PrefixFlow: Projective Consistency for Probabilistic Time-Series Forecasting

Probabilistic forecasts at different horizons share a common future prefix, yet direct generative forecasters need not yield consistent predictive distributions over it. We formalize this requirement as horizon-wise projective consistency. Using Energy Distance, we show that three recent generative forecasters exhibit systematic cross-horizon discrepancies beyond finite-sample Monte Carlo variation. To address this, we propose PrefixFlow, a variable-horizon Flow Matching model trained jointly across horizons and supporting any patch-aligned horizon up to a prescribed maximum. Unlike autoregressive forecasters that require sequential rollout, PrefixFlow generates the entire requested future in parallel. Its prefix-invariant conditioning and prefix-causal velocity field preserve the generative dynamics of an existing prefix under horizon extension; together with a projectively consistent Gaussian source, this yields projectively consistent predictive distributions. Across six benchmarks, PrefixFlow achieves the lowest average CRPS on five, with no detectable cross-horizon discrepancy beyond finite Monte Carlo variation.