Proximal Term Matters: Rethinking the Diffusion Models for Time-Series Data Imputation

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 the DM-based TSDI process from a proximal-operator perspective and uncover two inherent components: Wasserstein-distance-based proximal regularizer, which hinders the model's ability to counteract non-stationarity, and the dissipative regularizer, which amplifies diversity at the expense of fidelity. Building on this insight, we propose a novel framework called SPIRIT ($\underline{\text{S}}$emi-$\underline{\text{P}}$rox$\underline{\text{i}}$mal Transport $\underline{\text{R}}$egularized time-series $\underline{\text{I}}$mpu$\underline{\text{t}}$ation). Specifically, we introduce an entropy-induced Bregman divergence to relax the mass-preserving constraint in the Wasserstein distance, formulate the semi-proximal transport (SPT) discrepancy, and theoretically establish the robustness of SPT to non-stationary pattern. Subsequently, we remove the dissipative structure and derive the complete SPIRIT workflow, with SPT serving as the proximal operator. Extensive experiments demonstrate the efficacy of the proposed SPIRIT approach.