# Mind the Residual Gap: Probabilistic Downscaling under Real-World Bias

arXiv: https://arxiv.org/abs/2606.30821 · HTML: https://mlsanity.com/paper/2606.30821/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 37 of its 60 references that are in the map.
- First posted on arXiv 29 Jun 2026.

## Builds on (most cited first, 30 of 37)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [VGGT: Visual Geometry Grounded Transformer](https://mlsanity.com/paper/2503.11651/) (2025)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
- [Joint Distribution Optimal Transportation for Domain Adaptation](https://mlsanity.com/paper/1705.08848/) (2017)
- [Stochastic Optimization for Large-scale Optimal Transport](https://mlsanity.com/paper/1605.08527/) (2016)
- [Neural Optimal Transport](https://mlsanity.com/paper/2201.12220/) (2022)
- [Max-Sliced Wasserstein Distance and its use for GANs](https://mlsanity.com/paper/1904.05877/) (2019)
- [Residual Corrective Diffusion Modeling for Km-scale Atmospheric Downscaling](https://mlsanity.com/paper/2309.15214/) (2023)
- [Image-to-Image Regression with Distribution-Free Uncertainty Quantification and Applications in Imaging](https://mlsanity.com/paper/2202.05265/) (2022)
- [Subspace Robust Wasserstein Distances](https://mlsanity.com/paper/1901.08949/) (2019)
- [Robust Optimal Transport with Applications in Generative Modeling and Domain Adaptation](https://mlsanity.com/paper/2010.05862/) (2020)
- [Optimal Transport for Multi-source Domain Adaptation under Target Shift](https://mlsanity.com/paper/1803.04899/) (2018)
- [DiffCast: A Unified Framework via Residual Diffusion for Precipitation Nowcasting](https://mlsanity.com/paper/2312.06734/) (2023)
- [CasCast: Skillful High-resolution Precipitation Nowcasting via Cascaded Modelling](https://mlsanity.com/paper/2402.04290/) (2024)
- [Projection Robust Wasserstein Distance and Riemannian Optimization](https://mlsanity.com/paper/2006.07458/) (2020)
- [Generative Modeling through the Semi-dual Formulation of Unbalanced Optimal Transport](https://mlsanity.com/paper/2305.14777/) (2023)
- [Sliced-Wasserstein Autoencoder: An Embarrassingly Simple Generative Model](https://mlsanity.com/paper/1804.01947/) (2018)
- [Debias Coarsely, Sample Conditionally: Statistical Downscaling through Optimal Transport and Probabilistic Diffusion Models](https://mlsanity.com/paper/2305.15618/) (2023)
- [ResGrad: Residual Denoising Diffusion Probabilistic Models for Text to Speech](https://mlsanity.com/paper/2212.14518/) (2022)
- [Dynamical-generative downscaling of climate model ensembles](https://mlsanity.com/paper/2410.01776/) (2024)
- [Optimal transport maps for distribution preserving operations on latent spaces of Generative Models](https://mlsanity.com/paper/1711.01970/) (2017)
- [Turbulence in Focus: Benchmarking Scaling Behavior of 3D Volumetric Super-Resolution with BLASTNet 2.0 Data](https://mlsanity.com/paper/2309.13457/) (2023)

## Abstract (arXiv)

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.