OceanFlow: Coherent Flow Matching for Probabilistic Ocean Modeling

Probabilistic ocean modeling is essential for risk-aware marine operations, climate analysis, and scientific decision-making, where downstream decisions depend on the conditional distribution of future ocean states rather than a single deterministic trajectory. Recent data-driven ocean models have made deterministic global ocean modeling increasingly accurate and efficient, but probabilistic ocean modeling remains underdeveloped. Specifically, perturbation-driven ensembles can create spread without explicitly optimizing the joint distribution of their members, often yielding poor calibration and physical inconsistency. To address these issues, we propose OceanFlow, a coherent flow matching framework for probabilistic global ocean modeling. OceanFlow first establishes a sharp, stable mean anchor for the conditional ensemble. Flow matching then learns a coherent state-conditioned pathwise law that jointly reshapes the residual distribution around this anchor at each transition, preserving the predictive center while refining state-dependent uncertainty. We further introduce a Factorized Dynamics Operator (FDO), which combines factorized transitions with a learned state-conditioned response to parameterize the mean anchor and residual-flow velocity. Extensive experiments show that OceanFlow improves ensemble-mean accuracy, probabilistic reliability, and physical-consistency diagnostics over competitive baselines, supporting coherent flow matching as an effective route toward data-driven probabilistic ocean modeling. Code is available at https://github.com/YuanGao-YG/OceanFlow.