Segmental Diffusion: A Distance-Guided Diffusion for Time Series Forecasting

Diffusion models have recently shown promise for time series forecasting (TSF), but existing methods rely solely on reverse denoising from Gaussian noise, introducing uncertainty and disrupting temporal structures. We propose Segmental Diffusion (SegDiff), a distance-aware framework for TSF that retrieves semantically similar historical segments to guide each diffusion step via an index-guided conditioning mechanism. A pretrained encoder computes pairwise segment similarities to build the retrieval index. We further introduce a Distance-Aware (DA) Module to estimate transition deltas at each reverse step, explicitly modeling temporal evolution. Trend-aware input augmentation with polynomial regression and moving average smoothing, along with a frequency decomposition module, enhances temporal consistency. Extensive experiments on benchmarks show that SegDiff consistently outperforms existing approaches, validating that segment-level retrieval and distance-aware modeling improve both forecasting accuracy and interpretability.