CopuAdapt: An Attentional Copula Adapter for Improved Joint-Distribution Sampling in Probabilistic Time-Series Forecasting

Time-series Foundation Models (TSFMs) have demonstrated strong forecasting performance and generalization across diverse domains. For multivariate forecasting, many TSFMs adopt channel-independent modelling. These approaches, however, can struggle to capture cross-variable dependencies in joint forecast samples. We introduce CopuAdapt, a novel attentional copula adapter that augments frozen TSFMs with a learned multivariate dependence model without requiring foundation-model retraining. CopuAdapt constructs empirical marginal distributions from the backbone's forecast samples or quantiles and couples them through an attentional copula architecture operating in probability space. To capture regime-aware dependence, we employ a sparse attention mechanism that infers a directed acyclic graph of conditional independences for each forecasting window, supported by a JEPA-inspired auxiliary objective that learns forecast-relevant temporal memory representations. By leveraging these structural details to dynamically re-order marginal sampling, CopuAdapt strictly preserves the backbone's empirical marginals. Consequently, CopuAdapt, evaluated across the TSLib datasets, exactly preserves the Continuous Ranked Probability Score (CRPS) of the underlying TSFM while significantly improving joint-sampling sensitive metrics, including the Variogram Score (VS), and RBF-MMD, with a median improvement of 4 to 18% across metrics. Code for this paper can be found at https://anonymous.4open.science/r/CopuAdapt-6C85.