分析和改进用于时间序列数据插补的扩散模型：从近端递归的角度
Analyzing and Improving Diffusion Models for Time-Series Data Imputation: A Proximal Recursion Perspective
AI总结：
本文从近端递归角度提出SPIRIT框架，通过引入熵诱导的Bregman分歧和半近端传输正则化，改进扩散模型在时间序列数据插补中的性能。
摘要：
扩散模型（DMs）在时间序列数据插补（TSDI）中显示出前景；然而，在复杂场景中其性能仍不一致。我们将其归因于两个主要障碍：（1）非平稳的时间动态，这会偏移推断轨迹并导致对异常值敏感的插补；以及（2）目标不一致，因为插补倾向于准确的逐点恢复，而DMs本质上被训练为生成多样化的样本。为了更好地理解这些问题，我们通过近端操作视角分析基于DM的时间序列数据插补过程，并发现过程中的隐含Wasserstein距离正则化会阻碍模型对抗非平稳性和耗散正则化的能力，从而在牺牲保真度的情况下增加多样性。基于这一见解，我们提出了一种新的框架，称为SPIRIT（半近端传输正则化时间序列插补）。具体而言，我们引入熵诱导的Bregman分歧来放松Wasserstein距离中的质量保持约束，制定半近端传输（SPT）差异，并理论证明SPT对非平稳性的鲁棒性。随后，我们移除耗散结构并推导出完整的SPIRIT工作流程，其中SPT作为近端操作符。广泛的实验展示了所提SPIRIT方法的有效性。
英文摘要：
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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