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 fixed-marginal constraint is removed and paths are sampled directly, and remains present under native multivariate backbone inference.
These results support treating dependence reconstruction as a distinct post-processing problem for probabilistic TSFMs.