Mixtures of Localized Diffusion Processes for Time Series Forecasting

In many real-world long-horizon forecasting tasks, we observe only a limited subset of the variables governing a high-dimensional system, yet must predict its future evolution from these incomplete measurements. Under such partial observation, some localized temporal and frequency components of the future can be predicted reliably from the observed history, while others retain substantial residual variation. We propose MeLD, an end-to-end forecasting framework that adapts stochastic modeling to this localized unresolved structure. MeLD constructs a localized time-frequency frame over the observed history and uses context-dependent routing to identify components that are well explained by the available observations and those with larger unresolved uncertainty. The resolved components provide the conditional structure of the forecast, while the unresolved components define the subspace on which diffusion is applied as the central stochastic modeling mechanism. Across standard long-horizon forecasting benchmarks, we show that stochastic variation is not uniformly distributed across these components, and that diffusion becomes substantially more effective when concentrated on the few that remain unresolved.