Specifically, we summarize our contributions into the following points.

More advanced methods dealwith missing data byautoregressivelyreplacing missing observations with predicted ones, eventually using bidirectional architectures [5,6]toexploit both forwardandbackwardtemporal dependencies.

Traffic time series imputation is crucial for the safety and reliability of intelligent transportation systems, while diverse types of missing data, including random, fiber, and block missing make the imputation task challenging. Existing models often focus on disentangling and separately modeling spatial and temporal patterns based on relationships between data points. However, these approaches struggle to adapt to the random missing positions, and fail to learn long-term and large-scale dependencies, which are essential in extensive missing conditions. In this paper, patterns are categorized into two types to handle various missing data conditions: primary patterns, which originate from internal relationships between data points, and auxiliary patterns, influenced by external factors like timestamps and node attributes. Accordingly, we propose the Primary-Auxiliary Spatio-Temporal network (PAST). It comprises a graph-integrated module (GIM) and a cross-gated module (CGM). GIM captures primary patterns via dynamic graphs with interval-aware dropout and multi-order convolutions, and CGM extracts auxiliary patterns through bidirectional gating on embedded external features. The two modules interact via shared hidden vectors and are trained under an ensemble self-supervised framework. Experiments on three datasets under 27 missing data conditions demonstrate that the imputation accuracy of PAST outperforms seven state-of-the-art baselines by up to 26.2% in RMSE and 31.6% in MAE.

Specifically, we summarize our contributions into the following points.

Time Series Imputation (TSI), which aims to recover missing values in temporal data, remains a fundamental challenge due to the complex and often high-rate missingness in real-world scenarios. Existing models typically optimize the point-wise reconstruction loss, focusing on recovering numerical values (local information). However, we observe that under high missing rates, these models still perform well in the training phase yet produce poor imputations and distorted latent representation distributions (global information) in the inference phase. This reveals a critical optimization dilemma: current objectives lack global guidance, leading models to overfit local noise and fail to capture global information of the data. To address this issue, we propose a new training paradigm, Glocal Information Bottleneck (Glocal-IB). Glocal-IB is model-agnostic and extends the standard IB framework by introducing a Global Alignment loss, derived from a tractable mutual information approximation. This loss aligns the latent representations of masked inputs with those of their originally observed counterparts. It helps the model retain global structure and local details while suppressing noise caused by missing values, giving rise to better generalization under high missingness. Extensive experiments on nine datasets confirm that Glocal-IB leads to consistently improved performance and aligned latent representations under missingness. Our code implementation is available in https://github.com/Muyiiiii/NeurIPS-25-Glocal-IB.

Spatio-temporal data abounds in domain like traffic and environmental monitoring. However, it often suffers from missing values due to sensor malfunctions, transmission failures, etc. Recent years have seen continued efforts to improve spatio-temporal data imputation performance. Recently diffusion models have outperformed other approaches in various tasks, including spatio-temporal imputation, showing competitive performance. Extracting and utilizing spatio-temporal dependencies as conditional information is vital in diffusion-based methods. However, previous methods introduce error accumulation in this process and ignore the variability of the dependencies in the noisy data at different diffusion steps. In this paper, we propose AdaSTI (Adaptive Dependency Model in Diffusion-based Spatio-Temporal Imputation), a novel spatio-temporal imputation approach based on conditional diffusion model. Inside AdaSTI, we propose a BiS4PI network based on a bi-directional S4 model for pre-imputation with the imputed result used to extract conditional information by our designed Spatio-Temporal Conditionalizer (STC)network. We also propose a Noise-Aware Spatio-Temporal (NAST) network with a gated attention mechanism to capture the variant dependencies across diffusion steps. Extensive experiments on three real-world datasets show that AdaSTI outperforms existing methods in all the settings, with up to 46.4% reduction in imputation error.

To account also for spatial dependencies, Cini et al.