STDiff: A State Transition Diffusion Framework for Time Series Imputation in Industrial Systems

2025-08-26

AI Summary

This paper addresses the challenging task of imputing long contiguous missing segments in controlled, highly non-stationary time series arising in industrial systems. Method: We propose a dynamics-aware conditional denoising diffusion model that—uniquely—integrates state-space modeling and causal control theory into the diffusion process. By explicitly incorporating control inputs and environmental variables via causal convolution and temporal alignment, the model iteratively generates missing values starting from the most recent observable state, ensuring physical consistency with underlying system dynamics. Contribution/Results: Unlike conventional sliding-window approaches relying on static pattern assumptions, our method enables physically interpretable sequence reconstruction. Evaluated on both synthetic and real-world industrial datasets, it achieves the lowest imputation error for long missing segments, produces dynamically plausible trajectories, and significantly outperforms baseline models prone to over-smoothing.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Intelligent Robots: State Estimation
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Most deep learning methods for imputing missing values treat the task as completing patterns within a fixed time window. This assumption often fails in industrial systems, where dynamics are driven by control actions, are highly non-stationary, and can experience long, uninterrupted gaps. We propose STDiff, which reframes imputation as learning how the system evolves from one state to the next. STDiff uses a conditional denoising diffusion model with a causal bias aligned to control theory, generating missing values step-by-step based on the most recent known state and relevant control or environmental inputs. On a public wastewater treatment dataset with simulated missing blocks, STDiff consistently achieves the lowest errors, with its advantage increasing for longer gaps. On a raw industrial dataset with substantial real gaps, it produces trajectories that remain dynamically plausible, in contrast to window-based models that tend to flatten or over-smooth. These results support dynamics-aware, explicitly conditioned imputation as a robust approach for industrial time series, and we discuss computational trade-offs and extensions to broader domains.

Problem

• Imputing missing values in non-stationary industrial time series
• Handling long uninterrupted gaps in control-driven system data
• Generating dynamically plausible trajectories instead of pattern completion

Innovation

• State transition diffusion model for imputation
• Causal denoising aligned with control theory
• Step-by-step generation from recent states