Scientific machine learning · Generative AI · 2026

PODiff

Latent diffusion in Proper Orthogonal Decomposition space for efficient, interpretable scientific super-resolution.

Onkar Jadhav, Tim French, Matthew Rayson, Nicole L. Jones

The University of Western Australia

International Conference on Machine Learning (ICML), 2026

Paper arXiv Code Live demo

Abstract

Probabilistic super-resolution of high-dimensional spatial fields using diffusion models is often computationally prohibitive due to the cost of operating directly in pixel space. We propose PODiff, a structured conditional generative framework that performs diffusion in a fixed, variance-ordered Proper Orthogonal Decomposition (POD) coefficient space, exploiting the orthogonality of POD modes to impose an interpretable, variance-ordered latent geometry. This design enables efficient ensemble generation, preserves dominant spatial structure, and yields spatially interpretable, well-calibrated uncertainty at substantially lower computational cost. We evaluate PODiff on sea surface temperature downscaling over the West Australian coast and on a controlled advection--diffusion benchmark. PODiff achieves reconstruction accuracy comparable to pixel-space and learned-latent diffusion while using a substantially smaller structured latent space, requiring significantly less memory, and producing more reliable uncertainty estimates than deterministic and Monte Carlo Dropout baselines.

Introduction

Scientific super-resolution is not only a reconstruction problem. A useful model must also represent the range of plausible fine-scale states consistent with a coarse input. Pixel-space diffusion can generate such ensembles, but it carries a high memory and inference cost for large spatial fields. Autoencoder-based latent diffusion is cheaper, although a learned nonlinear latent space makes individual coordinates—and their uncertainty—hard to interpret physically.

Simplified PODiff workflow showing low-resolution conditioning, diffusion in POD coefficient space, reconstruction and uncertainty quantification — **Simplified PODiff framework.** Conditional diffusion operates in a compact, variance-ordered POD space before reconstruction and ensemble uncertainty quantification.

Goal: Generate plausible high-resolution scientific fields and spatial uncertainty efficiently from coarse observations.
Key idea: Perform conditional diffusion in a fixed, variance-ordered POD coefficient space and reconstruct samples through the same orthonormal basis.
Takeaway: A compact and physically interpretable latent representation supports efficient ensembles and well-calibrated uncertainty at lower computational cost.

Methodology

PODiff first computes a fixed Proper Orthogonal Decomposition basis from high-resolution training fields. Fine-scale targets are projected into variance-ordered POD coefficients, and a conditional diffusion model learns to generate those coefficients from a coarse observation. Reverse-diffusion samples are decoded through the same orthonormal basis to produce an ensemble of high-resolution fields.

This construction separates spatial representation from probabilistic generation. Dominant modes capture coherent large-scale structure, while later modes represent progressively finer variability.

Temporal mean sea-surface-temperature field, selected POD modes, and explained-variance spectrum — **Figure 6.** Temporal mean SST field (left), selected POD spatial modes (Modes 1, 5, 10, 20, and 40), and the associated explained-variance spectrum with cumulative variance. Lower-index modes capture dominant large-scale structure, while higher-index modes exhibit increasingly localised spatial variability. Source.

Results and significance

An interpretable latent geometry whose coordinates correspond to ordered physical modes rather than learned features.
Substantially lower memory and computational cost than direct pixel-space diffusion.
Direct analysis of mode-wise and spatial predictive uncertainty.
A common framework for Western Australian sea-surface-temperature downscaling and a controlled advection–diffusion benchmark.

PODiff achieved reconstruction quality comparable to pixel-space diffusion while using less memory and producing better-calibrated uncertainty than deterministic and Monte Carlo Dropout baselines. The work was accepted at ICML 2026 and provides a reusable route for probabilistic super-resolution of high-dimensional scientific fields.

Reconstruction accuracy

Qualitative comparison of U-Net, RandOrthDiff and PODiff sea-surface-temperature reconstructions with ROMS ground truth and signed errors — **Figure 2.** Qualitative comparison of SST downscaling methods for 31 January 2011. The top row shows U-Net, RandOrthDiff-K40, PODiff-K40 and ROMS ground truth; the bottom row shows the corresponding signed reconstruction errors. PODiff-K40 has the lowest errors, particularly near strong thermal gradients and the coast. Source.

**Table 1.** Reconstruction error metrics for SST downscaling. Lower values indicate better performance.
Model	RMSE	MAE	Extreme RMSE	Extreme MAE
PODiff-K40	0.3923	0.2976	0.4836	0.3537
PODiff-K20	0.5171	0.3923	0.6373	0.4661
PODiff-K10	0.7725	0.5861	0.9521	0.6964
POD-proj	0.7084	0.5223	0.8896	0.6305
PixelDiff	0.4118	0.3158	0.4899	0.3600
U-Net	0.6788	0.5141	0.8366	0.6109
U-Net (reduced)	0.6819	0.5273	0.8415	0.6111
RBF	0.7784	0.5804	0.7899	0.5936
RandOrthDiff	0.9987	0.7577	1.2309	0.9003

Values are in °C and are averaged over all 365 test days in 2011; extreme events are climatological 90th-percentile exceedances. Standard deviations across five training runs are below 0.01 for all models. Source: paper Table 1.

Uncertainty quantification

PODiff empirical coverage plotted against nominal confidence level — **Figure 3.** Reliability curves for PODiff, computed from ensembles of 100 samples per day and averaged over 20 randomly selected test days. The thick curve is the mean reliability; thin curves show individual days. Source.

Spatial distribution of PODiff predictive uncertainty over the Western Australian sea-surface-temperature domain — **Figure 4.** Spatial distribution of predictive uncertainty, shown as the posterior standard deviation averaged over 20 randomly selected test days with 100 samples per day. Source.

Computational efficiency

**Table 3.** Computational cost for SST downscaling at 640 × 480 resolution.
Method	Parameters	Peak GPU memory	Training time	Inference / sample
U-Net	33M	8.8 GB	8.2 h	0.05 s
PODiff (K=40)	0.20M	1.4 GB	3.8 h	0.08 s
RandOrthDiff (K=40)	0.20M	1.4 GB	3.8 h	0.08 s
PixelDiff	33M	12.5 GB	48 h	1.24 s

Diffusion-model inference includes all denoising steps; U-Net inference is one deterministic forward pass. Measurements were made on AMD Instinct MI250X GPUs on Setonix. Source: paper Table 3.

Technology and data

Python, PyTorch, diffusion models, POD/SVD, xarray, NetCDF, Western Australian sea-surface-temperature fields, Setonix and NCI/Gadi HPC environments.

Research outputs

Paper arXiv Code Live demo

PODiff ICML 2026 poster — ICML 2026 poster summarising the PODiff formulation, SST experiments and uncertainty evaluation.

Download the original PowerPoint poster

BibTeX

Cite the accepted ICML 2026 paper:

@inproceedings{jadhav2026podiff,
  title     = {{PODiff}: Latent Diffusion in Proper Orthogonal
               Decomposition Space for Scientific Super-Resolution},
  author    = {Jadhav, Onkar and French, Tim and Rayson, Matthew
               and Jones, Nicole L.},
  booktitle = {Proceedings of the 43rd International Conference
               on Machine Learning},
  year      = {2026},
  url       = {https://openreview.net/forum?id=xCnJEgFKVC}
}