用傅里叶分解与轻量去噪器，提升时间序列概率预测精度与效率。
Effective Probabilistic Time Series Forecasting with Fourier Adaptive Noise-Separated Diffusion
- 基于傅里叶分解的组件专用架构，分量建模更精准。
- 降低认知不确定性，专注处理随机不确定性，长期预测更可靠。
- 比当前最优点预测方法还提升9%，适合高精度时序任务。
我们提出傅里叶自适应轻量扩散架构（FALDA），一种新型时间序列概率预测框架。首先引入扩散残差回归（DMRR）框架，统一扩散式概率回归方法。FALDA利用傅里叶分解实现分量特异性建模，通过条件扩散模型估计未来噪声，提出轻量去噪器DEMA（带AdaLN的分解MLP），利用历史噪声信息增强去噪性能。数学分析与实证验证表明，FALDA有效降低认知不确定性，使概率学习聚焦于随机不确定性。在六个真实世界基准上的实验显示，FALDA在多数数据集上持续优于现有概率预测方法，长期预测表现更优且计算效率更高；同时相比最先进点预测方法，整体性能提升达9%。
原文摘要 · Abstract (English)
We propose the Fourier Adaptive Lite Diffusion Architecture (FALDA), a novel probabilistic framework for time series forecasting. First, we introduce the Diffusion Model for Residual Regression (DMRR) framework, which unifies diffusion-based probabilistic regression methods. Within this framework, 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. Through mathematical analysis and empirical validation, we demonstrate that FALDA effectively reduces epistemic uncertainty, allowing probabilistic learning to primarily focus on aleatoric uncertainty. 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%.
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