OnART: Online Adaptation of Rectified Flow for Probabilistic Time-Series Forecasting with Feedback Delay

Probabilistic time-series forecasting is essential for decisions under uncertainty, yet existing generative forecasters are predominantly fixed after offline training, while online methods largely adapt point predictors without updating predictive uncertainty. We address the resulting problem of adapting an entire predictive distribution from sparse, delayed feedback without destabilizing its learned transport. We introduce OnART, an online adaptation framework that turns Rectified Flow into an efficient delayed-feedback probabilistic forecaster. Offline re-flow straightens the conditional transport and enables one-step generation, limiting the trajectory interference induced by online updates. At deployment, a newly observed residual provides a new endpoint but no source from which to update the learned transport. OnART selects, for each variable, the Gaussian source paired with the nearest forecast-time residual endpoint. This choice exactly minimizes the change from the cached displacement target to the new re-flow displacement target among the stored candidates; online training then intentionally moves the selected source toward the new endpoint. Generated replay anchors the cached forecast-time mappings while this update is applied. The point forecaster learns from all causally available values, and the rectified velocity model learns from the assigned pair and generated replay after the feedback delay. Across seven multivariate benchmarks, OnART consistently improves probabilistic forecasting performance while preserving competitive point accuracy. These results establish minimal-shift source assignment and replay as effective mechanisms for online adaptation of probabilistic forecasts.