用于无配对数据翻译的薛定谔桥流
Schrödinger Bridge Flow for Unpaired Data Translation
AI总结：
针对现有无配对数据翻译方法无法近似最优输运映射、相关OT近似技术训练成本高或误差大的问题，提出无需训练多类DDM模型的薛定谔桥流算法，在多项无配对数据翻译任务中验证了性能。
摘要：
质量输运问题出现在机器学习的诸多领域中，其目标是计算将一个分布映射到另一个分布的映射函数。生成对抗网络（GANs）、去噪扩散模型（DDMs）等生成建模技术已被成功改造用于解决这类输运问题，分别衍生出CycleGAN和Bridge Matching方法。然而，这些方法并未对最优输运（OT）映射进行近似，而OT映射具备诸多优良特性是已知的。现有针对高维、数据充足问题近似OT映射的技术，比如基于DDM的Rectified Flow和薛定谔桥流程，要么需要在每次迭代中完整训练一个DDM类模型，要么使用可能引入显著误差的小批量技术。我们提出一种计算薛定谔桥（OT的动态熵正则化版本）的新算法，该算法无需训练多个类DDM模型。该算法对应于路径测度流的一种离散化形式，我们将其称为薛定谔桥流，其唯一不动点就是薛定谔桥。我们在多种无配对数据翻译任务上验证了该算法的性能。
英文摘要：
Mass transport problems arise in many areas of machine learning whereby one wants to compute a map transporting one distribution to another. Generative modeling techniques like Generative Adversarial Networks (GANs) and Denoising Diffusion Models (DDMs) have been successfully adapted to solve such transport problems, resulting in CycleGAN and Bridge Matching respectively. However, these methods do not approximate Optimal Transport (OT) maps, which are known to have desirable properties. Existing techniques approximating OT maps for high-dimensional data-rich problems, such as DDM-based Rectified Flow and Schrödinger Bridge procedures, require fully training a DDM-type model at each iteration, or use mini-batch techniques which can introduce significant errors. We propose a novel algorithm to compute the Schrödinger Bridge, a dynamic entropy-regularised version of OT, that eliminates the need to train multiple DDM-like models. This algorithm corresponds to a discretisation of a flow of path measures, which we call the Schrödinger Bridge Flow, whose only stationary point is the Schrödinger Bridge. We demonstrate the performance of our algorithm on a variety of unpaired data translation tasks.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
