Physics-Guided Flow-Map Matching for Precipitation Nowcasting
Precipitation nowcasting, generating future radar fields from past observations, is critical for flood warning and disaster response. It is also a demanding benchmark for spatiotemporal generative modeling, with chaotic dynamics, heavy-tailed intensities, and rare high-intensity structures that matter most. Deterministic models minimize a pixel loss and are driven toward the conditional mean, which blurs exactly those structures, while generative models that add a stochastic residual on top of a deterministic backbone inherit the same blur. We propose Physics-Guided Flow-Map Matching (PG-FMM), a conditional flow-map model that decouples predictable advection from uncertain small-scale detail. A frozen Lagrangian advection prior transports the radar field and supplies an explicit motion forecast, and a flow-map generative head, conditioned on the past frames and the prior rollout rather than summed onto it, produces sharp stochastic detail in four sampling steps. The prior serves only as guidance, so the head replaces blurred structure instead of inheriting it. Extensive experiments on four radar benchmarks show that PG-FMM outperforms state-of-the-art methods on 18 of 24 metrics, with the largest gains at heavy-rain thresholds, where the critical success index improves by up to 58.9%. The project page can be found at https://neurogica.github.io/PG-FMM.