In cosmology, the quest for primordial $B$-modes in cosmic microwave background (CMB) observations has highlighted the critical need for a refined model of the Galactic dust foreground. We investigate diffusion-based modeling of the dust foreground and its interest for component separation. Under the assumption of a Gaussian CMB with known cosmology (or covariance matrix), we show that diffusion models can be trained on examples of dust emission maps such that their sampling process directly coincides with posterior sampling in the context of component separation. We illustrate this on simulated mixtures of dust emission and CMB. We show that common summary statistics (power spectrum, Minkowski functionals) of the components are well recovered by this process. We also introduce a model conditioned by the CMB cosmology that outperforms models trained using a single cosmology on component separation. Such a model will be used in future work for diffusion-based cosmological inference.

在宇宙学中，为了观测宇宙微波背景中的原始$B$-模式，提出了对银河尘埃前景进行精确建模的关键需求。我们对尘埃前景的基于扩散的建模及其在成分分离中的价值进行了研究。在假设为具有已知宇宙学（或协方差矩阵）的高斯CMB的情况下，我们展示了扩散模型可以通过尘埃辐射地图的示例被训练，使其采样过程与成分分离的后验采样直接对应。我们在尘埃辐射与CMB的模拟混合中进行了说明。我们展示了通过这一过程能够恢复出组分的常用摘要统计特征（功率谱、Minkowski函数）的能力。我们还引入了一种在CMB宇宙学基础上进行条件设定的模型，该模型胜过仅基于单一宇宙学的模型在成分分离中的表现。这样的模型将用于未来的基于扩散的宇宙学推断工作中。

用扩散模型从宇宙微波背景观测中去除尘埃