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 optimally find an invertible transport map between $P$ and $Q$ by minimizing the transport cost. The trained optimal transport flow subsequently allows for performing many downstream tasks, including infinitesimal density ratio estimation (DRE) and distribution interpolation in the latent space for generative models. The effectiveness of the proposed model on high-dimensional data is demonstrated by strong empirical performance on high-dimensional DRE, OT baselines, and image-to-image translation.

翻译：基于流的模型在生成任务中被广泛应用，包括归一化流，其中神经网络将数据分布 $P$ 映射到正态分布。本文开发了一种基于流的模型，可将 $P$ 映射到任意分布 $Q$，且两种分布仅可通过有限样本进行访问。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代价，以最优方式找到 $P$ 与 $Q$ 之间的可逆输运映射。经过训练的最优输运流能够支持多种下游任务，包括无穷小密度比估计（DRE）以及生成模型在潜空间中的分布插值。在高维DRE、最优输运基线和图像到图像翻译任务上的强实证性能，证明了所提模型在高维数据上的有效性。