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.

翻译：能量基模型在机器学习领域已为人所知数十年。自本世纪初关于能量基模型的奠基性工作以来，涌现出大量利用能量势（非归一化似然函数）解决生成建模问题的有效方法。相比之下，最优传输领域（尤其是神经最优传输求解器）的探索尚不充分，仅局限于近期少量研究工作（不包括基于WGAN的方法——这类方法将最优传输作为损失函数使用，而非对最优传输映射本身进行建模）。本文工作填补了能量基模型与熵正则化最优传输之间的空白。我们提出了新颖的方法论，使前者领域的最新进展与技术改进能够用于丰富后者领域。我们通过二维玩具场景以及标准无配对图像到图像翻译任务验证了方法的适用性。为简化起见，我们选择简单的短程/长程能量基模型作为能量引导熵正则化最优传输方法的骨干架构，将更复杂能量基模型的应用留待未来研究。