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Boundary-enhanced time series data imputation with long-term dependency diffusion models

Chunjing Xiao, Xue Jiang, Xianghe Du, Wei Yang, Wei Lu, Xiaomin Wang, Kevin Chetty

TL;DR

This work tackles missing data imputation in multivariate time series by leveraging diffusion-based generative modeling. It identifies boundary distortion between missing and observed regions and limited ability to capture long-range dependencies as key weaknesses of prior diffusion methods. The proposed DSDI framework introduces a weight-reducing injection of autoregressively predicted missing values into the reverse diffusion and a multi-scale TemS4-based U-Net to model long-term temporal structure. Empirical results on DACMI, ETT, and AQI show consistent improvements over state-of-the-art baselines, indicating strong practical impact for sectors like healthcare, energy, and air-quality monitoring.

Abstract

Data imputation is crucial for addressing challenges posed by missing values in multivariate time series data across various fields, such as healthcare, traffic, and economics, and has garnered significant attention. Among various methods, diffusion model-based approaches show notable performance improvements. However, existing methods often cause disharmonious boundaries between missing and known regions and overlook long-range dependencies in missing data estimation, leading to suboptimal results. To address these issues, we propose a Diffusion-based time Series Data Imputation (DSDI) framework. We develop a weight-reducing injection strategy that incorporates the predicted values of missing points with reducing weights into the reverse diffusion process to mitigate boundary inconsistencies. Further, we introduce a multi-scale S4-based U-Net, which combines hierarchical information from different levels via multi-resolution integration to capture long-term dependencies. Experimental results demonstrate that our model outperforms existing imputation methods.

Boundary-enhanced time series data imputation with long-term dependency diffusion models

TL;DR

This work tackles missing data imputation in multivariate time series by leveraging diffusion-based generative modeling. It identifies boundary distortion between missing and observed regions and limited ability to capture long-range dependencies as key weaknesses of prior diffusion methods. The proposed DSDI framework introduces a weight-reducing injection of autoregressively predicted missing values into the reverse diffusion and a multi-scale TemS4-based U-Net to model long-term temporal structure. Empirical results on DACMI, ETT, and AQI show consistent improvements over state-of-the-art baselines, indicating strong practical impact for sectors like healthcare, energy, and air-quality monitoring.

Abstract

Data imputation is crucial for addressing challenges posed by missing values in multivariate time series data across various fields, such as healthcare, traffic, and economics, and has garnered significant attention. Among various methods, diffusion model-based approaches show notable performance improvements. However, existing methods often cause disharmonious boundaries between missing and known regions and overlook long-range dependencies in missing data estimation, leading to suboptimal results. To address these issues, we propose a Diffusion-based time Series Data Imputation (DSDI) framework. We develop a weight-reducing injection strategy that incorporates the predicted values of missing points with reducing weights into the reverse diffusion process to mitigate boundary inconsistencies. Further, we introduce a multi-scale S4-based U-Net, which combines hierarchical information from different levels via multi-resolution integration to capture long-term dependencies. Experimental results demonstrate that our model outperforms existing imputation methods.
Paper Structure (19 sections, 20 equations, 6 figures, 2 tables, 1 algorithm)

This paper contains 19 sections, 20 equations, 6 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Problem Definition
  4. Diffusion Model
  5. Related Work
  6. RNN-based Methods
  7. VAE-based Models
  8. GAN-based Approaches
  9. Diffusion-based Techniques
  10. DSDI Model
  11. Conditional Diffusion Imputation using Known Values
  12. Weight-Reducing Injection on Missing Points
  13. Multi-Scale TemS4-based U-Net
  14. Experimental Evaluation
  15. Experimental Settings
  16. ...and 4 more sections

Figures (6)

  • Figure 1: The DSDI framework.
  • Figure 2: The architecture of the multi-scale TemS4-based U-Net.
  • Figure 3: MAE and RMSE at different missing rates.
  • Figure 4: The ablation study.
  • Figure 5: The impact of the diffusion steps.
  • ...and 1 more figures