Zero-Shot Statistical Downscaling via Diffusion Posterior Sampling

TL;DR

This work tackles zero-shot downscaling under unpaired data by formulating $p(\mathbf{X}|\mathbf{Y}) \propto p(\mathbf{Y}|\mathbf{X})p(\mathbf{X})$ and introducing ZSSD, which combines a Physics-Consistent Climate Prior conditioned on geophysical boundaries and cyclic time with Unified Coordinate Guidance to stabilize diffusion posterior sampling across diverse GCM grids. The two-stage approach learns a terrain- and time-aware diffusion prior and then performs high-resolution posterior sampling with a unified down/up-sampling pipeline that preserves large-scale consistency while allowing fine-scale detail. Empirical results show ZSSD surpasses zero-shot baselines on unpaired CMIP6 tasks, robustly reconstructs tropical cyclone-scale structures, and improves 99th percentile metrics, demonstrating strong cross-domain generalization from ERA5 to heterogeneous GCMs. The method enables cross-model downscaling without model-specific retraining, offering a scalable tool for assessing regional climate risks under future warming, albeit with slower inference due to iterative diffusion steps.

Abstract

Conventional supervised climate downscaling struggles to generalize to Global Climate Models (GCMs) due to the lack of paired training data and inherent domain gaps relative to reanalysis. Meanwhile, current zero-shot methods suffer from physical inconsistencies and vanishing gradient issues under large scaling factors. We propose Zero-Shot Statistical Downscaling (ZSSD), a zero-shot framework that performs statistical downscaling without paired data during training. ZSSD leverages a Physics-Consistent Climate Prior learned from reanalysis data, conditioned on geophysical boundaries and temporal information to enforce physical validity. Furthermore, to enable robust inference across varying GCMs, we introduce Unified Coordinate Guidance. This strategy addresses the vanishing gradient problem in vanilla DPS and ensures consistency with large-scale fields. Results show that ZSSD significantly outperforms existing zero-shot baselines in 99th percentile errors and successfully reconstructs complex weather events, such as tropical cyclones, across heterogeneous GCMs.

Figures (12)

• Figure 1: Schematic comparison of different downscaling paradigms. (Top) Supervised models learn a deterministic mapping $f_\theta$ from coarse ($\text{X}'$) to high-resolution ($\text{X}$) ERA5 data. (Middle) Vanilla DPS utilizes an unconditional diffusion prior $p_\theta(\text{X})$ with standard guidance. (Bottom) Ours (ZSSD) introduces a conditioned Physics-Consistent Climate Prior $p_\theta(\text{X}|\text{C})$ and employs Unified Coordinate Guidance during inference. $\text{C}$ denotes boundary conditions and temporal information.
• Figure 2: Overview of the ZSSD framework. The method consists of two stages. Left (Stage 1): We train a diffusion prior on ERA5 data conditioned on static terrain (DEM, LSM) and cyclic time embeddings (month, day, hour). Right (Stage 2): During inference (Reverse Stochastic Differential Equation, Reverse SDE), we employ unified coordinate guidance. The raw input $\mathbf{Y}_{\text{raw}}$ is first processed by $\mathcal{A}_{\text{low}}(\cdot)$ to isolate reliable large-scale components, and subsequently interpolated to the unified high-resolution coordinate system via $\mathcal{A}_{\text{high}}(\cdot)$. Crucially, the estimated clean state $\hat{\mathbf{X}}_0$ undergoes this identical transformation pipeline. The guidance signal is then obtained by computing the gradient of the distance between these two aligned representations with respect to $\mathbf{X}_t$.
• Figure 3: Spectral and spatial demonstration of ZSSD capabilities. (a) Annual mean power spectra of 10m Wind Speed (WS10m). (b) Visual comparison of WS10m and Tropical Cyclones. The top row displays raw outputs from various GCMs. The bottom row shows the corresponding high-resolution fields reconstructed by our ZSSD framework, revealing detailed vortex structures. Columns correspond to samples from (left to right): 2001-02-24 00:00, 2002-01-26 00:00, 2001-01-01 00:00, 2001-01-03 00:00, and 2001-03-16 00:00.
• Figure 4: Impact of conditions on generated climate states. The Top Row (without constraints) lacks the physical terrain blocking effect over the Andes (red box) and exhibits inconsistent artifacts of high pressure (red ellipses). In contrast, the Bottom Row (with constraints) successfully reproduces physically valid states, showing correct wind deceleration induced by topography and removing the spurious pressure anomalies.
• Figure 5: Impact of $\mathcal{A}_{\text{high}}(\cdot)$ operator. (a) Bias distributions. (b) Evolution of gradients during diffusion posterior sampling, illustrating the trajectory from timestep $t=1000$ to $0$ for both methods.