Analyzing and Improving Diffusion Models for Time-Series Data Imputation: A Proximal Recursion Perspective

2026-02-01

AI Summary

Diffusion models for time series imputation often suffer from poor fidelity and sensitivity to outliers due to their misalignment with the non-stationary dynamics of real-world data. This work reveals that, from a proximal operator perspective, the implicit Wasserstein regularization in these models enhances diversity at the expense of accuracy. To address this trade-off, we propose SPIRIT, a Semi-Proximal Optimal Transport (SPT) framework that relaxes the Wasserstein mass conservation constraint via an entropy-induced Bregman divergence, thereby eliminating dissipative structures. We theoretically establish SPIRIT’s robustness to non-stationarity and demonstrate through experiments that it significantly improves imputation accuracy and robustness in complex scenarios while effectively balancing diversity and fidelity.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Time-Series/Data Streams
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

Diffusion models (DMs) have shown promise for Time-Series Data Imputation (TSDI); however, their performance remains inconsistent in complex scenarios. We attribute this to two primary obstacles: (1) non-stationary temporal dynamics, which can bias the inference trajectory and lead to outlier-sensitive imputations; and (2) objective inconsistency, since imputation favors accurate pointwise recovery whereas DMs are inherently trained to generate diverse samples. To better understand these issues, we analyze DM-based TSDI process through a proximal-operator perspective and uncover that an implicit Wasserstein distance regularization inherent in the process hinders the model's ability to counteract non-stationarity and dissipative regularizer, thereby amplifying diversity at the expense of fidelity. Building on this insight, we propose a novel framework called SPIRIT (Semi-Proximal Transport Regularized time-series Imputation). Specifically, we introduce entropy-induced Bregman divergence to relax the mass preserving constraint in the Wasserstein distance, formulate the semi-proximal transport (SPT) discrepancy, and theoretically prove the robustness of SPT against non-stationarity. Subsequently, we remove the dissipative structure and derive the complete SPIRIT workflow, with SPT serving as the proximal operator. Extensive experiments demonstrate the effectiveness of the proposed SPIRIT approach.

Problem

• Time-Series Data Imputation
• Diffusion Models
• Non-stationary Temporal Dynamics
• Objective Inconsistency
• Wasserstein Distance

Innovation

• Diffusion Models
• Time-Series Imputation
• Proximal Operator
• Semi-Proximal Transport
• Non-stationarity