PODiff: Latent Diffusion in Proper Orthogonal Decomposition Space for Scientific Super-Resolution
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866909013622390784 |
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| author | Jadhav, Onkar French, Tim Rayson, Matthew Jones, Nicole L. |
| author_facet | Jadhav, Onkar French, Tim Rayson, Matthew Jones, Nicole L. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_03399 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | PODiff: Latent Diffusion in Proper Orthogonal Decomposition Space for Scientific Super-Resolution Jadhav, Onkar French, Tim Rayson, Matthew Jones, Nicole L. Machine Learning Atmospheric and Oceanic Physics 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. |
| title | PODiff: Latent Diffusion in Proper Orthogonal Decomposition Space for Scientific Super-Resolution |
| topic | Machine Learning Atmospheric and Oceanic Physics |
| url | https://arxiv.org/abs/2605.03399 |