Domain-to-domain translation involves generating a target domain sample given
a condition in the source domain. Most existing methods focus on fixed input
and output domains, i.e. they only work for specific configurations (i.e. for
two domains, either $D_1\rightarrow{}D_2$ or $D_2\rightarrow{}D_1$). This paper
proposes Multi-Domain Diffusion (MDD), a conditional diffusion framework for
multi-domain translation in a semi-supervised context. Unlike previous methods,
MDD does not require defining input and output domains, allowing translation
between any partition of domains within a set (such as $(D_1,
D_2)\rightarrow{}D_3$, $D_2\rightarrow{}(D_1, D_3)$, $D_3\rightarrow{}D_1$,
etc. for 3 domains), without the need to train separate models for each domain
configuration. The key idea behind MDD is to leverage the noise formulation of
diffusion models by incorporating one noise level per domain, which allows
missing domains to be modeled with noise in a natural way. This transforms the
training task from a simple reconstruction task to a domain translation task,
where the model relies on less noisy domains to reconstruct more noisy domains.
We present results on a multi-domain (with more than two domains) synthetic
image translation dataset with challenging semantic domain inversion.

该研究论文介绍了一种新的多域翻译方法，称为 MDD（Multi-Domain Diffusion），它通过一种条件扩散框架在半监督环境中进行多域翻译，不需要定义输入和输出域，可以在给定的域集合内进行任意分区的翻译。