Diffusion and flow models achieve high generative quality but remain computationally expensive due to slow multi-step sampling. Distillation methods accelerate them by training fast student generators, yet most existing objectives lack a unified theoretical foundation. In this work, we propose Di-Bregman, a compact framework that formulates diffusion distillation as Bregman divergence-based density-ratio matching. This convex-analytic view connects several existing objectives through a common lens. Experiments on CIFAR-10 and text-to-image generation demonstrate that Di-Bregman achieves improved one-step FID over reverse-KL distillation and maintains high visual fidelity compared to the teacher model. Our results highlight Bregman density-ratio matching as a practical and theoretically-grounded route toward efficient one-step diffusion generation.