PODiff: Latent Diffusion in Proper Orthogonal Decomposition Space for Scientific Super-Resolution

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.

In many scientific problems, we need high-resolution maps, but generating them directly can be very expensive. This is especially important in areas like ocean and climate modelling, where we also need to know how confident we are in the prediction. In this work, we introduce PODiff, a method that converts low-resolution scientific data into high-resolution fields while also estimating uncertainty. Instead of working with every pixel of a large image, PODiff works with a much smaller set of important patterns in the data, which makes it faster and more memory efficient. We test it on sea surface temperature downscaling along the Western Australian coast and on a controlled physics problem. The results show that PODiff can produce accurate high-resolution predictions with useful uncertainty estimates, while requiring much less computation than standard diffusion-based methods.