Joint Prior-Fitted Prediction for Partially Observed Multivariate Time Series

Multivariate time series are rarely observed as a complete history followed by a fully unknown future. In healthcare, measurements can be missing within the context, channels can stop at different times, and some covariates may be already available over the forecast horizon. Many time-series foundation models operate on fixed forecast blocks and return point predictions or marginal predictive summaries, leaving cross-time and cross-variable dependence unavailable as an explicit joint density. We introduce JointTimePFN, a mask-conditional prior-data fitted network that predicts arbitrary missing cells in a fixed-length time-by-channel grid. Its query-size-agnostic low-rank Gaussian head returns a coherent joint posterior predictive distribution and its marginals in one forward pass. The model combines mask-aware bidirectional temporal encoding, rotary embeddings, and a broad linear model of coregionalization prior. This structured prior naturally motivates posterior predictive checks against exact and MCMC-based multi-output Gaussian process references, both in-prior and under distribution shift. When the reference posterior exhibits substantial dependence across prediction targets, the joint head closes 64% of the gap left by a correlation-free baseline and mostly outperforms autoregressive chaining of its marginals in joint likelihood on these synthetic references. On MIMIC-IV, a single model checkpoint performs competitively with baselines across zero-shot forecasting, known-future conditioning, ragged horizons, and interior imputation, while improving joint likelihood over its diagonal counterpart.