Adaptive Flow Matching for Resolving Small-Scale Physics

Conditional diffusion and flow models are effective for super-resolving small-scale details in natural images. However, in physical sciences such as weather, three major challenges arise: (i) spatially misaligned input-output distributions (PDEs at different resolutions lead to divergent trajectories), (ii) misaligned and distinct input-output channels (channel synthesis), (iii) several channels with diverse stochasticity scales (multiscale). To address these, we propose to first encode inputs into a latent base distribution that is closer to the target, then apply Flow Matching to generate small-scale physics. The encoder captures deterministic components, while Flow Matching adds stochastic details. To handle uncertainty in the deterministic part, we inject noise via an adaptive noise scaling mechanism, dynamically adjusted by maximum-likelihood estimates of the encoder’s predictions. Experiments on real-world weather data (including super-resolution from 25 km to 2 km scales in Taiwan) and in synthetic Kolmogorov flow datasets show that our proposed Adaptive Flow Matching (AFM) framework outperforms existing methods and produces better-calibrated ensembles.

Authors

• Stathi Fotiadis
• Noah D. Brenowitz
• Tomas Geffner
• Yair Cohen
• Michael S. Pritchard
• Arash Vahdat
• Morteza Mardani

Keywords

• flow matching
• diffusion models
• weather downscaling
• distribution misalignment