Effective Probabilistic Time Series Forecasting with Fourier Adaptive Noise-Separated Diffusion

TL;DR

FALDA introduces a Fourier-based probabilistic framework for time series forecasting that reduces epistemic uncertainty and outperforms existing methods in accuracy and efficiency.

Contribution

The paper presents FALDA, a novel Fourier adaptive diffusion model with a lightweight denoiser, advancing probabilistic time series forecasting.

Findings

FALDA outperforms existing probabilistic forecasting methods on six benchmarks.

FALDA achieves up to 9% improvement over state-of-the-art point forecasting.

FALDA enhances computational efficiency without sacrificing accuracy.

Abstract

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%.