Diffusion models have demonstrated remarkable performance in modeling complex data priors, catalyzing their widespread adoption in solving various inverse problems. However, the inherently iterative nature of diffusion-based inverse algorithms often requires hundreds to thousands of steps, with performance degradation occurring under fewer steps which limits their practical applicability. While high-order diffusion ODE solvers have been extensively explored for efficient diffusion sampling without observations, their application to inverse problems remains underexplored due to the diverse forms of inverse algorithms and their need for repeated trajectory correction based on observations. To address this gap, we first introduce a canonical form that decomposes existing diffusion-based inverse algorithms into three modules to unify their analysis. Inspired by the linear subspace search strategy in the design of high-order diffusion ODE solvers, we propose the Learnable Linear Extrapolation (LLE) method, a lightweight approach that universally enhances the performance of any diffusion-based inverse algorithm that fits the proposed canonical form. Extensive experiments demonstrate consistent improvements of the proposed LLE method across multiple algorithms and tasks, indicating its potential for more efficient solutions and boosted performance of diffusion-based inverse algorithms with limited steps. Codes for reproducing our experiments are available at https://github.com/weigerzan/LLE_inverse_problem.

Time series anomaly detection (TSAD) is becoming increasingly vital due to the rapid growth of time series data across various sectors. Anomalies in web service data, for example, can signal critical incidents such as system failures or server malfunctions, necessitating timely detection and response. However, most existing TSAD methodologies rely heavily on manual feature engineering or require extensive labeled training data, while also offering limited interpretability. To address these challenges, we introduce a pioneering framework called the Time Series Anomaly Multimodal Analyzer (TAMA), which leverages the power of Large Multimodal Models (LMMs) to enhance both the detection and interpretation of anomalies in time series data. By converting time series into visual formats that LMMs can efficiently process, TAMA leverages few-shot in-context learning capabilities to reduce dependence on extensive labeled datasets. Our methodology is validated through rigorous experimentation on multiple real-world datasets, where TAMA consistently outperforms state-of-the-art methods in TSAD tasks. Additionally, TAMA provides rich, natural language-based semantic analysis, offering deeper insights into the nature of detected anomalies. Furthermore, we contribute one of the first open-source datasets that includes anomaly detection labels, anomaly type labels, and contextual description, facilitating broader exploration and advancement within this critical field. Ultimately, TAMA not only excels in anomaly detection but also provides a comprehensive approach for understanding the underlying causes of anomalies, pushing TSAD forward through innovative methodologies and insights.