We present a distilled multi-time-step (DMTS) strategy to accelerate molecular dynamics simulations using foundation neural network models. DMTS uses a dual-level neural network, where the target accurate potential is coupled to a simpler but faster model obtained via a distillation process. The 3.5 Å cutoff distilled model is sufficient to capture the fast-varying forces, i.e., mainly bonded interactions, from the accurate potential, allowing its use in a reversible reference system propagator algorithm (RESPA)-like formalism. The approach conserves accuracy, preserving both static and dynamic properties, while enabling us to evaluate the costly model only every 3 to 6 fs depending on the system. Consequently, large simulation speedups over standard 1 fs integration are observed: nearly 4-fold in homogeneous systems and 3-fold in large solvated proteins through leveraging active learning for enhanced stability. Such a strategy is applicable to any neural network potential and reduces the performance gap with classical force fields.