Distillation of Synthetic Data for Time Series Foundation Models

Choosing the wrong synthetic generator for time-series foundation model pretraining is costly: under identical training budgets, the best and worst generators produce up to a $2\times$ gap in forecasting error, yet the field has no principled way to make this choice. The problem is compounded by the fact that generator rankings are not stable across architectures: across 11 generator families evaluated on Chronos-T5-Mini and Moirai-Small trained from scratch, we find that which generators are useful depends on the model architecture. Rather than solving the generator selection problem, we sidestep it: a simple equal-weight mixture of all generators matches or beats the best individual generator for both architectures, and composing this mixture with real data yields the strongest pretraining corpora overall. Synthetic pretraining is therefore a corpus composition problem, not a generator selection problem, and composition choices should be validated per model family rather than assumed to transfer.

The deployment of Time-Series Foundation Models (TSFMs) in physical sciences is hindered by a critical trade-off: while these models encode rich, universal temporal dynamics, they suffer from severe distributional misalignment when applied zero-shot to specific scientific domains, and their computational cost prohibits deployment in edge-computing sensor networks. We address a fundamental challenge: How can we extract latent structural knowledge from misaligned foundation models (FM) to train lightweight, specialized forecasters? We propose Gated Uncertainty-Aware Routing for Distillation (Guard), a novel framework that reframes multiteacher distillation as an instance-wise decision process with two adaptive mechanisms: (1) a Contextual Router that dynamically selects the most relevant teacher based on local input statistics, exploiting complementarity across diverse foundation models; and (2) an Uncertainty-Gated Temperature mechanism that acts as a "circuit-breaker," automatically attenuating distillation strength when teacher confidence diverges from domain reality. We evaluate our proposed lightweight framework on four climate-critical domains: meteorology, ecosystem carbon flux, soil moisture, and energy grids. Our method significantly reduces RMSE relative to a fixed-weight multi-teacher distillation baseline, successfully distilling knowledge from pretrained FMs (teachers) even when they exhibit suboptimal zero-shot accuracy due to distribution shift between the original and target data domains. We demonstrate that these domain-misaligned teachers can still serve as critical correctives, outperforming the globally superior FMs on 28.5% of the hardest instances. Ultimately, this enables high-precision scientific forecasting suitable for resource-constrained edge deployment. Code is available at https://github.com/RupasreeDey/GUARD-KDD2026.

Time series foundation models (TSFMs) have emerged as general-purpose models for time series analysis, but pretraining alone is often insufficient for reliable downstream deployment. Bridging this gap requires further intervention to handle domain shift, task heterogeneity, limited supervision, and computational constraints, which motivates post-training as a broad class of methods to adapt, augment, compose, calibrate, or specialize pretrained TSFMs for downstream tasks. In this work, we analyze TSFM post-training methods based on their locus of intervention in the prediction pipeline, yielding five categories: parameter adaptation, context augmentation, model composition, output processing and uncertainty control, and compression and specialization. Within each category, we study main representative methods and discuss their current limitations. We further identify future directions toward controlled adaptation, reliable context construction, uncertainty-aware model composition, calibrated output processing, and deployment-aware specialization. Overall, by providing a unifying framework for the emerging TSFM post-training landscape, this work aims to support future research to navigate the design space between a pretrained TSFM and its reliable downstream deployment.