A PDE-Informed Latent Diffusion Model for 2-m Temperature Downscaling

TL;DR

This paper introduces a physics-informed latent diffusion model for high-resolution 2-m temperature downscaling, integrating PDE-based loss to improve physical consistency in atmospheric data reconstruction.

Contribution

It develops a PDE-conditioned diffusion model with a residual UNet architecture, incorporating a PDE loss to enforce physical realism in temperature downscaling.

Findings

PDE loss regularizes the diffusion model, improving physical plausibility.

Fine-tuning with PDE loss further reduces residuals and enhances results.

Conventional diffusion training already achieves low PDE residuals.

Abstract

This work presents a physics-conditioned latent diffusion model tailored for dynamical downscaling of atmospheric data, with a focus on reconstructing high-resolution 2-m temperature fields. Building upon a pre-existing diffusion architecture and employing a residual formulation against a reference UNet, we integrate a partial differential equation (PDE) loss term into the model's training objective. The PDE loss is computed in the full resolution (pixel) space by decoding the latent representation and is designed to enforce physical consistency through a finite-difference approximation of an effective advection-diffusion balance. Empirical observations indicate that conventional diffusion training already yields low PDE residuals, and we investigate how fine-tuning with this additional loss further regularizes the model and enhances the physical plausibility of the generated fields. The entirety of our codebase is available on Github, for future reference and development.