Energy-Based Models (EBMs) are known in the Machine Learning community for the decades. Since the seminal works devoted to EBMs dating back to the noughties there have been appearing a lot of efficient methods which solve the generative modelling problem by means of energy potentials (unnormalized likelihood functions). In contrast, the realm of Optimal Transport (OT) and, in particular, neural OT solvers is much less explored and limited by few recent works (excluding WGAN based approaches which utilize OT as a loss function and do not model OT maps themselves). In our work, we bridge the gap between EBMs and Entropy-regularized OT. We present the novel methodology which allows utilizing the recent developments and technical improvements of the former in order to enrich the latter. We validate the applicability of our method on toy 2D scenarios as well as standard unpaired image-to-image translation problems. For the sake of simplicity, we choose simple short- and long- run EBMs as a backbone of our Energy-guided Entropic OT method, leaving the application of more sophisticated EBMs for future research.

该研究桥接了EBMs和熵正则化OT之间的差距，并提出了新的方法，可在玩具2D场景和标准无配对图像到图像转换问题上应用。

基于能量引导的熵正则神经最优输运