Generating samples given a specific label requires estimating conditional distributions. We derive a tractable upper bound of the Wasserstein distance between conditional distributions to lay the theoretical groundwork to learn conditional distributions. Based on this result, we propose a novel conditional generation algorithm where conditional distributions are fully characterized by a metric space defined by a statistical distance. We employ optimal transport theory to propose the Wasserstein geodesic generator, a new conditional generator that learns the Wasserstein geodesic. The proposed method learns both conditional distributions for observed domains and optimal transport maps between them. The conditional distributions given unobserved intermediate domains are on the Wasserstein geodesic between conditional distributions given two observed domain labels. Experiments on face images with light conditions as domain labels demonstrate the efficacy of the proposed method.

翻译：针对特定标签生成样本需要估计条件分布。我们推导了条件分布之间Wasserstein距离的可处理上界，为学习条件分布奠定了理论基础。基于这一结果，我们提出了一种新颖的条件生成算法，其中条件分布由统计距离定义的度量空间完全刻画。运用最优传输理论，我们提出了Wasserstein测地线生成器——一种学习Wasserstein测地线的新型条件生成器。该方法同时学习观测域的条件分布以及它们之间的最优传输映射。对于未观测中间域的条件分布，位于两个观测域标签所对应条件分布之间的Wasserstein测地线上。以光照条件作为域标签的人脸图像实验验证了所提方法的有效性。