Training-free conditional generation aims to leverage the unconditional diffusion models to implement the conditional generation, where flow-matching (FM) and diffusion probabilistic models (DPMs) are two mature unconditional diffusion models that achieve high-quality generation. Two questions were asked in this paper: What are the underlying connections between FM and DPMs in training-free conditional generation? Can we leverage DPMs to improve the training-free conditional generation for FM? We first show that a probabilistic diffusion path can be associated with the FM and DPMs. Then, we reformulate the ordinary differential equation (ODE) of FM based on the score function of DPMs, and thus, the conditions in FM can be incorporated as those in DPMs. Finally, we propose two posterior sampling methods to estimate the conditional term and achieve a training-free conditional generation of FM. Experimental results show that our proposed method could be implemented for various conditional generation tasks. Our method can generate higher-quality results than the state-of-the-art methods.

本研究探讨了流匹配（FM）与扩散概率模型（DPMs）在无训练条件生成中的连接，填补了相关研究领域的空白。通过将DPM的得分函数与流匹配的常微分方程进行重构，提出了两种后验采样方法，从而实现流匹配的无训练条件生成。实验表明，该方法在多个条件生成任务中生成的结果优于最新的技术。

揭示流匹配与无训练条件生成中的扩散概率模型之间的联系