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

arXiv: https://arxiv.org/abs/2605.03399 · HTML: https://mlsanity.com/paper/2605.03399/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 16 of its 28 references that are in the map.
- First posted on arXiv 5 May 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 16 of 16)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [Latent diffusion models for generative precipitation nowcasting with accurate uncertainty quantification](https://mlsanity.com/paper/2304.12891/) (2023)
- [A graph convolutional autoencoder approach to model order reduction for parametrized PDEs](https://mlsanity.com/paper/2305.08573/) (2023)
- [Synthetic Lagrangian Turbulence by Generative Diffusion Models](https://mlsanity.com/paper/2307.08529/) (2023)
- [Generative Diffusion-based Downscaling for Climate](https://mlsanity.com/paper/2404.17752/) (2024)
- [Generative Adversarial Reduced Order Modelling](https://mlsanity.com/paper/2305.15881/) (2023)
- [Diffusion models as probabilistic neural operators for recovering unobserved states of dynamical systems](https://mlsanity.com/paper/2405.07097/) (2024)

## Built on by (most cited first, 2 of 2)

- [Patch-PODiff-ViT: Structured Latent Diffusion with Patchwise POD for Super-Resolution and Uncertainty Quantification](https://mlsanity.com/paper/2606.31290/) (2026)
- [Deep Learning-Based Statistical Downscaling of Sea Surface Temperature Using a Residual Corrective Neural Network](https://mlsanity.com/paper/2608.10022/) (2026)

## Abstract (arXiv)

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.