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:我们将基于扩散的基因模型定义为无限的维度,并将其应用于功能的基因模型。我们首先在无限的维度限度内制定这种模型,然后才分解,我们就能获得一种从样本测量到目标测量的距离的取样算法。此外,我们提出了在无限的维度空间进行有条件取样的新方法,并表明我们的方法优于先前建议的程序。