# Probabilistic Super-Resolution for Urban Micrometeorology via a Schr"odinger Bridge

arXiv: https://arxiv.org/abs/2510.12148 · HTML: https://mlsanity.com/paper/2510.12148/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 29 of its 56 references that are in the map.
- First posted on arXiv 14 Oct 2025.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 29 of 29)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Accurate Image Super-Resolution Using Very Deep Convolutional Networks](https://mlsanity.com/paper/1511.04587/) (2015)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [A survey of the Schr"odinger problem and some of its connections with optimal transport](https://mlsanity.com/paper/1308.0215/) (2013)
- [Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theory](https://mlsanity.com/paper/2110.11291/) (2021)
- [Residual Corrective Diffusion Modeling for Km-scale Atmospheric Downscaling](https://mlsanity.com/paper/2309.15214/) (2023)
- [Flow map matching with stochastic interpolants: A mathematical framework for consistency models](https://mlsanity.com/paper/2406.07507/) (2024)
- [Stochastic interpolants with data-dependent couplings](https://mlsanity.com/paper/2310.03725/) (2023)
- [Probabilistic Forecasting with Stochastic Interpolants and F"ollmer Processes](https://mlsanity.com/paper/2403.13724/) (2024)
- [Fast, Scale-Adaptive, and Uncertainty-Aware Downscaling of Earth System Model Fields with Generative Machine Learning](https://mlsanity.com/paper/2403.02774/) (2024)
- [Diffusion Model-based Probabilistic Downscaling for 180-year East Asian Climate Reconstruction](https://mlsanity.com/paper/2402.06646/) (2024)
- [Fast and accurate learned multiresolution dynamical downscaling for precipitation](https://mlsanity.com/paper/2101.06813/) (2021)
- [Physics-Informed Neural Network Super Resolution for Advection-Diffusion Models](https://mlsanity.com/paper/2011.02519/) (2020)
- [Implicit Image-to-Image Schrodinger Bridge for Image Restoration](https://mlsanity.com/paper/2403.06069/) (2024)
- [Can AI be enabled to dynamical downscaling? A Latent Diffusion Model to mimic km-scale COSMO5.0CLM9 simulations](https://mlsanity.com/paper/2406.13627/) (2024)
- [Understanding Diffusion Models by Feynman's Path Integral](https://mlsanity.com/paper/2403.11262/) (2024)
- [Fourier neural operator for real-time simulation of 3D dynamic urban microclimate](https://mlsanity.com/paper/2308.03985/) (2023)
- [A Generative Framework for Probabilistic, Spatiotemporally Coherent Downscaling of Climate Simulation](https://mlsanity.com/paper/2412.15361/) (2024)
- [Speed-accuracy relations for diffusion models: Wisdom from nonequilibrium thermodynamics and optimal transport](https://mlsanity.com/paper/2407.04495/) (2024)

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

- [Variational Optimality of F"ollmer Processes in Generative Diffusions](https://mlsanity.com/paper/2602.10989/) (2026)

## Abstract (arXiv)

This study employs a neural network that represents the solution to a Schr"odinger bridge problem to perform super-resolution of 2-m temperature in an urban area. Schr"odinger bridges generally describe transformations between two data distributions based on diffusion processes. We use a specific Schr"odinger-bridge model (SM) that directly transforms low-resolution data into high-resolution data, unlike denoising diffusion probabilistic models (simply, diffusion models; DMs) that generate high-resolution data from Gaussian noise. Low-resolution and high-resolution data were obtained from separate numerical simulations with a physics-based model under common initial and boundary conditions. Compared with a DM, the SM attains comparable accuracy at one-fifth the computational cost, requiring 50 neural-network evaluations per datum for the DM and only 10 for the SM. Furthermore, high-resolution samples generated by the SM exhibit larger variance, implying superior uncertainty quantification relative to the DM. Owing to the reduced computational cost of the SM, our results suggest the feasibility of real-time ensemble micrometeorological prediction using SM-based super-resolution.