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

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.

💡 Research Summary

This paper investigates why diffusion‑model (DM) based time‑series data imputation (TSDI) often underperforms in realistic, non‑stationary scenarios. The authors identify two fundamental obstacles: (1) non‑stationary temporal dynamics that bias the inference trajectory, and (2) an objective mismatch because DMs are trained to generate diverse samples while imputation requires accurate pointwise recovery. By casting the DM inference process as a proximal recursion, they reveal that the standard formulation implicitly contains a 2‑Wasserstein distance regularization together with a dissipative term originating from the drift‑diffusion SDE. The Wasserstein term enforces strict mass conservation, which becomes problematic when the underlying distribution shifts or contains outliers; the dissipative term injects entropy, encouraging diversity at the expense of deterministic accuracy.

To address these issues, the authors propose a novel “semi‑proximal transport” (SPT) discrepancy. Instead of the hard marginal constraint in optimal transport, SPT relaxes the target marginal using an entropy‑induced Bregman divergence. Formally,

\