# Controlling Ensemble Variance in Diffusion Models: An Application for Reanalyses Downscaling

arXiv: https://arxiv.org/abs/2501.14822 · HTML: https://mlsanity.com/paper/2501.14822/

## 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 26 of its 60 references that are in the map.
- First posted on arXiv 21 Jan 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, 26 of 26)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Simple diffusion: End-to-end diffusion for high resolution images](https://mlsanity.com/paper/2301.11093/) (2023)
- [On the Importance of Noise Scheduling for Diffusion Models](https://mlsanity.com/paper/2301.10972/) (2023)
- [GenCast: Diffusion-based ensemble forecasting for medium-range weather](https://mlsanity.com/paper/2312.15796/) (2023)
- [Residual Corrective Diffusion Modeling for Km-scale Atmospheric Downscaling](https://mlsanity.com/paper/2309.15214/) (2023)
- [DeepSD: Generating High Resolution Climate Change Projections through Single Image Super-Resolution](https://mlsanity.com/paper/1703.03126/) (2017)
- [A Generative Deep Learning Approach to Stochastic Downscaling of Precipitation Forecasts](https://mlsanity.com/paper/2204.02028/) (2022)
- [Generative Adversarial Networks (GANs Survey): Challenges, Solutions, and Future Directions](https://mlsanity.com/paper/2005.00065/) (2020)
- [Stabilizing Generative Adversarial Networks: A Survey](https://mlsanity.com/paper/1910.00927/) (2019)
- [Latent diffusion models for generative precipitation nowcasting with accurate uncertainty quantification](https://mlsanity.com/paper/2304.12891/) (2023)
- [ClimateLearn: Benchmarking Machine Learning for Weather and Climate Modeling](https://mlsanity.com/paper/2307.01909/) (2023)
- [Debias Coarsely, Sample Conditionally: Statistical Downscaling through Optimal Transport and Probabilistic Diffusion Models](https://mlsanity.com/paper/2305.15618/) (2023)
- [Diffusion Model-based Probabilistic Downscaling for 180-year East Asian Climate Reconstruction](https://mlsanity.com/paper/2402.06646/) (2024)
- [A Survey on Training Challenges in Generative Adversarial Networks for Biomedical Image Analysis](https://mlsanity.com/paper/2201.07646/) (2022)
- [Precipitation nowcasting with generative diffusion models](https://mlsanity.com/paper/2308.06733/) (2023)
- [Dynamical-generative downscaling of climate model ensembles](https://mlsanity.com/paper/2410.01776/) (2024)
- [Wind speed super-resolution and validation: from ERA5 to CERRA via diffusion models](https://mlsanity.com/paper/2401.15469/) (2024)
- [DiffESM: Conditional Emulation of Temperature and Precipitation in Earth System Models with 3D Diffusion Models](https://mlsanity.com/paper/2409.11601/) (2024)
- [Image Embedding for Denoising Generative Models](https://mlsanity.com/paper/2301.07485/) (2022)
- [Transformer based super-resolution downscaling for regional reanalysis: Full domain vs tiling approaches](https://mlsanity.com/paper/2410.12728/) (2024)

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

- [Vision Transformers for Multi-Variable Climate Downscaling: Emulating Regional Climate Models with a Shared Encoder and Multi-Decoder Architecture](https://mlsanity.com/paper/2506.22447/) (2025)

## Abstract (arXiv)

In recent years, diffusion models have emerged as powerful tools for generating ensemble members in meteorology. In this work, we demonstrate how a Denoising Diffusion Implicit Model (DDIM) can effectively control ensemble variance by varying the number of diffusion steps. Introducing a theoretical framework, we relate diffusion steps to the variance expressed by the reverse diffusion process. Focusing on reanalysis downscaling, we propose an ensemble diffusion model for the full ERA5-to-CERRA domain, generating variance-calibrated ensemble members for wind speed at full spatial and temporal resolution. Our method aligns global mean variance with a reference ensemble dataset and ensures spatial variance is distributed in accordance with observed meteorological variability. Additionally, we address the lack of ensemble information in the CARRA dataset, showcasing the utility of our approach for efficient, high-resolution ensemble generation.