Title: FFT-DM: A Decomposable Forward Process in Diffusion Models for Time-Series Forecasting
Primary area: learning on time series and dynamical systems
Keywords: Diffusion Model, Forward Diffusion Process, Fourier Decomposition, Non auto-regressive, Forecasting

Abstract: We introduce FFT-DM (Fast Fourier Transform–Diffusion Model), 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, FFT-DM 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, FFT-DM 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—including Electricity, ETTm1, Temperature, PTB-XL, and MuJoCo, FFT-DM consistently outperforms strong diffusion baselines and rivals state-of-the-art models such as Sashimi, with negligible computational overhead (~7\%).
The code for the paper is available at https://anonymous.4open.science/r/FFT-DM-8E36.

TL;DR: The paper proposes a general Diffusion Model, with an architecture-agnostic forward diffusion process that decomposes signals and applies SNR-scaled noise, demonstrated on time-series forecasting.