A Decomposable Forward Process in Diffusion Models for Time-Series Forecasting

TL;DR

This paper presents a spectral decomposition-based forward diffusion process for time-series forecasting that enhances the preservation of temporal patterns and improves forecast accuracy without significant computational costs.

Contribution

It introduces a model-agnostic diffusion process that stages noise injection based on spectral component energy, improving long-term pattern recoverability in time-series forecasting.

Findings

Spectral decomposition improves diffusion model performance on benchmarks.

The method preserves temporal structures like seasonality more effectively.

No significant computational overhead introduced.

Abstract

We introduce a model-agnostic forward diffusion process for time-series forecasting that decomposes signals into spectral components, preserving structured temporal patterns such as seasonality more effectively than standard diffusion. Unlike prior work that modifies the network architecture or diffuses directly in the frequency domain, our proposed method alters only the diffusion process itself, making it compatible with existing diffusion backbones (e.g., DiffWave, TimeGrad, CSDI). By staging noise injection according to component energy, it maintains high signal-to-noise ratios for dominant frequencies throughout the diffusion trajectory, thereby improving the recoverability of long-term patterns. This strategy enables the model to maintain the signal structure for a longer period in the forward process, leading to improved forecast quality. Across standard forecasting benchmarks, we show that applying spectral decomposition strategies, such as the Fourier or Wavelet transform, consistently improves upon diffusion models using the baseline forward process, with negligible computational overhead. The code for this paper is available at https://anonymous.4open.science/r/D-FDP-4A29.