GeNCoup: Cross-Channel Coupling for Probabilistic Forecast Trajectories

Probabilistic time-series forecasters generate ensembles of future trajectories to represent predictive uncertainty. For these ensembles to form coherent multivariate scenarios, they require accurate marginals and realistic dependence across channels over time. Channel-independent generative forecasters already capture within-channel temporal dynamics, but leave cross-channel coupling unspecified. Existing plug-and-play methods recover this coupling post hoc, often at the expense of the temporal dynamics already encoded in the trajectories. We introduce Generative Noise Coupling (GeNCoup), which injects cross-channel dependence directly into the sampling process of a frozen generative forecaster. Instead of drawing channel noise independently, GeNCoup jointly samples the noise across channels at each noise feature using a cross-channel covariance (R), while preserving each channel's original noise distribution. This introduces cross-channel dependence without changing the forecaster's marginal predictions or within-channel temporal dynamics. Building on this framework, we introduce GeNCoup-Corr, which derives the coupling from empirical cross-channel correlations, and GeNCoup-Dyn, which learns it by optimizing a joint forecast score. Across six forecasters from four generative families, eight long-horizon datasets, and four prediction horizons, GeNCoup outperforms baselines in joint forecast quality while preserving both marginal accuracy and temporal dynamics.