vision-Language Models and Enhanced Reasoning Chains](https://mlsanity.com/paper/2505.18700/) (2025)
- [GeoGen: A Two-stage Coarse-to-Fine Framework for Fine-grained Synthetic Location-based Social Network Trajectory Generation](https://mlsanity.com/paper/2510.07735/) (2025)
- [Diffusion Transformers as Open-World Spatiotemporal Foundation Models](https://mlsanity.com/paper/2411.12164/) (2024)
- [POI-Enhancer: An LLM-based Semantic Enhancement Framework for POI Representation Learning](https://mlsanity.com/paper/2502.10038/) (2025)
- [Unraveling Spatio-Temporal Foundation Models via the Pipeline Lens: A Comprehensive Review](https://mlsanity.com/paper/2506.01364/) (2025)
- [Holistic Semantic Representation for Navigational Trajectory Generation](https://mlsanity.com/paper/2501.02737/) (2025)
- [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)
- [ParkDiffusion: Heterogeneous Multi-Agent Multi-Modal Trajectory Prediction for Automated Parking using Diffusion Models](https://mlsanity.com/paper/2505.00586/) (2025)
- [TrajFlow: Nation-wide Pseudo GPS Trajectory Generation with Flow Matching Models](https://mlsanity.com/paper/2603.15009/) (2026)
- [BrainMRDiff: A Diffusion Model for Anatomically Consistent Brain MRI Synthesis](https://mlsanity.com/paper/2504.04532/) (2025)
- [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)
- [SynHAT: A Two-stage Coarse-to-Fine Diffusion Framework for Synthesizing Human Activity Traces](https://mlsanity.com/paper/2604.14705/) (2026)
- [Spatio-Temporal Trajectory Foundation Model - Recent Advances and Future Directions](https://mlsanity.com/paper/2511.20729/) (2025)
- [Learning to Wander: Improving the Global Image Geolocation Ability of LMMs via Actionable Reasoning](https://mlsanity.com/paper/2603.10463/) (2026)
- [Towards Physics-informed Diffusion for Anomaly Detection in Trajectories](https://mlsanity.com/paper/2506.06999/) (2025)
- [UniMove: A Unified Model for Multi-city Human Mobility Prediction](https://mlsanity.com/paper/2508.06986/) (2025)
- [Bus-Conditioned Zero-Shot Trajectory Generation via Task Arithmetic](https://mlsanity.com/paper/2602.13071/) (2026)
- [TrajDLM: Topology-Aware Block Diffusion Language Model for Trajectory Generation](https://mlsanity.com/paper/2605.10020/) (2026)
- [Learning Generalized and Flexible Trajectory Models from Omni-Semantic Supervision](https://mlsanity.com/paper/2505.17437/) (2025)
- [LLMs Meet Cross-Modal Time Series Analytics: Overview and Directions](https://mlsanity.com/paper/2507.10620/) (2025)
- [MoveFM-R: Advancing Mobility Foundation Models via Language-driven Semantic Reasoning](https://mlsanity.com/paper/2509.22403/) (2025)
- [Multi-Scale Diffusion Transformer for Jointly Simulating User Mobility and Mobile Traffic Pattern](https://mlsanity.com/paper/2510.10158/) (2025)

## Abstract (arXiv)

Generating trajectory data is among promising solutions to addressing privacy concerns, collection costs, and proprietary restrictions usually associated with human mobility analyses. However, existing trajectory generation methods are still in their infancy due to the inherent diversity and unpredictability of human activities, grappling with issues such as fidelity, flexibility, and generalizability. To overcome these obstacles, we propose ControlTraj, a Controllable Trajectory generation framework with the topology-constrained diffusion model. Distinct from prior approaches, ControlTraj utilizes a diffusion model to generate high-fidelity trajectories while integrating the structural constraints of road network topology to guide the geographical outcomes. Specifically, we develop a novel road segment autoencoder to extract fine-grained road segment embedding. The encoded features, along with trip attributes, are subsequently merged into the proposed geographic denoising UNet architecture, named GeoUNet, to synthesize geographic trajectories from white noise. Through experimentation across three real-world data settings, ControlTraj demonstrates its ability to produce human-directed, high-fidelity trajectory generation with adaptability to unexplored geographical contexts.