Mind the Residual Gap: Probabilistic Downscaling under Real-World Bias
cs.LG, cs.CE
Submitted: 2026-06-29
Updated: 2026-09-27
Code: https://github.com/sdean-group/ReMatch
License: http://creativecommons.org/licenses/by/4.0/
The gist: Probabilistic downscaling models the conditional distribution of high-resolution fields given coarse inputs and is a core challenge in atmospheric science, climate modeling, and other multiscale
Terminology
Abstract
Probabilistic downscaling models the conditional distribution of high-resolution fields given coarse inputs and is a core challenge in atmospheric science, climate modeling, and other multiscale physical systems. A widely used paradigm decomposes the problem into a deterministic mean predictor followed by a stochastic residual generator. While effective in idealized settings, this mean-residual approach frequently produces biased and underdispersive ensembles in real-world applications. We identify a fundamental source of this failure: residual target misspecification, where the residual distribution induced during training systematically differs from the correction distribution required at test time, a mismatch amplified by downscaling bias. We theoretically connect this misspecification to underdispersion through the spread-skill ratio and show that conditional residual distribution matching controls both residual-energy and conditional-mean mismatch. Motivated by this analysis, we introduce ReMatch (Residual Distribution Matching), which aligns training residual targets toward a held-out calibration regime via optimal transport. On a controlled synthetic benchmark with varying bias levels and a real-world HRRR-ERA5 wind-field downscaling task, ReMatch substantially reduces underdispersion, improves calibration, and outperforms strong mean-residual and super-resolution baselines. Our code is available at https://github.com/sdean-group/ReMatch.git.
Sources
- Optimal transport maps for distribution preserving operations on latent spaces of Generative Models
- ResGrad: Residual Denoising Diffusion Probabilistic Models for Text to Speech
- CasCast: Skillful High-resolution Precipitation Nowcasting via Cascaded Modelling
- Classifier-Free Diffusion Guidance
- Neural Optimal Transport
- RDIT: Residual-based Diffusion Implicit Models for Probabilistic Time Series Forecasting
- Latent Space Optimal Transport for Generative Models
- RainDiff: End-to-end Precipitation Nowcasting Via Token-wise Attention Diffusion
- Score-Based Generative Modeling through Stochastic Differential Equations
- Optimal Transport for Latent Integration with An Application to Heterogeneous Neuronal Activity Data
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