Generative models transform random noise into images, while their inversion aims to reconstruct structured noise for recovery and editing.This paper addresses two key tasks: (i) inversion and (ii) editing of real images using stochastic equivalents of rectified flow models (e.g., Flux).While Diffusion Models (DMs) dominate the field of generative modeling for images, their inversion suffers from faithfulness and editability challenges due to nonlinear drift and diffusion.Existing DM inversion methods require costly training of additional parameters or test-time optimization of latent variables.Rectified Flows (RFs) offer a promising alternative to DMs, yet their inversion remains underexplored. We propose RF inversion using dynamic optimal control derived via a linear quadratic regulator, and prove that the resulting vector field is equivalent to a rectified stochastic differential equation. We further extend our framework to design a stochastic sampler for Flux.Our method achieves state-of-the-art performance in zero-shot inversion and editing, surpassing prior works in stroke-to-image synthesis and semantic image editing, with large-scale human evaluations confirming user preference.See our project page https://rf-inversion.github.io/ for code and demo.