# Conditional Flow Matching for Probabilistic Downscaling of Maximum 3-day Snowfall in Alaska

arXiv: https://arxiv.org/abs/2604.25172 · HTML: https://mlsanity.com/paper/2604.25172/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 7 of its 11 references that are in the map.
- First posted on arXiv 28 Apr 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 7 of 7)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Residual Corrective Diffusion Modeling for Km-scale Atmospheric Downscaling](https://mlsanity.com/paper/2309.15214/) (2023)
- [Kilometer-Scale Convection Allowing Model Emulation using Generative Diffusion Modeling](https://mlsanity.com/paper/2408.10958/) (2024)

## Abstract (arXiv)

Precipitation in complex terrain is governed by orographic processes operating at scales of a few kilometers, yet climate models typically run at resolutions of 50--100~km where this topographic detail is absent. Dynamical downscaling with high-resolution regional models such as WRF can resolve these processes, but the computational cost -- months of wall-clock time per scenario -- precludes the large ensembles needed for uncertainty quantification. We present WxFlow, a conditional generative model based on flow matching that learns to map coarse-resolution climate model output and high-resolution topography to calibrated probabilistic ensembles of fine-scale precipitation fields. Applied to 4~km WRF simulations of maximum 3-day snowfall over southeast Alaska, WxFlow achieves 87.8% improvement in spectral fidelity and dramatically lower Continuous Ranked Probability Scores relative to conventional lapse-rate-corrected bicubic downscaling, while generating 50-member ensembles in seconds on a laptop. Ensemble spread is spatially coherent and governed by topography, reflecting physically plausible uncertainty structure. All code is available at https://github.com/glide-ism/wrf-flow.