Shared autonomy combines human user and AI copilot actions to control complex systems such as robotic arms. When a task is challenging, requires high dimensional control, or is subject to corruption, shared autonomy can significantly increase task performance by using a trained copilot to effectively correct user actions in a manner consistent with the user's goals. To significantly improve the performance of shared autonomy, we introduce Diffusion Sequence Copilots (DiSCo): a method of shared autonomy with diffusion policy that plans action sequences consistent with past user actions. DiSCo seeds and inpaints the diffusion process with user-provided actions with hyperparameters to balance conformity to expert actions, alignment with user intent, and perceived responsiveness. We demonstrate that DiSCo substantially improves task performance in simulated driving and robotic arm tasks. Project website: https://sites.google.com/view/disco-shared-autonomy/