Aich et al. (2026) Conditional diffusion models for downscaling and bias correction of Earth system model precipitation

Identification

• Journal: Geoscientific model development
• Year: 2026
• Date: 2026-03-03
• Authors: Michael Aich, Philipp Hess, Baoxiang Pan, Sebastian Bathiany, Yu Huang, Niklas Boers
• DOI: 10.5194/gmd-19-1791-2026

Research Groups

• Technical University of Munich, Germany; Munich Climate Center, TUM School of Engineering and Design, Department of Aerospace and Geodesy, Earth System Modelling Group
• Potsdam Institute for Climate Impact Research, Potsdam, Germany
• Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China
• Global Systems Institute and Department of Mathematics, University of Exeter, Exeter, UK

Short Summary

This paper introduces a machine learning framework utilizing conditional diffusion models for simultaneous bias correction and downscaling of Earth System Model (ESM) precipitation. The approach outperforms existing statistical and deep learning methods, particularly for extreme events, by improving spatial structure and statistical fidelity while preserving climate change signals.

Objective

• To develop a novel machine learning framework based on conditional diffusion models for simultaneous bias correction and downscaling of Earth System Model (ESM) precipitation, addressing limitations of existing methods in improving spatial structure, handling unpaired data, and ensuring stable training.

Study Configuration

• Spatial Scale: Downscaling from 1° × 1.25° (ESM) to 0.25° × 0.25° (target resolution). Study regions include the South American continent (0° N to 63° S, -90° W to -27° E) and South Asia (0.75° to 64.5° N, 42° to 105.75° E).
• Temporal Scale: Daily total precipitation data. Training period: 1 January 1992 to 1 January 2011. Evaluation period: 2 January 2011 to 1 December 2014 (extended to 1995–2014 for some analyses). Future climate scenarios (SSP5-8.5) from 2015 to 2100.

Methodology and Data

• Models used:
  • Conditional Diffusion Model (DM) based on a Denoising Diffusion Probabilistic Model (DDPM) architecture with an "Efficient U-Net" backbone.
  • Quantile Mapping (QM) / Quantile Delta Mapping (QDM) for large-scale bias correction and as a benchmark.
  • EDM (Karras et al., 2022), VQ-VAE-based generative model, UNet, and Transformer models were used for comparative analysis.
• Data sources:
  • Observation/Reanalysis: ERA5 daily total precipitation data at 0.25° horizontal resolution (Hersbach et al., 2020).
  • Earth System Models (ESMs):
    • GFDL-ESM4 (Dunne et al., 2020) daily precipitation data at 1° latitudinal and 1.25° longitudinal resolution (historical and SSP5-8.5 scenarios).
    • MPI-ESM-HR (Gutjahr et al., 2019) daily precipitation data at 0.9375° × 0.9375° spatial resolution (for ablation study).

Main Results

• The conditional diffusion model (DM) produces high-resolution, detailed precipitation outputs visually indistinguishable from ERA5 reanalysis, outperforming bilinear upsampling and QM-corrected fields in sharpness and detail.
• DM significantly improves the representation of small-scale spatial patterns, aligning better with the ERA5 power spectral density (PSD) compared to QM and other deep learning models (EDM, VQ-VAE, UNet, Transformer).
• The DM reduces the mean absolute bias of GFDL precipitation climatology from 0.69 mm d⁻¹ to 0.32 mm d⁻¹ relative to ERA5, performing comparably to the QM benchmark (0.26 mm d⁻¹).
• The model effectively corrects biases in extreme precipitation events (R95p metric) and yields more realistic return periods for extreme rainfall events (e.g., 4.18 years for events > 50 mm d⁻¹ compared to 3.33 years for raw GFDL, against ERA5's 4.11 years).
• Spatial correlation between climatologies improves from 0.83 (GFDL vs. ERA5) to 0.98 (DM-corrected GFDL vs. ERA5).
• DM generates superior statistics for consecutive dry days (CDD) and consecutive wet days (CWD) compared to the QM benchmark and raw GFDL.
• The framework demonstrates robust generalization to different geographical regions (South Asia) and different ESMs (MPI-ESM-HR) with minimal adjustments.
• The DM ensemble provides accurate uncertainty estimates, with lower mean CRPS values (0.76 mm d⁻¹) compared to a bilinear baseline (0.90 mm d⁻¹) and near-perfect alignment in spread-skill plots.
• The model robustly preserves climate change signals (mean and extreme precipitation indices) in future high-emission scenarios (SSP5-8.5) without retraining, maintaining the direction and magnitude of trends.

Contributions

• Introduction of a novel machine learning framework using conditional diffusion models for simultaneous bias correction and downscaling of ESM precipitation with a single neural network.
• Resolution of the fundamental challenges of unpaired ESM-observation data and distribution shift through a shared embedding space, enabling supervised training for improved performance and flexibility.
• Demonstration of superior performance over traditional statistical methods (Quantile Mapping) and state-of-the-art deep learning models in improving spatial structure, correcting biases, and accurately capturing extreme events.
• Enhanced data efficiency compared to unconditional models by focusing on learning small-scale features conditioned on large-scale patterns.
• Provision of accurate uncertainty estimates through the generation of diverse ensembles.
• Proven robustness and generalization capability across different geographical regions, various ESMs, and future climate change scenarios (SSP5-8.5) without requiring extensive retraining.
• Introduction of a flexible control mechanism for the spatial scales to be corrected via a noising scale hyperparameter.

Funding

• Excellence Strategy of the Federal Government and the Länder through the TUM Innovation Network EarthCare
• ClimTip project (European Union’s Horizon Europe research and innovation programme, grant agreement no. 101137601)
• Volkswagen Foundation
• National Key R&D Program of China (grant no. 2021YFA0718000)
• Alexander von Humboldt Foundation (Humboldt Research Fellowship)

Citation

@article{Aich2026Conditional,
  author = {Aich, Michael and Hess, Philipp and Pan, Baoxiang and Bathiany, Sebastian and Huang, Yu and Boers, Niklas},
  title = {Conditional diffusion models for downscaling and bias correction of Earth system model precipitation},
  journal = {Geoscientific model development},
  year = {2026},
  doi = {10.5194/gmd-19-1791-2026},
  url = {https://doi.org/10.5194/gmd-19-1791-2026}
}