Finding a transformation between two unknown probability distributions from finite samples is crucial for modeling complex data distributions and performing tasks such as sample generation, domain adaptation and statistical inference. One powerful framework for such transformations is normalizing flow, which transforms an unknown distribution into a standard normal distribution using an invertible network. In this paper, we introduce a novel model called SyMOT-Flow that trains an invertible transformation by minimizing the symmetric maximum mean discrepancy between samples from two unknown distributions, and an optimal transport cost is incorporated as regularization to obtain a short-distance and interpretable transformation. The resulted transformation leads to more stable and accurate sample generation. Several theoretical results are established for the proposed model and its effectiveness is validated with low-dimensional illustrative examples as well as high-dimensional bi-modality medical image generation through the forward and reverse flows.

翻译：从有限样本中寻找两个未知概率分布之间的变换，对于建模复杂数据分布及执行样本生成、领域适应和统计推断等任务至关重要。归一化流是实现此类变换的强大框架，它利用可逆网络将未知分布转换为标准正态分布。本文提出一种名为SyMOT-Flow的新型模型，通过最小化两个未知分布样本之间的对称最大均值差异来训练可逆变换，并引入最优输运成本作为正则化项以获得短距离且可解释的变换。所得变换能够实现更稳定、更精确的样本生成。我们为该模型建立了若干理论结果，并通过低维示例及高维双模态医学图像的正反向流生成验证了其有效性。