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.
| Comments: | Accepted at ICML 2026 |
| Subjects: | Machine Learning (cs.LG); Atmospheric and Oceanic Physics (physics.ao-ph) |
| Cite as: | arXiv:2605.03399 [cs.LG] |
| (or arXiv:2605.03399v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.03399 arXiv-issued DOI via DataCite (pending registration) |
From: Onkar Jadhav [view email]
[v1]
Tue, 5 May 2026 06:21:04 UTC (3,201 KB)
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