Imitation learning empowers artificial agents to mimic behavior by learning from demonstrations. Recently, diffusion models, which have the ability to model high-dimensional and multimodal distributions, have shown impressive performance on imitation learning tasks. These models learn to shape a policy by diffusing actions (or states) from standard Gaussian noise. However, the target policy to be learned is often significantly different from Gaussian and this mismatch can result in poor performance when using a small number of diffusion steps (to improve inference speed) and under limited data. The key idea in this work is that initiating from a more informative source than Gaussian enables diffusion methods to overcome the above limitations. We contribute both theoretical results, a new method, and empirical findings that show the benefits of using an informative source policy. Our method, which we call BRIDGER, leverages the stochastic interpolants framework to bridge arbitrary policies, thus enabling a flexible approach towards imitation learning. It generalizes prior work in that standard Gaussians can still be applied, but other source policies can be used if available. In experiments on challenging benchmarks, BRIDGER outperforms state-of-the-art diffusion policies and we provide further analysis on design considerations when applying BRIDGER.