Enhancing Diffusion Weather Model's Physical Consistency with Test-time Guidance

Diffusion-based data-driven weather models now surpass numerical weather prediction in forecast skill, but the meteorology community still does not fully trust their output, because the predictions can violate basic physical principles. Violations such as hydrostatic imbalance and dry-air mass drift not only make a single forecast step look questionable, they also compound over the autoregressive rollouts that operational forecasting relies on. Physics-informed training or fine-tuning can reduce these violations, but the computational cost can be prohibitive. Recent advances in test-time steering offer another opportunity to enforce physical principles, by guiding a frozen diffusion model during sampling. Existing methods such as Manifold Preserving Guided Diffusion, however, measure the violation on a coarse estimate of the final state, which limits how much they can correct. We therefore propose Intermediate Gradient Guidance (IGG), a training-free, plug-and-play method that measures the violation on the intermediate state itself and steers each sampling step of a frozen diffusion model toward states that better satisfy a target physical constraint. Our experiments show that IGG improves physical consistency by up to 72.4%, with no loss in forecast skill and negligible extra computation.