HyperDiff: High-Order Structure-Driven Diffusion for Multivariate Probabilistic Forecasting

Multivariate probabilistic forecasting must model both future uncertainty and how that uncertainty is organized across interacting variables. Existing generative forecasters can represent flexible predictive distributions, but they rarely use dynamic group-wise dependence as an explicit uncertainty prior. We propose HyperDiff, a high-order structure-driven diffusion framework that treats a window-conditioned hypergraph as a data-dependent structural prior. HyperDiff learns group-wise relations from each historical window, uses them to organize history-derived volatility while preserving variable-specific heteroscedasticity, and feeds the resulting conditions into a variable-specific diffusion schedule. A deterministic history-based forecast provides the trend center, allowing reverse diffusion to focus on stochastic deviations around a plausible trajectory. Experiments on seven multivariate benchmarks and four forecasting horizons show that HyperDiff achieves lower CRPS and QICE than the evaluated probabilistic forecasting baselines. These results support high-order structural conditioning for multivariate probabilistic forecasting. Code is available at https://anonymous.4open.science/r/HyperDiff-1D2B.