We propose Functional Flow Matching (FFM), a function-space generative model that generalizes the recently-introduced Flow Matching model to operate in infinite-dimensional spaces. Our approach works by first defining a path of probability measures that interpolates between a fixed Gaussian measure and the data distribution, followed by learning a vector field on the underlying space of functions that generates this path of measures. Our method does not rely on likelihoods or simulations, making it well-suited to the function space setting. We provide both a theoretical framework for building such models and an empirical evaluation of our techniques. We demonstrate through experiments on several real-world benchmarks that our proposed FFM method outperforms several recently proposed function-space generative models.

翻译：我们提出功能流匹配（Functional Flow Matching，FFM），一种函数空间生成模型，将近期提出的流匹配模型推广至无限维空间。该方法首先定义一条连接固定高斯测度与数据分布的概率测度路径，随后学习生成该测度路径的函数空间上的向量场。我们的方法不依赖似然函数或模拟，因此特别适合函数空间场景。我们既为该类模型的构建提供了理论框架，也对相关技术进行了实证评估。通过对多个真实世界基准数据集的实验，我们验证了提出的FFM方法在性能上优于近期提出的若干函数空间生成模型。