Flow-based models are widely used in generative tasks, including normalizing flow, where a neural network transports from a data distribution $P$ to a normal distribution. This work develops a flow-based model that transports from $P$ to an arbitrary $Q$ where both distributions are only accessible via finite samples. We propose to learn the dynamic optimal transport between $P$ and $Q$ by training a flow neural network. The model is trained to find an invertible transport map between $P$ and $Q$ optimally by minimizing the transport cost. The trained optimal transport flow allows for performing many downstream tasks, including infinitesimal density ratio estimation and distribution interpolation in the latent space for generative models. The effectiveness of the proposed model on high-dimensional data is empirically demonstrated in mutual information estimation, energy-based generative models, and image-to-image translation.

翻译：基于流的模型广泛应用于生成任务，包括归一化流，其中神经网络将数据分布$P$输运到正态分布。本研究开发了一种基于流的模型，可将$P$输运到任意分布$Q$，且两种分布仅能通过有限样本访问。我们提出通过训练流神经网络来学习$P$与$Q$之间的动态最优输运。该模型通过最小化输运成本，寻找$P$与$Q$之间的可逆输运映射，进行最优训练。训练得到的最优输运流可用于执行多项下游任务，包括无穷小密度比估计以及生成模型中潜在空间的分布插值。通过互信息估计、基于能量的生成模型和图像到图像翻译等任务，实验验证了所提模型在高维数据上的有效性。