We define diffusion-based generative models in infinite dimensions, and apply them to the generative modeling of functions. By first formulating such models in the infinite-dimensional limit and only then discretizing, we are able to obtain a sampling algorithm that has \emph{dimension-free} bounds on the distance from the sample measure to the target measure. Furthermore, we propose a new way to perform conditional sampling in an infinite-dimensional space and show that our approach outperforms previously suggested procedures.

翻译：我们定义了无限维空间中的扩散生成模型，并将其应用于函数的生成式建模。通过首先在无限维极限下构建此类模型，再进行离散化，我们获得了一种采样算法，该算法在样本测度与目标测度之间的距离上具有\emph{维数无关}的界。此外，我们提出了一种在无限维空间中进行条件采样的新方法，并证明我们的方法优于先前提出的方案。