# Residual Corrective Diffusion Modeling for Km-scale Atmospheric Downscaling

arXiv: https://arxiv.org/abs/2309.15214 · HTML: https://mlsanity.com/paper/2309.15214/

## Key facts

- Cited by 110 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 34 of its 79 references that are in the map.
- First posted on arXiv 24 Sep 2023.

## 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, 30 of 34)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [On Distillation of Guided Diffusion Models](https://mlsanity.com/paper/2210.03142/) (2022)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [Tackling the Generative Learning Trilemma with Denoising Diffusion GANs](https://mlsanity.com/paper/2112.07804/) (2021)
- [Simple diffusion: End-to-end diffusion for high resolution images](https://mlsanity.com/paper/2301.11093/) (2023)
- [Skillful Precipitation Nowcasting using Deep Generative Models of Radar](https://mlsanity.com/paper/2104.00954/) (2021)
- [FuXi: A cascade machine learning forecasting system for 15-day global weather forecast](https://mlsanity.com/paper/2306.12873/) (2023)
- [Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere](https://mlsanity.com/paper/2306.03838/) (2023)
- [Conditional Image Generation with Score-Based Diffusion Models](https://mlsanity.com/paper/2111.13606/) (2021)
- [Fast Sampling of Diffusion Models via Operator Learning](https://mlsanity.com/paper/2211.13449/) (2022)
- [Stochastic Super-Resolution for Downscaling Time-Evolving Atmospheric Fields with a Generative Adversarial Network](https://mlsanity.com/paper/2005.10374/) (2020)
- [A Generative Deep Learning Approach to Stochastic Downscaling of Precipitation Forecasts](https://mlsanity.com/paper/2204.02028/) (2022)
- [Latent diffusion models for generative precipitation nowcasting with accurate uncertainty quantification](https://mlsanity.com/paper/2304.12891/) (2023)
- [Increasing the accuracy and resolution of precipitation forecasts using deep generative models](https://mlsanity.com/paper/2203.12297/) (2022)
- [DeepDownscale: a Deep Learning Strategy for High-Resolution Weather Forecast](https://mlsanity.com/paper/1808.05264/) (2018)
- [SEEDS: Emulation of Weather Forecast Ensembles with Diffusion Models](https://mlsanity.com/paper/2306.14066/) (2023)

## Built on by (most cited first, 30 of 110)

- [DiffDA: a Diffusion Model for Weather-scale Data Assimilation](https://mlsanity.com/paper/2401.05932/) (2024)
- [Heavy-Tailed Diffusion Models](https://mlsanity.com/paper/2410.14171/) (2024)
- [Foundation Models for Weather and Climate Data Understanding: A Comprehensive Survey](https://mlsanity.com/paper/2312.03014/) (2023)
- [Kilometer-Scale Convection Allowing Model Emulation using Generative Diffusion Modeling](https://mlsanity.com/paper/2408.10958/) (2024)
- [Probabilistic Weather Forecasting with Hierarchical Graph Neural Networks](https://mlsanity.com/paper/2406.04759/) (2024)
- [Continuous Ensemble Weather Forecasting with Diffusion models](https://mlsanity.com/paper/2410.05431/) (2024)
- [Probabilistic Emulation of a Global Climate Model with Spherical DYffusion](https://mlsanity.com/paper/2406.14798/) (2024)
- [Dynamical-generative downscaling of climate model ensembles](https://mlsanity.com/paper/2410.01776/) (2024)
- [Machine learning emulation of precipitation from km-scale UK regional climate simulations using a diffusion model](https://mlsanity.com/paper/2407.14158/) (2024)
- [Can AI be enabled to dynamical downscaling? A Latent Diffusion Model to mimic km-scale COSMO5.0CLM9 simulations](https://mlsanity.com/paper/2406.13627/) (2024)
- [Elucidated Rolling Diffusion Models for Probabilistic Forecasting of Complex Dynamics](https://mlsanity.com/paper/2506.20024/) (2025)
- [Swift: An Autoregressive Consistency Model for Efficient Weather Forecasting](https://mlsanity.com/paper/2509.25631/) (2025)
- [EnScale: Temporally-consistent multivariate generative downscaling via proper scoring rules](https://mlsanity.com/paper/2509.26258/) (2025)
- [DiffObs: Generative Diffusion for Global Forecasting of Satellite Observations](https://mlsanity.com/paper/2404.06517/) (2024)
- [Dynamical Diffusion: Learning Temporal Dynamics with Diffusion Models](https://mlsanity.com/paper/2503.00951/) (2025)
- [Quantum State Generation with Structure-Preserving Diffusion Model](https://mlsanity.com/paper/2404.06336/) (2024)
- [Diff-SPORT: Diffusion-based Sensor Placement Optimization and Reconstruction of Turbulent flows in urban environments](https://mlsanity.com/paper/2506.00214/) (2025)
- [Multimodal Atmospheric Super-Resolution With Deep Generative Models](https://mlsanity.com/paper/2506.22780/) (2025)
- [AERIS: Argonne Earth Systems Model for Reliable and Skillful Predictions](https://mlsanity.com/paper/2509.13523/) (2025)
- [Observation-Guided Meteorological Field Downscaling at Station Scale: A Benchmark and a New Method](https://mlsanity.com/paper/2401.11960/) (2024)
- [CaFA: Global Weather Forecasting with Factorized Attention on Sphere](https://mlsanity.com/paper/2405.07395/) (2024)
- [SRViT: Vision Transformers for Estimating Radar Reflectivity from Satellite Observations at Scale](https://mlsanity.com/paper/2406.16955/) (2024)
- [Stochastic Flow Matching for Resolving Small-Scale Physics](https://mlsanity.com/paper/2410.19814/) (2024)
- [Universal Diffusion-Based Probabilistic Downscaling](https://mlsanity.com/paper/2602.11893/) (2026)
- [Downscaling Extreme Precipitation with Wasserstein Regularized Diffusion](https://mlsanity.com/paper/2410.00381/) (2024)
- [Efficient Kilometer-Scale Precipitation Downscaling with Conditional Wavelet Diffusion](https://mlsanity.com/paper/2507.01354/) (2025)
- [When and how can inexact generative models still sample from the data manifold?](https://mlsanity.com/paper/2508.07581/) (2025)
- [MAUSAM: An Observations-focused assessment of Global AI Weather Prediction Models During the South Asian Monsoon](https://mlsanity.com/paper/2509.01879/) (2025)
- [FloeNet: A mass-conserving global sea ice emulator that generalizes across climates](https://mlsanity.com/paper/2603.12449/) (2026)
- [DiffScale: Continuous Downscaling and Bias Correction of Subseasonal Wind Speed Forecasts using Diffusion Models](https://mlsanity.com/paper/2503.23893/) (2025)

## Abstract (arXiv)

The state of the art for physical hazard prediction from weather and climate requires expensive km-scale numerical simulations driven by coarser resolution global inputs. Here, a generative diffusion architecture is explored for downscaling such global inputs to km-scale, as a cost-effective machine learning alternative. The model is trained to predict 2km data from a regional weather model over Taiwan, conditioned on a 25km global reanalysis. To address the large resolution ratio, different physics involved at different scales and prediction of channels beyond those in the input data, we employ a two-step approach where a UNet predicts the mean and a corrector diffusion (CorrDiff) model predicts the residual. CorrDiff exhibits encouraging skill in bulk MAE and CRPS scores. The predicted spectra and distributions from CorrDiff faithfully recover important power law relationships in the target data. Case studies of coherent weather phenomena show that CorrDiff can help sharpen wind and temperature gradients that co-locate with intense rainfall in cold front, and can help intensify typhoons and synthesize rain band structures. Calibration of model uncertainty remains challenging. The prospect of unifying methods like CorrDiff with coarser resolution global weather models implies a potential for global-to-regional multi-scale machine learning simulation.