Planning electricity supply, anticipating traffic, investing in the Stock market, and assessing how a patient’s health may evolve all involve uncertainty about the future. This seminar presents two complementary approaches to improving time-series forecasting through structured guidance and expert specialization. The first study investigates predicted quantiles as distributional controls for diffusion forecasting. Quantile forecasts summarize uncertainty at individual future time steps, while diffusion forecasters represent it through sampled future trajectories. We systematically investigate guidance mechanisms and identify residual control throughout the denoising network as the most consistently effective approach. We introduce Control-TS, which learns a quantile-control pathway while keeping the pretrained backbone frozen. Across eight benchmarks, Control-TS improves the backbone’s probabilistic accuracy, achieves competitive performance against state-of-the-art forecasting models, and retains gains in capacity-matched comparisons. Further analyses examine the roles of quantile granularity, predictor choice, and forecast quality. We also introduce the Conditional Linear Predictive Score (CLPS) to assess the downstream forecasting utility of generated futures.
The second contribution disentangles the roles of capacity, parameter sharing, and routing in multivariate time-series forecasting. We introduce GalaxyTS, an expressive synthetic dataset with controllable predictive structure and known optimal forecasts, revealing when specialization helps and how channels should share experts. These insights motivate an identity-only router that introduces no additional routing parameters and improves on the learned identity-only baseline. Our plug-and-play framework combines this router with low-rank residual experts to adapt pretrained forecasters, recovering their original predictions exactly when corrections are disabled. Evaluation across multiple architectures, forecast horizons, and established benchmarks demonstrates accuracy gains over the original forecasters and competitive performance with low computational overhead.