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

arXiv: https://arxiv.org/abs/2510.23866 · HTML: https://mlsanity.com/paper/2510.23866/

## Key facts

- Cited by 1 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 13 of its 32 references that are in the map.
- First posted on arXiv 27 Oct 2025.

## 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, 13 of 13)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Skillful Precipitation Nowcasting using Deep Generative Models of Radar](https://mlsanity.com/paper/2104.00954/) (2021)
- [Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformers](https://mlsanity.com/paper/2111.13587/) (2021)
- [Residual Corrective Diffusion Modeling for Km-scale Atmospheric Downscaling](https://mlsanity.com/paper/2309.15214/) (2023)
- [DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecasting](https://mlsanity.com/paper/2306.01984/) (2023)
- [Neural networks for post-processing ensemble weather forecasts](https://mlsanity.com/paper/1805.09091/) (2018)
- [A Generative Deep Learning Approach to Stochastic Downscaling of Precipitation Forecasts](https://mlsanity.com/paper/2204.02028/) (2022)
- [Latent diffusion models for generative precipitation nowcasting with accurate uncertainty quantification](https://mlsanity.com/paper/2304.12891/) (2023)
- [DeepDownscale: a Deep Learning Strategy for High-Resolution Weather Forecast](https://mlsanity.com/paper/1808.05264/) (2018)
- [Generative Diffusion-based Downscaling for Climate](https://mlsanity.com/paper/2404.17752/) (2024)
- [Precipitation Downscaling with Spatiotemporal Video Diffusion](https://mlsanity.com/paper/2312.06071/) (2023)
- [Score-Based Metropolis-Hastings Algorithms](https://mlsanity.com/paper/2501.00467/) (2024)

## Built on by (most cited first, 1 of 1)

- [PhysWave: Physics-Guided Latent Diffusion Models for Controllable Spatial Audio Generation](https://mlsanity.com/paper/2608.29549/) (2026)

## Abstract (arXiv)

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.