arXiv:2610.37557v1 Announce Type: new Abstract: Threading a quadrotor through a moving narrow gap is a demanding test of agile flight, requiring centimeter-level spatial alignment and precise temporal execution. We address this challenge using a control policy that operates directly on onboard visual and inertial measurements to output collective thrust and body-rate commands. The task is difficult because success lies on a thin feasible manifold: small errors in timing, position, attitude, or visual observability cause collision. Prior planning and learning methods rely on privileged state, teachers, planners, or distillation; learning dynamic narrow-gap traversal directly, from scratch, remains open. We introduce a differentiable moving-gap formulation that gates centering, alignment, and smooth collision terms by signed distance to a time-varying gap plane, turning a sparse traversal event into a dense pathwise objective. We integrate this formulation into a visual-feature-to-command policy trained in one stage from random initialization, without a teacher, planner, or distillation. We validate our approach in both synthetic and real-world experiments. In controlled benchmarks, we demonstrate that pathwise gradients significantly outperform score-function gradients for precision-critical tasks, yielding a 99.3% success rate in simulation after only a few minutes of training on a single GPU. Furthermore, the policy transfers directly to a real quadrotor, successfully crossing a dynamic narrow gap from varied initial conditions using onboard sensing and inertial measurements, achieving an 80% success rate over 10 physical trials.