# Towards Physics-informed Diffusion for Anomaly Detection in Trajectories

arXiv: https://arxiv.org/abs/2506.06999 · HTML: https://mlsanity.com/paper/2506.06999/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 104 references that are in the map.
- First posted on arXiv 8 Jun 2025.

## Builds on (most cited first, 30 of 41)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [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)
- [Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems](https://mlsanity.com/paper/2003.04919/) (2020)
- [CityFlow: A Multi-Agent Reinforcement Learning Environment for Large Scale City Traffic Scenario](https://mlsanity.com/paper/1905.05217/) (2019)
- [A Survey on Deep Learning for Human Mobility](https://mlsanity.com/paper/2012.02825/) (2020)
- [DiffTraj: Generating GPS Trajectory with Diffusion Probabilistic Model](https://mlsanity.com/paper/2304.11582/) (2023)
- [Deep Gravity: enhancing mobility flows generation with deep neural networks and geographic information](https://mlsanity.com/paper/2012.00489/) (2020)
- [LSTM-TrajGAN: A Deep Learning Approach to Trajectory Privacy Protection](https://mlsanity.com/paper/2006.10521/) (2020)
- [ControlTraj: Controllable Trajectory Generation with Topology-Constrained Diffusion Model](https://mlsanity.com/paper/2404.15380/) (2024)
- [MobTCast: Leveraging Auxiliary Trajectory Forecasting for Human Mobility Prediction](https://mlsanity.com/paper/2110.01401/) (2021)
- [TrajGAIL: Generating Urban Vehicle Trajectories using Generative Adversarial Imitation Learning](https://mlsanity.com/paper/2007.14189/) (2020)
- [Contrastive Trajectory Similarity Learning with Dual-Feature Attention](https://mlsanity.com/paper/2210.05155/) (2022)
- [Continuous Trajectory Generation Based on Two-Stage GAN](https://mlsanity.com/paper/2301.07103/) (2023)
- [Large Language Models for Spatial Trajectory Patterns Mining](https://mlsanity.com/paper/2310.04942/) (2023)
- [Origin-Destination Travel Time Oracle for Map-based Services](https://mlsanity.com/paper/2307.03048/) (2023)
- [LDPTrace: Locally Differentially Private Trajectory Synthesis](https://mlsanity.com/paper/2302.06180/) (2023)
- [Spatiotemporal-Augmented Graph Neural Networks for Human Mobility Simulation](https://mlsanity.com/paper/2306.09381/) (2023)
- [NUMOSIM: A Synthetic Mobility Dataset with Anomaly Detection Benchmarks](https://mlsanity.com/paper/2409.03024/) (2024)
- [Urban Anomalies: A Simulated Human Mobility Dataset with Injected Anomalies](https://mlsanity.com/paper/2410.01844/) (2024)
- [Towards a Tighter Bound on Possible-Rendezvous Areas: Preliminary Results](https://mlsanity.com/paper/2206.12756/) (2022)
- [PateGail: A Privacy-Preserving Mobility Trajectory Generator with Imitation Learning](https://mlsanity.com/paper/2407.16729/) (2024)
- [Revisiting Synthetic Human Trajectories: Imitative Generation and Benchmarks Beyond Datasaurus](https://mlsanity.com/paper/2409.13790/) (2024)
- [Spatial Computing Opportunities in Biomedical Decision Support: The Atlas-EHR Vision](https://mlsanity.com/paper/2305.09675/) (2023)
- [Guaranteeing Consistency in a Motion Planning and Control Architecture Using a Kinematic Bicycle Model](https://mlsanity.com/paper/1804.08290/) (2018)
- [CBLab: Supporting the Training of Large-scale Traffic Control Policies with Scalable Traffic Simulation](https://mlsanity.com/paper/2210.00896/) (2022)
- [Trajectory Anomaly Detection with Language Models](https://mlsanity.com/paper/2409.15366/) (2024)

## Built on by (most cited first, 2 of 2)

- [Towards Fine-Tuning-Based Site Calibration for Knowledge-Guided Machine Learning: A Summary of Results](https://mlsanity.com/paper/2512.16013/) (2025)
- [Mobility Anomaly Generation using LLM-Driven Behavior with Kinematic Constraints](https://mlsanity.com/paper/2606.10314/) (2026)

## Abstract (arXiv)

Given trajectory data, a domain-specific study area, and a user-defined threshold, we aim to find anomalous trajectories indicative of possible GPS spoofing (e.g., fake trajectory). The problem is societally important to curb illegal activities in international waters, such as unauthorized fishing and illicit oil transfers. The problem is challenging due to advances in AI generated in deep fakes generation (e.g., additive noise, fake trajectories) and lack of adequate amount of labeled samples for ground-truth verification. Recent literature shows promising results for anomalous trajectory detection using generative models despite data sparsity. However, they do not consider fine-scale spatiotemporal dependencies and prior physical knowledge, resulting in higher false-positive rates. To address these limitations, we propose a physics-informed diffusion model that integrates kinematic constraints to identify trajectories that do not adhere to physical laws. Experimental results on real-world datasets in the maritime and urban domains show that the proposed framework results in higher prediction accuracy and lower estimation error rate for anomaly detection and trajectory generation methods, respectively. Our implementation is available at https://github.com/arunshar/Physics-Informed-Diffusion-Probabilistic-Model.