Adaptive Flow Matching for Resolving Small-Scale Physics

Stathi Fotiadis, Noah D Brenowitz, Tomas Geffner, Yair Cohen, Michael Pritchard, Arash Vahdat, Morteza Mardani
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:17489-17521, 2025.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-fotiadis25a, title = {Adaptive Flow Matching for Resolving Small-Scale Physics}, author = {Fotiadis, Stathi and Brenowitz, Noah D and Geffner, Tomas and Cohen, Yair and Pritchard, Michael and Vahdat, Arash and Mardani, Morteza}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {17489--17521}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/fotiadis25a/fotiadis25a.pdf}, url = {https://proceedings.mlr.press/v267/fotiadis25a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Adaptive Flow Matching for Resolving Small-Scale Physics %A Stathi Fotiadis %A Noah D Brenowitz %A Tomas Geffner %A Yair Cohen %A Michael Pritchard %A Arash Vahdat %A Morteza Mardani %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-fotiadis25a %I PMLR %P 17489--17521 %U https://proceedings.mlr.press/v267/fotiadis25a.html %V 267 %X 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.
APA
Fotiadis, S., Brenowitz, N.D., Geffner, T., Cohen, Y., Pritchard, M., Vahdat, A. & Mardani, M.. (2025). Adaptive Flow Matching for Resolving Small-Scale Physics. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:17489-17521 Available from https://proceedings.mlr.press/v267/fotiadis25a.html.

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