RAF-Diff: Rational Adaptive Functional Diffusion for Time Series Analysis

Time series analysis tasks such as forecasting, imputation, anomaly detection, and classification are crucial for applications spanning climate science, finance, retail, and cloud infrastructure. We present Rational Adaptive Functional Diffusion ($\text{RAF-Diff}$), a conditional diffusion model that introduces two innovations: (i) a Rational Adaptive Correlation Projection (RACP) in the forward process and (ii) a Rational Denoising Transformer (R-DiT) architecture, specifically designed for time series modeling. Unlike traditional fixed Gaussian noise based forward process, our RACP module makes the forward process trainable and data-adaptive, capturing complex inter-feature correlations through learned rational function transformations. Our R-DiT architecture with its rational function layers provides superior expressiveness for capturing periodic time series signals. $\text{RAF-Diff}$ achieves superior performance across four fundamental time series analysis tasks, significantly outperforming existing prominent models in forecasting (eight datasets), imputation (six datasets), classification (ten datasets) and anomaly detection (five datasets). Comprehensive ablation studies across all tasks validate the utility of each $\text{RAF-Diff}$ component, demonstrating the model's robustness in diverse time series challenges.