# EnScale: Temporally-consistent multivariate generative downscaling via proper scoring rules

arXiv: https://arxiv.org/abs/2509.26258 · HTML: https://mlsanity.com/paper/2509.26258/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 72 references that are in the map.
- First posted on arXiv 30 Sep 2025.

## Builds on (most cited first, 28 of 28)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017)
- [Neural General Circulation Models for Weather and Climate](https://mlsanity.com/paper/2311.07222/) (2023)
- [Residual Corrective Diffusion Modeling for Km-scale Atmospheric Downscaling](https://mlsanity.com/paper/2309.15214/) (2023)
- [Stochastic Super-Resolution for Downscaling Time-Evolving Atmospheric Fields with a Generative Adversarial Network](https://mlsanity.com/paper/2005.10374/) (2020)
- [A Generative Deep Learning Approach to Stochastic Downscaling of Precipitation Forecasts](https://mlsanity.com/paper/2204.02028/) (2022)
- [Skillful joint probabilistic weather forecasting from marginals](https://mlsanity.com/paper/2506.10772/) (2025)
- [Engression: Extrapolation through the Lens of Distributional Regression](https://mlsanity.com/paper/2307.00835/) (2023)
- [Probabilistic Forecasting with Generative Networks via Scoring Rule Minimization](https://mlsanity.com/paper/2112.08217/) (2021)
- [Increasing the accuracy and resolution of precipitation forecasts using deep generative models](https://mlsanity.com/paper/2203.12297/) (2022)
- [Hard-Constrained Deep Learning for Climate Downscaling](https://mlsanity.com/paper/2208.05424/) (2022)
- [Isotonic Distributional Regression](https://mlsanity.com/paper/1909.03725/) (2019)
- [Advancing Parsimonious Deep Learning Weather Prediction using the HEALPix Mesh](https://mlsanity.com/paper/2311.06253/) (2023)
- [Fast, Scale-Adaptive, and Uncertainty-Aware Downscaling of Earth System Model Fields with Generative Machine Learning](https://mlsanity.com/paper/2403.02774/) (2024)
- [Generative machine learning methods for multivariate ensemble post-processing](https://mlsanity.com/paper/2211.01345/) (2022)
- [Machine learning emulation of a local-scale UK climate model](https://mlsanity.com/paper/2211.16116/) (2022)
- [Dynamical-generative downscaling of climate model ensembles](https://mlsanity.com/paper/2410.01776/) (2024)
- [DiffESM: Conditional Emulation of Temperature and Precipitation in Earth System Models with 3D Diffusion Models](https://mlsanity.com/paper/2409.11601/) (2024)
- [A Generative Framework for Probabilistic, Spatiotemporally Coherent Downscaling of Climate Simulation](https://mlsanity.com/paper/2412.15361/) (2024)
- [Easy Uncertainty Quantification (EasyUQ): Generating Predictive Distributions from Single-valued Model Output](https://mlsanity.com/paper/2212.08376/) (2022)
- [Transferability and explainability of deep learning emulators for regional climate model projections: Perspectives for future applications](https://mlsanity.com/paper/2311.03378/) (2023)
- [Reverse Markov Learning: Multi-Step Generative Models for Complex Distributions](https://mlsanity.com/paper/2502.13747/) (2025)
- [Enforcing tail calibration when training probabilistic forecast models](https://mlsanity.com/paper/2506.13687/) (2025)

## Built on by (most cited first, 10 of 10)

- [High-Resolution Probabilistic Data-Driven Weather Modeling with a Stretched-Grid](https://mlsanity.com/paper/2511.23043/) (2025)
- [Universal Diffusion-Based Probabilistic Downscaling](https://mlsanity.com/paper/2602.11893/) (2026)
- [Score-based generative emulation of impact-relevant Earth system model outputs](https://mlsanity.com/paper/2510.04358/) (2025)
- [Physics-Constrained Adaptive Flow Matching for Climate Downscaling](https://mlsanity.com/paper/2604.03459/) (2026)
- [Downscaling weather forecasts from Low- to High-Resolution with Diffusion Models](https://mlsanity.com/paper/2604.03303/) (2026)
- [On the sensitivity of machine-learned probabilistic weather forecast models to scale-aware scoring rules](https://mlsanity.com/paper/2607.19161/) (2026)
- [How Can Machine Learning Emulators Best Support Climate Science?](https://mlsanity.com/paper/2603.22320/) (2026)
- [Regional Climate Model Emulation with Diffusion Approaches: What is the Added Value of Generative Machine Learning?](https://mlsanity.com/paper/2606.14570/) (2026)
- [Generalized Engression Models](https://mlsanity.com/paper/2610.01823/) (2026)
- [Artificial intelligence pathways from weather to climate](https://mlsanity.com/paper/2610.09770/) (2026)

## Abstract (arXiv)

The practical use of future climate projections from global circulation models (GCMs) is often limited by their coarse spatial resolution, requiring downscaling to generate high-resolution data. Regional climate models (RCMs) provide this refinement, but are computationally expensive. To address this issue, machine learning (ML) models can learn the downscaling function, mapping coarse GCM outputs to high-resolution fields. Among these, generative approaches aim to capture the full conditional distribution of RCM data given coarse-scale GCM data, which is characterized by large variability and thus challenging to model accurately. We introduce EnScale, a generative ML framework emulating the full GCM-to-RCM map by training on multiple pairs of GCM and corresponding RCM data. It first adjusts large-scale mismatches between GCM and coarsened RCM data, followed by a super-resolution step to generate high-resolution fields. To efficiently model the high-dimensional output, the super-resolution step employs a novel class of sparse local stochastic layers. Both steps employ generative models optimized with the energy score, a proper scoring rule. Compared to state-of-the-art ML downscaling approaches, our setup reduces computational cost by about one order of magnitude. EnScale jointly emulates multiple variables -- temperature, precipitation, solar radiation, and wind -- spatially consistent over Central Europe. In addition, we propose a variant EnScale-t that enables temporally consistent downscaling. We establish a comprehensive evaluation framework across various categories including calibration, spatial and temporal structure, extremes, and multivariate dependencies. Comparison with diverse benchmarks demonstrates EnScale(-t)'s competitive performance and computational efficiency, offering a promising approach for accurate and temporally consistent RCM emulation.