🤖 AI Summary
This work addresses the computational expense and difficulty in uncertainty quantification associated with super-resolving high-dimensional spatial fields when modeling directly in pixel space. The authors propose PODiff, the first method to introduce diffusion models into the coefficient space of Proper Orthogonal Decomposition (POD), constructing a conditional generative framework within a fixed, variance-ordered latent space. By leveraging the orthogonality of POD modes, PODiff establishes an interpretable latent geometry that enables efficient and structure-preserving ensemble generation. Evaluated on sea surface temperature downscaling and convection–diffusion benchmark tasks, PODiff achieves reconstruction accuracy comparable to pixel-space diffusion models with substantially lower memory consumption and demonstrates superior uncertainty calibration compared to both deterministic approaches and Monte Carlo Dropout.
📝 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 diffusion while requiring significantly less memory and producing more reliable uncertainty estimates than deterministic and Monte Carlo Dropout baselines.