Title: Effective Probabilistic Time Series Forecasting with Fourier Adaptive Noise-Separated Diffusion
Primary area: generative models
Keywords: generative modeling, diffusion model, long-term time series forecasting, deep learning

Abstract: Existing diffusion-based time series forecasting methods often target on mixed temporal patterns or undifferentiated residuals, limiting the potential of distinct temporal components. In this paper, we propose the Fourier Adaptive Lite Diffusion Architecture (FALDA), a novel probabilistic framework for time series forecasting. FALDA leverages Fourier-based decomposition to incorporate a component-specific architecture, enabling tailored modeling of individual temporal components. A conditional diffusion model is utilized to estimate the future noise term, while our proposed lightweight denoiser, DEMA (Decomposition MLP with AdaLN), conditions on the historical noise term to enhance denoising performance. Grounded in rigorous mathematical proof, we introduce the Diffusion Model for Residual Regression (DMRR), a framework which methodologically unifies diffusion-based probabilistic regression method and theoretically demonstrate that FALDA effectively reduces epistemic uncertainty, allowing probabilistic learning to primarily focus on aleatoric uncertainty through further probabilistic analysis. Experiments on six real-world benchmarks demonstrate that FALDA consistently outperforms existing probabilistic forecasting approaches across most datasets for long-term time series forecasting while achieving enhanced computational efficiency without compromising accuracy. Notably, FALDA also achieves superior overall performance compared to state-of-the-art (SOTA) point forecasting approaches, with improvements of up to 9\%. The code will be made publicly available.