Simulation-based inference has received a lot of attention recently due to the fact that the dynamics, in many models, are not available analytically but only through simulation. Iterated filtering algorithms enable simulation-based inference by perturbation and solving a recursive sequence of filtering problems. However, their application to multi-modal high-dimensional data suffers from local modes and possibly slow convergence rates. We introduce an efficient variant of iterated filtering, which can escape local modes and have better convergence rates. We test the new algorithm with some standard benchmarks, showing their out-performance over other alternatives.