Ocean wave forecasting is essential for maritime safety, offshore operations, and coastal resilience, yet remains challenging due to systematic biases in physics-based models. Physical models, while widely used, rely on approximations and parameterizations that limit their accuracy under complex ocean-atmosphere conditions. To enhance ocean wave forecasting, we propose BridgeCast, within a physics-AI hybrid framework for bias correction. BridgeCast is a probabilistic model based on conditional flow matching (CFM) that learns to transform physical model forecasts into reanalysis-like fields. It treats physical forecasts as corrupted observations and employs a continuous-time generative process to bridge their distribution toward that of reanalysis data. BridgeCast is parameterized by a Transformer-based architecture that enables spatiotemporal modeling, incorporation of exogenous atmospheric variables, and flexible inference via both ordinary and stochastic differential equation formulations. Extensive experiments on real-world datasets demonstrate that BridgeCast consistently outperforms state-of-the-art baselines across regions and forecast lead times.

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