# Towards diffusion models for large-scale sea-ice modelling

arXiv: https://arxiv.org/abs/2406.18417 · HTML: https://mlsanity.com/paper/2406.18417/

## Key facts

- Cited by 4 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 30 of its 65 references that are in the map.
- First posted on arXiv 26 Jun 2024.

## 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, 30 of 30)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [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)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [On Layer Normalization in the Transformer Architecture](https://mlsanity.com/paper/2002.04745/) (2020)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [Simple diffusion: End-to-end diffusion for high resolution images](https://mlsanity.com/paper/2301.11093/) (2023)
- [GenCast: Diffusion-based ensemble forecasting for medium-range weather](https://mlsanity.com/paper/2312.15796/) (2023)
- [Noise2Music: Text-conditioned Music Generation with Diffusion Models](https://mlsanity.com/paper/2302.03917/) (2023)
- [D2C: Diffusion-Denoising Models for Few-shot Conditional Generation](https://mlsanity.com/paper/2106.06819/) (2021)
- [Reflected Diffusion Models](https://mlsanity.com/paper/2304.04740/) (2023)
- [Diffusion Models for Constrained Domains](https://mlsanity.com/paper/2304.05364/) (2023)
- [Simple and Effective VAE Training with Calibrated Decoders](https://mlsanity.com/paper/2006.13202/) (2020)
- [Latent diffusion models for generative precipitation nowcasting with accurate uncertainty quantification](https://mlsanity.com/paper/2304.12891/) (2023)
- [Debias Coarsely, Sample Conditionally: Statistical Downscaling through Optimal Transport and Probabilistic Diffusion Models](https://mlsanity.com/paper/2305.15618/) (2023)
- [SEEDS: Emulation of Weather Forecast Ensembles with Diffusion Models](https://mlsanity.com/paper/2306.14066/) (2023)
- [End-To-End Latent Variational Diffusion Models for Inverse Problems in High Energy Physics](https://mlsanity.com/paper/2305.10399/) (2023)

## Built on by (most cited first, 4 of 4)

- [Ensemble Kalman filter in latent space using a variational autoencoder pair](https://mlsanity.com/paper/2502.12987/) (2025)
- [Cross-Cultural Fashion Design via Interactive Large Language Models and Diffusion Models](https://mlsanity.com/paper/2501.15571/) (2025)
- [Earth Science Foundation Models: From Perception to Reasoning and Discovery](https://mlsanity.com/paper/2605.12542/) (2026)
- [Probabilistic bias adjustment of seasonal forecasts using generative machine learning: A case study of Arctic sea ice predictions](https://mlsanity.com/paper/2605.29172/) (2026)

## Abstract (arXiv)

We make the first steps towards diffusion models for unconditional generation of multivariate and Arctic-wide sea-ice states. While targeting to reduce the computational costs by diffusion in latent space, latent diffusion models also offer the possibility to integrate physical knowledge into the generation process. We tailor latent diffusion models to sea-ice physics with a censored Gaussian distribution in data space to generate data that follows the physical bounds of the modelled variables. Our latent diffusion models reach similar scores as the diffusion model trained in data space, but they smooth the generated fields as caused by the latent mapping. While enforcing physical bounds cannot reduce the smoothing, it improves the representation of the marginal ice zone. Therefore, for large-scale Earth system modelling, latent diffusion models can have many advantages compared to diffusion in data space if the significant barrier of smoothing can be resolved.