Patch-PODiff-ViT Improves Super-Resolution with Uncertainty.

Diffusion models are powerful for super-resolution and generative tasks, but often suffer from high computational costs in pixel space or lack interpretable uncertainty in learned latent spaces. This paper introduces Patch-PODiff-ViT, a novel framework that addresses these limitations. Instead of relying on a learned nonlinear autoencoder, it defines its latent space using patchwise Proper Orthogonal Decomposition (POD), which creates a fixed, linear, and orthonormal basis over local image patches. This results in a low-dimensional, variance-ordered token representation that preserves spatial structure, allowing for efficient diffusion processes within this structured latent space, managed by a Vision Transformer. A significant advantage is the ability to analytically propagate latent coefficient uncertainty directly to physical-space predictive variance, eliminating the need for computationally expensive Monte Carlo estimations. The method achieves strong reconstruction with fewer parameters and lower memory across various image types.