Target-Guided Flow Matching

Flow Matching has become an important generative modeling framework, which is trained by regressing the vector fields of fixed conditional probability paths. We prove that the probability path is jointly determined by the source distribution and the velocity field. This result motivates designing a source distribution that captures the statistical structure of the target distribution to improve the generative performance of Flow Matching. To this end, we propose Target-Guided Flow Matching (TGFlow), which utilizes the marginal second-order statistics (i.e., the variance of each dimension) of the target data to construct an initial source distribution. TGFlow preserves the analytical forms of the conditional velocity field and optimization objective of Flow Matching, requires no additional training costs, and shortens the average length of actual generation trajectories, bringing the generated distribution closer to the target distribution. Experiments on 2D synthetic datasets and high-dimensional image datasets such as CIFAR-10 and ImageNet demonstrate that TGFlow improves generation quality while reducing NFE. We further verify that TGFlow supports various samplers and can be extended to a broader range of source distributions.