Energy-guided Entropic Neural Optimal Transport
This work addresses the limited exploration of neural OT solvers by bridging it with EBMs, offering a scalable approach for domain-specific applications like image translation, though it is incremental as it builds on existing EBM and OT techniques.
The authors tackled the gap between energy-based models (EBMs) and entropy-regularized optimal transport (OT) by developing a novel methodology that leverages EBM advancements to enhance neural OT solvers, achieving scalability in high-resolution unpaired image-to-image translation on AFHQ 512x512 datasets.
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 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 a novel methodology which allows utilizing the recent developments and technical improvements of the former in order to enrich the latter. From the theoretical perspective, we prove generalization bounds for our technique. In practice, we validate its applicability in toy 2D and image domains. To showcase the scalability, we empower our method with a pre-trained StyleGAN and apply it to high-res AFHQ $512\times 512$ unpaired I2I translation. For simplicity, we choose simple short- and long-run EBMs as a backbone of our Energy-guided Entropic OT approach, leaving the application of more sophisticated EBMs for future research. Our code is available at: https://github.com/PetrMokrov/Energy-guided-Entropic-OT