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 diffusion while requiring significantly less memory and producing more reliable uncertainty estimates than deterministic and Monte Carlo Dropout baselines.