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Interweaving Marginals into Multivariate Sample Paths: Training-Free Dependence Construction for Probabilistic Time Series Foundation Models

arXiv · AI, language, vision and robotics · article · Sep 22, 2026 · UTC

Probabilistic time series foundation models (TSFMs) provide coordinate-wise predictive distributions, but these marginals do not determine a joint distribution over multivariate future trajectories. We study training-free coupling of frozen TSFM marginals into multivariate forecast sample paths. Our primary evaluation fixes the empirical marginal sample multiset at every channel--horizon coordinate across methods, isolating the effect of coupling alone. Historical temporal and channel relations substantially improve their corresponding dependence diagnostics. The same pattern persists when the

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