The rapid development of artificial intelligence (AI) has unearthed the potential to assist humans in controlling advanced technologies. Shared autonomy (SA) facilitates control by combining inputs from a human pilot and an AI copilot. In prior SA studies, the copilot is constantly active in determining the action played at each time step. This limits human autonomy and may have deleterious effects on performance. In general, the amount of helpful copilot assistance can vary greatly depending on the task dynamics. We therefore hypothesize that human autonomy and SA performance improve through dynamic and selective copilot intervention. To address this, we develop a goal-agnostic intervention assistance (IA) that dynamically shares control by having the copilot intervene only when the expected value of the copilot's action exceeds that of the human's action across all possible goals. We implement IA with a diffusion copilot (termed IDA) trained on expert demonstrations with goal masking. We prove a lower bound on the performance of IA that depends on pilot and copilot performance. Experiments with simulated human pilots show that IDA achieves higher performance than pilot-only and traditional SA control in variants of the Reacher environment and Lunar Lander. We then demonstrate that IDA achieves better control in Lunar Lander with human-in-the-loop experiments. Human participants report greater autonomy with IDA and prefer IDA over pilot-only and traditional SA control. We attribute the success of IDA to preserving human autonomy while simultaneously offering assistance to prevent the human pilot from entering universally bad states.