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

TL;DR

This paper analyzes the limitations of diffusion models in time-series data imputation, identifies key issues related to non-stationarity and objective inconsistency, and proposes a novel SPIRIT framework with theoretical robustness and improved performance.

Contribution

It introduces a proximal recursion perspective to understand diffusion models, and develops SPIRIT, a new framework that enhances imputation robustness against non-stationarity.

Findings

SPIRIT outperforms existing methods in complex scenarios.

Theoretical proof of robustness against non-stationarity.

Effective handling of diversity-fidelity trade-off.

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.