Recent advancements in diffusion models have established new benchmarks in both generative tasks and downstream applications. In contrast, flow matching models have shown promising improvements in performance but have not been as extensively explored, particularly due to the difficulty of inheriting knowledge from a pretrained diffusion prior foundation model.In this work, we propose a novel method to bridge the gap between pretrained diffusion models and flow matching models by aligning their trajectories and matching their objectives. Our approach mathematically formalizes this alignment and enables the efficient transfer of knowledge from diffusion priors to flow matching models. We demonstrate that our method outperforms traditional diffusion and flow matching finetuning, achieving competitive results across a variety of tasks.