FAIP-Diff: Fluctuation-Aware Information-Preserving Diffusion for Time-Series Forecasting

Conventional probabilistic forecasting methods often rely on predefined distributional assumptions to characterize multiple possible future outcomes. Diffusion models have become a promising alternative, as they can flexibly learn data distributions without restrictive parametric assumptions. However, existing diffusion-based time-series forecasting methods have not fully solved the problem of temporal pattern distortion that occurs during the diffusion process of non-stationary time series. Moreover, we found that temporal pattern distortion manifests in temporal fluctuation suppression during forward noising and denoising trajectory drift during reverse sampling. To address these questions, we propose FAIP-Diff, a fluctuation-aware information-preserving diffusion framework for probabilistic time series forecasting. FAIP-Diff estimates the conditional mean and volatility as forecasting priors. To alleviate temporal fluctuation suppression during forward noising, FAIP-Diff introduces an adaptive noise remodulation strategy that adjusts the corruption process based on position-dependent forecasting difficulty, enhancing learning in fluctuation-sensitive regions. Second, to mitigate denoising trajectory drift during reverse sampling, FAIP-Diff develops a constrained-space guided sampling mechanism that softly rectifies the predicted noise at each denoising step, steering generated trajectories toward realistic temporal patterns while preserving predictive diversity. Additionally, we introduce a volatility-aware weighted training objective that further alleviates temporal pattern distortion through adaptive loss weighting. Experiments across diverse real-world benchmarks demonstrate that FAIP-Diff delivers more accurate and reliable forecasts, particularly under complex non-stationary dynamics.