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，基于流模型已发展出众多方法。然而，当前许多流模型在设计时并未考虑如何为条件分布随条件变化的模式引入显式归纳偏置，这可能导致在风格迁移等任务中出现意外行为。本研究提出扩展流匹配（EFM），作为流匹配方法的直接扩展，其通过学习与“从条件空间到分布空间的连续映射”相对应的“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（一种旨在最小化狄利克雷能量或分布对条件敏感度的EFM变体）验证了这一特性。我们将阐述相关理论，并提供实验结果表明EFM在条件生成任务中具有竞争力。