Generate the Forest before the Trees - A Hierarchical Diffusion model for Climate Downscaling

Declan J. Curran; Sanaa Hobeichi; Hira Saleem; Hao Xue; Flora D. Salim

cs.CVJun 24, 2025

Generate the Forest before the Trees - A Hierarchical Diffusion model for Climate Downscaling

Authors: Declan J. Curran, Sanaa Hobeichi, Hira Saleem, Hao Xue, Flora D. Salim

Organizations: School of Computer Science and Engineering, University of New South Wales, Sydney, New South Wales, Australia · ARC Centre of Excellence for the Weather of the 21st Century and Climate Change Research Centre, University of New South Wales, Sydney, New South Wales, Australia

Abstract

Downscaling is essential for generating the high-resolution climate data needed for local planning, but traditional methods remain computationally demanding. Recent years have seen impressive results from AI downscaling models, particularly diffusion models, which have attracted attention due to their ability to generate ensembles and overcome the smoothing problem common in other AI methods. However, these models typically remain computationally intensive. We introduce a Hierarchical Diffusion Downscaling (HDD) model, which introduces an easily-extensible hierarchical sampling process to the diffusion framework. A coarse-to-fine hierarchy is imposed via a simple downsampling scheme. HDD achieves competitive accuracy on ERA5 reanalysis datasets and CMIP6 models, significantly reducing computational load by running on up to half as many pixels with competitive results. Additionally, a single model trained at 0.25° resolution transfers seamlessly across multiple CMIP6 models with much coarser resolution. HDD thus offers a lightweight alternative for probabilistic climate downscaling, facilitating affordable large-ensemble high-resolution climate projections. See a full code implementation at: https://github.com/HDD-Hierarchical-Diffusion-Downscaling/HDD-Hierarchical-Diffusion-Downscaling.

Figures & tables

Panel of Figure 1 — Figure 1: Radially Averaged Power Spectral Density (RAPSD) of the 10 metre U wind component. Left: High frequency finer features are the first to be corrupted by random noise. Conversely, the reverse diffusion process generates in a coarse-to-fine manner, contributing to the strong image generation capabilities of diffusion models. Enforcing this coarse-to-fine relationship explicitly can further improve results. Right: Weather data exhibits a clear power law. Coarser scales are much less information dense and closer to random noise. It is therefore, easier to model the coarser scales first, and progressively add higher frequency details. See appendix B for further details. Bottom: Progressively coarser wind data over grids of size 0.5 °(L1), 1.0 °(L2), 2.0 °(L3), 4.0 °(L4), 8 °(L5)

Figure 2: During training, the destruction kernel $q()$ progressively adds noise to the image and gradually destroys its dimensions according to the shape of the scheduler. At inference, the UNET $p()$ learns the inverse of this process, producing probabilistic downscaled outputs consistent with the original distribution. Note that although a UNET is used for $p()$ here, any function approximator could be applied. This hierarchical process is intuitive for image data, and in the climate setting we also show that competitive results can be achieved while processing up to half the pixels at inference.

Model	RMSE	PSNR	CRPS
Bilinear Interpolation	0.362755	9.54	–
Earth-ViT (Finetuned PanguWeather ( Curran et al., 2024a ) )	0.317410	10.63	–
Base EDM - 500 steps	0.000143	31.45	0.0002319
HDD (Ours)	0.000128	33.34	0.0002308

Table 1: Performance of models trained on the ERA5 downscaling task over Australia, evaluated using Root Mean Squared Error (RMSE), Peak Signal-to-Noise Ratio (PSNR) and Continuous Ranked Probability Score (CRPS). Best performance for each metric shown in bold. The ’Base EDM’ model corresponds to the backbone for popular downscaling model Corrdiff from NVIDIA ( Mardani et al., 2023 ; Karras et al., 2022 ) . The inclusion of different shape schedules is further examined in the ablation analysis in Section 5.2

Figure 3: The dimensions of the downscaled image as it evolves with the number of steps. Note that in the extreme case where we equally our dimension jumps over the steps, we only process one third as many pixels at inference - see section four for further breakdown on this.

Model	RMSE	PSNR
Equally Spaced Steps	0.000131	33.262
Move in tandem – 1 denoise step per shape step	0.000129	33.40
2 denoise steps per shape step	0.000129	33.36
3 denoise steps per shape step (Ours)	0.000128	33.34
50 denoise steps per shape step	0.000131	33.21
500 denoise steps per shape step	0.000133	33.11

Table 2: Same task as in section 5.1 but with differing shape schedules ablated. RMSE/PSNR are on the normalised residual.

Model	NRMSE	MAD	SCorr	MAPE	kgCO 2 Emitted
CCAM-1704	0.78	0.97	0.87	0.38	$\sim$ 1032kg
Earth-ViT	0.33	1.30	0.82	0.44	$\sim$ 51kg Training + $\sim$ 2kg inference
Base EDM	0.54	1.30	0.81	0.55	$\sim$ 105kg Training + $\sim$ 5kg inference
HDD	0.45	1.09	0.85	1.18	$\sim$ 50kg Training + $\sim$ 2kg 8 8 8 Values for HDD calculated based on theoretical speedup values in section 4 with 30% overhead for data loading etc. – see appendix D for more information inference

Table 3: Relevant climate metrics SCorr, MAPE from ( Isphording et al., 2024 ) and Computational Efficiency for MIROC5–driven downscaling runs

Panel of Figure 4 — Figure 4: HDD applied over the Australian extent of the CNRM-CERFACS General Circulation Model. Leftmost panel shows the coarse GCM input; the two panels to the right are independent HDD ensemble draws conditioned on the same coarse input, illustrating the spread of plausible high-resolution outcomes produced by the probabilistic downscaler.

GCM	Resolution	Model	NRMSE	MAD	MAPE	SpCor
MIROC5	$1.41^{\circ}{\times}1.41^{\circ}$	CCAM-2008	0.62	0.85	0.49	0.88
	$1.41^{\circ}{\times}1.41^{\circ}$	CCAM-1704	0.78	0.97	0.38	0.87
	$1.41^{\circ}{\times}1.41^{\circ}$	Earth-ViT	0.33	1.30	0.44	0.82
	$1.41^{\circ}{\times}1.41^{\circ}$	EDM	0.54	1.30	0.55	0.81
	$1.41^{\circ}{\times}1.41^{\circ}$	HDD	0.45	1.09	1.18	0.85
CNRM-CM5	$1.406^{\circ}{\times}1.401^{\circ}$	CCAM-1704	0.68	0.87	0.54	0.82

Table 4: Performance across MIROC5, CNRM-CM5, HadGEM, and GFDL-ESM2M. Best values for the downscaled benchmarks within each GCM group are highlighted in bold and second best are italicised.

GCM (input resolution)	$\Delta$ NRMSE (%)	$\Delta$ MAD (%)	$\Delta$ MAPE (%)	$\Delta$ SpCor (%)
MIROC5 ( $1.41^{\circ}{\times}1.41^{\circ}$ )	$+16.7$	$+16.2$	$-114.5$	$+4.9$
CNRM-CM5 ( $1.406^{\circ}{\times}1.401^{\circ}$ )	$-10.7$	$-9.5$	$-128.0$	$+1.3$
HadGEM3 ( $1.875^{\circ}{\times}1.25^{\circ}$ )	$+47.9$	$+33.7$	$-111.1$	$+11.8$
GFDL-ESM2M ( $2.5^{\circ}{\times}2.0^{\circ}$ )	$+30.1$	$+28.9$	$+22.9$	$+20.3$

Table 5: Paired comparison (HDD vs. EDM): percentage change by GCM/input resolution. Sign convention (unified, per Reviewer 4FPr’s request). All entries are signed so that positive = HDD improves on EDM and negative = HDD degrades relative to EDM , regardless of whether the underlying metric is lower-is-better or higher-is-better. Concretely: for NRMSE/MAD/MAPE (lower better) we report

100\times(\mathrm{EDM}-\mathrm{HDD})/\mathrm{EDM}

; for SpCor (higher better) we report

100\times(\mathrm{HDD}-\mathrm{EDM})/\mathrm{EDM}

. Large-magnitude negative MAPE entries (e.g., MIROC5, HadGEM3) therefore indicate that HDD’s MAPE more than doubled relative to EDM on those GCMs — this is explicitly flagged and discussed in the limitations paragraph below.

Appendix figures & tables6 assets

Supplementary material from the paper’s appendix.

Appendix

Driving GCM	Model / RCM	NRMSE	MAD	SCorr	MAPE	kgCO 2 Train 11 11 11 Emissions for hard-disk diffusion (HDD) runs are estimated using the theoretical speed-up in Section 4 of the manuscript with a 30 % overhead for data handling; see Appendix D for details.
MIROC5	HDD	0.45	1.0865	0.85	1.1752	$\sim$ 53 kg
CNRM-CM5	HDD	0.62	1.3897	0.79	0.5185	$\sim$ 53 kg
MIROC5	Base EDM	0.54	1.2961	0.81	0.5505	$\sim$ 105 kg
CNRM-CM5	Base EDM	0.56	1.2654	0.78	0.2481	$\sim$ 105 kg
CNRM-CM5	Earth-ViT	0.50	1.1044	0.80	0.3498	$\sim$ 51 kg
CNRM-CM5	CCAM-1704	0.68	0.8698	0.89	0.2600	1032 kg (total)

Appendix

Table 6: Downscaling performance metrics and estimated carbon footprint for machine-learning (ML) and dynamical-downscaling (DD) configurations over Australia (1976–2005). Results for both HDD and the base EDM were both performed using 50 inference steps and 3 denoise steps per shape step for the HDD models

Fundamental rainfall characteristic	Quantifying metric	Benchmark threshold
How much does it rain?	Mean absolute percentage error (MAPE)	MAPE $\leq 0.75$
Where does it rain?	Spatial correlation (SCor)	SCor $\geq 0.7$
When does it rain?	Amplitude : normalised root mean squared error (NRMSE) Phase : mean absolute deviation (MAD; months) of the maximum-rainfall month	Amplitude : NRMSE $\leq 0.6$ Phase : MAD $\leq 2$

Appendix

Table 7: Minimum-standard rainfall metrics (adapted from [ Isphording et al., 2024 ] ). Metrics are computed from area-weighted average total rainfall over Australia using the AGCD observational dataset. Amplitude is the difference between maximum and mean monthly rainfall; phase is the month of maximum rainfall.

Model	RMSE	PSNR	CRPS
Base EDM – 50 Steps	0.000197	29.17	0.0002415
HDD – 50 steps – 3 denoise steps per shape step	0.000157	31.40	0.0002402

Appendix

Table 8: Results extended to include CRPS metric. HDD reports values over a probabilistic distribution which are closer to the true underlying value

Inference sampling
Hyperparameter	Value
Number of steps	50 14 14 14 Note that steps varied across ablations per experiments section. However 50 was used as a good baseline to maintain high quality results and efficient sampling
Noise schedule
$\sigma_{\min}$	0.002
$\sigma_{\max}$	80
$\rho$	7

Appendix

Table 9: Hyperparameters used for sampling and inference. Note that these were generally kept the same as the original EDM implementation in [ Karras et al., 2022 ]

Model	RMSE	PSNR	CRPS
Base EDM (50 steps)	0.000197	29.17	0.000324
HDD (Ours - 50 steps)	0.000059	30.61	0.000157

Appendix

Table 10: Downscaling performance over the European domain (normalised residual RMSE / PSNR / CRPS). HDD demonstrates superior performance across standard deterministic and probabilistic metrics compared to the baseline.

$\sigma$ Level Index	Shape Steps per Split	RMSE
2	10	0.583962
2	25	0.590721
2	50	0.628742
7	10	0.583874
7	25	0.591166
7	50	0.629259

Appendix

Table 11: Ablation on the alignment between noise levels (

\sigma

) and shape schedule steps. Gradual shape step increases yield optimal performance and remain robust to varying noise levels.

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