Anchor-Preserving Coarse-to-Fine Diffusion for Probabilistic Time Series Forecasting

Probabilistic time series forecasts should represent uncertainty at both individual time steps and aggregated temporal resolutions. Reliable uncertainty at individual steps, however, does not necessarily imply reliable aggregate uncertainty. Coarse-to-fine generation can use deterministic coarse forecasts to guide refinement. Yet fixing every sample's aggregate to the same forecast eliminates aggregate uncertainty, while conditioning alone does not guarantee that the aggregate ensemble mean matches it. Preliminary experiments on two datasets show that combining a point forecast with centered stochastic deviations reduces CRPS. With fixed final coarse scenarios, controlled comparisons provide limited support for centering before detail generation. We propose an anchor-preserving coarse-to-fine diffusion framework that constrains the coarse ensemble mean rather than individual aggregate outcomes. Residual diffusion generates stochastic coarse scenarios, which are centered around a deterministic anchor before conditional detail generation. A conditional detail diffusion model then refines each scenario using projected detail with zero block averages, so refinement cannot alter its coarse aggregate. The resulting forecasts satisfy sample-wise coherence and coarse ensemble-mean preservation up to numerical precision while retaining stochastic aggregate variation. The proposed method achieves the lowest mean CRPS in 15 of 24 dataset–horizon settings among methods with complete three-seed results, but substantially underperforms on Electricity and Traffic. Matched-mean evaluation of shared forecast ensembles further shows that fine-resolution gains need not translate into better aggregate forecasts.