Energy-Based Models (EBMs) are known in the Machine Learning community for 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. From the theoretical perspectives, we prove generalization bounds for our approach. In practice, we validate its applicability on toy 2D scenarios as well as standard unpaired image-to-image translation problems. For simplicity, we choose simple 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（EBMs）在机器学习领域已存在数十年。自21世纪初关于EBMs的开创性工作以来，大量高效方法通过能量势（未归一化的似然函数）解决生成建模问题。相比之下，最优输运（OT）领域，特别是神经OT求解器，研究尚不充分，仅局限于少量近期工作（排除基于WGAN的方法——它们仅将OT作为损失函数而未建模OT映射本身）。本工作弥合了EBMs与熵正则化OT之间的鸿沟。我们提出一种新颖方法论，利用前者领域的最新进展与技术改进来丰富后者。从理论角度，我们证明了方法的泛化界；在实践中，我们在二维玩具场景及标准无配对图像到图像翻译问题中验证了其适用性。为简化起见，我们选择简单的长运行时EBMs作为所提出的能量引导熵正则化OT方法的主干，将更复杂EBMs的应用留待未来研究。