Abstract: Recent imitation learning (IL) algorithms – such as flow-matching and diffusion policies – demonstrate remarkable performance in learning complex manipulation tasks. However, these policies often fail even when operating within their training distribution due to extreme sensitivity to initial conditions and irreducible approximation errors that lead to compounding drift. This makes it unsafe to deploy IL policies in the field where out-of-distribution scenarios are prevalent. A prerequisite for safe deployment is enabling the policy to determine whether it can execute a task the way it was learned from demonstrations. This paper presents a principled approach to identify, for a trained IL policy, a safe set from where the policy is guaranteed to succeed in completing the learned task. We propose a Lipschitz-continuous Q-value function that maps state-action pairs to a safety score based on three task-agnostic criteria: visibility, recognizability, and graspability. The zero-superlevel set of this function defines a Control Invariant Set over state-action pairs. When the nominal policy proposes an action outside this set, we leverage Nagumo’s theorem to compute a recovery action via gradient ascent on the Q-function, steering the policy back to safety. To learn this Q-function, we construct a photorealistic digital twin using Gaussian Splatting that enables systematic collection of failure data without risk to physical hardware. Experiments with a Franka Emika robot demonstrate that flow-matching policies, which fail under run-time perturbations, achieve consistent task success when guided by the proposed safety watchdog.