The task of conditional generation is one of the most important applications of generative models, and numerous methods have been developed to date based on the celebrated flow-based models. However, many flow-based models in use today are not built to allow one to introduce an explicit inductive bias to how the conditional distribution to be generated changes with respect to conditions. This can result in unexpected behavior in the task of style transfer, for example. In this research, we introduce extended flow matching (EFM), a direct extension of flow matching that learns a ``matrix field'' corresponding to the continuous map from the space of conditions to the space of distributions. We show that we can introduce inductive bias to the conditional generation through the matrix field and demonstrate this fact with MMOT-EFM, a version of EFM that aims to minimize the Dirichlet energy or the sensitivity of the distribution with respect to conditions. We will present our theory along with experimental results that support the competitiveness of EFM in conditional generation.

翻译：条件生成任务是生成模型最重要的应用之一，基于著名的流模型已发展出众多方法。然而，当前使用的许多流模型并未构建为允许显式引入归纳偏置，以控制待生成条件分布随条件变化的方式。例如，这可能导致风格迁移任务中出现意外行为。本研究提出扩展流匹配（EFM），作为流匹配的直接扩展，其学习对应于从条件空间到分布空间连续映射的“矩阵场”。我们证明可以通过矩阵场为条件生成引入归纳偏置，并以MMOT-EFM（旨在最小化狄利克雷能量或分布对条件敏感度的EFM变体）验证这一事实。我们将提出相关理论及实验结果表明EFM在条件生成任务中的竞争力。