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

• URL: http://arxiv.org/abs/2602.01182v1
• Date: Sun, 01 Feb 2026 12:11:57 GMT
• Title: Analyzing and Improving Diffusion Models for Time-Series Data Imputation: A Proximal Recursion Perspective
• Abstract summary: Diffusion models (DMs) have shown promise for Time-Series Data Imputation.<n>DMs' performance remains inconsistent in complex scenarios.<n>We propose a novel framework called SPIRIT (Semi-Proximal Transport Regularized time-series Imputation)
• Score: 45.713195454899875
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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