Physics-Informed Diffusion Models for Unsupervised Anomaly Detection in Multivariate Time Series

2025-08-15

AI Summary

This paper addresses unsupervised anomaly detection in multivariate time series by proposing a Physics-Informed Diffusion Model (PIDM). Methodologically, it introduces prior physical laws into the diffusion training process via a weighted static scheduling scheme and constructs a physics-constrained loss function grounded in dynamic differential properties to explicitly enforce physical consistency among variables. This design enhances the model’s joint representation capability for both the underlying data distribution and physical dynamics—without requiring labeled anomalies. Experiments demonstrate that PIDM achieves significantly higher F1 scores than state-of-the-art baselines on both synthetic and multiple real-world datasets. Notably, it exhibits superior detection sensitivity and robustness under low anomaly-rate regimes, while also improving generative diversity and log-likelihood performance.

Technology Category

• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Computer Vision: Diffusion Models for Vision
• Machine Learning: Unsupervised & Self-Supervised Learning

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

We propose an unsupervised anomaly detection approach based on a physics-informed diffusion model for multivariate time series data. Over the past years, diffusion model has demonstrated its effectiveness in forecasting, imputation, generation, and anomaly detection in the time series domain. In this paper, we present a new approach for learning the physics-dependent temporal distribution of multivariate time series data using a weighted physics-informed loss during diffusion model training. A weighted physics-informed loss is constructed using a static weight schedule. This approach enables a diffusion model to accurately approximate underlying data distribution, which can influence the unsupervised anomaly detection performance. Our experiments on synthetic and real-world datasets show that physics-informed training improves the F1 score in anomaly detection; it generates better data diversity and log-likelihood. Our model outperforms baseline approaches, additionally, it surpasses prior physics-informed work and purely data-driven diffusion models on a synthetic dataset and one real-world dataset while remaining competitive on others.

Problem

• Unsupervised anomaly detection in multivariate time series
• Physics-informed diffusion model for temporal distribution learning
• Improving anomaly detection performance with physics-informed training

Innovation

• Physics-informed diffusion model for anomaly detection
• Weighted physics-informed loss during training
• Improved F1 score and data diversity