Volatility-Whitened Probabilistic Residual Modeling for Long-Term Time Series Forecasting

Compared with deterministic methods that output only point estimates, probabilistic forecasting can characterize both future trends and their uncertainty simultaneously, making it more suitable for decision-making in complex real-world scenarios. In recent years, diffusion models, owing to their powerful generative modeling capability, have been introduced into the field of time series forecasting. However, we find that most existing diffusion-based forecasting methods directly construct the diffusion process in the original future space, which is easily affected by heteroscedastic scale imbalance, causing highly volatile dimensions to dominate the denoising learning and leading to unstable corrections near observation boundaries. Motivated by these issues, we propose VolaRM, a volatility-whitened probabilistic residual modeling framework for long-term time series forecasting. By constructing a conditional probabilistic base distribution, it represents future targets as whitened residuals relative to this base distribution and performs conditional modeling in the normalized residual space, thereby alleviating scale imbalance across variables and forecasting horizons. Meanwhile, a specific gating mechanism is introduced to enhance boundary continuity and the stability of long-term forecasting. Extensive experiments on eight real-world datasets from different application domains demonstrate the effectiveness of VolaRM.