Not All Frequencies Are Equal: Energy-Adaptive Diffusion for Time Series Forecasting

Abstract

Diffusion models have achieved remarkable success in generative modeling, yet their application to time series forecasting remains suboptimal. Existing approaches apply uniform Gaussian noise across all time steps, assuming all frequency components should be corrupted at the same rate. However, energy distribution across frequencies in time series is highly non-uniform: when uniform noise is added, high-frequency components are disproportionately overwhelmed while low-frequency trends remain inadequately diffused. We propose EADiff, an energy-adaptive diffusion framework operating in the wavelet domain to address this frequency-energy imbalance. Our key insight is that high-energy components require stronger perturbation while low-energy details need gentler corruption to preserve informative structures. We introduce a learnable modulation mechanism that automatically adjusts noise levels for each frequency band on a per-instance basis. Built upon this adaptive scheduler, we design a conditional diffusion framework where low-frequency trends serve as generation conditions, and noise-level-aware loss weighting naturally emphasizes different frequency components according to their signal characteristics. This cohesive design enables the model to respect the intrinsic multi-scale structure throughout both forward and reverse processes. Extensive experiments demonstrate that EADiff consistently outperforms existing diffusion-based and state-of-the-art deterministic methods.