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.

翻译：我们首次尝试利用扩散模型实现多变量及全北极海冰状态的无条件生成。尽管潜在空间扩散旨在降低计算成本，但潜在扩散模型也为将物理知识整合到生成过程提供了可能。我们针对海冰物理特性定制了潜在扩散模型，通过在数据空间采用截断高斯分布来生成符合建模变量物理边界的数据。我们的潜在扩散模型取得了与数据空间训练的扩散模型相近的评分，但潜在映射会导致生成场平滑化。虽然强制物理边界无法减轻平滑效应，但能改善边缘冰区的表征效果。因此对于大规模地球系统建模而言，若能解决显著的平滑化障碍，潜在扩散模型相较于数据空间扩散模型将具有诸多优势。