Training generative models to sample from unnormalized density functions is an important and challenging task in machine learning. Traditional training methods often rely on the reverse Kullback-Leibler (KL) divergence due to its tractability. However, the mode-seeking behavior of reverse KL hinders effective approximation of multi-modal target distributions. To address this, we propose to minimize the reverse KL along diffusion trajectories of both model and target densities. We refer to this objective as the reverse diffusive KL divergence, which allows the model to capture multiple modes. Leveraging this objective, we train neural samplers that can efficiently generate samples from the target distribution in one step. We demonstrate that our method enhances sampling performance across various Boltzmann distributions, including both synthetic multi-modal densities and n-body particle systems.