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.

翻译：无训练条件生成旨在利用无条件扩散模型实现条件生成，其中流匹配与扩散概率模型是两种成熟的无条件扩散模型，能够实现高质量生成。本文提出两个核心问题：在无训练条件生成中，FM与DPMs之间存在何种本质关联？能否借助DPMs改进FM的无训练条件生成性能？我们首先证明概率扩散路径可与FM及DPMs建立关联。随后基于DPMs的得分函数重构FM的常微分方程，从而使FM中的条件项能够以DPMs的整合方式进行处理。最后提出两种后验采样方法估计条件项，实现FM的无训练条件生成。实验结果表明，所提方法可适用于多种条件生成任务，且生成质量优于当前最先进方法。