Multi-fingered hands are emerging as powerful platforms for performing fine manipulation tasks, including tool use. However, environmental perturbations or execution errors can impede task performance, motivating the use of recovery behaviors that enable normal task execution to resume. In this work, we take advantage of recent advances in diffusion models to construct a framework that autonomously identifies when recovery is necessary and optimizes contact-rich trajectories to recover. We use a diffusion model trained on the task to estimate when states are not conducive to task execution, framed as an out-of-distribution detection problem. We then use diffusion sampling to project these states in-distribution and use trajectory optimization to plan contact-rich recovery trajectories. We also propose a novel diffusion-based approach that distills this process to efficiently diffuse the full parameterization, including constraints, goal state, and initialization, of the recovery trajectory optimization problem, saving time during online execution. We compare our method to a reinforcement learning baseline and other methods that do not explicitly plan contact interactions, including on a hardware screwdriver-turning task where we show that recovering using our method improves task performance by 96% and that ours is the only method evaluated that can attempt recovery without causing catastrophic task failure. Videos can be found at https://dtourrecovery.github.io/.