Semantic Image Inversion and Editing using Rectified Stochastic
  Differential Equations
Authors: name: Litu Rout, name: Yujia Chen, name: Nataniel Ruiz, name: Constantine Caramanis, name: Sanjay Shakkottai, name: Wen-Sheng Chu

Generative models transform random noise into images; their inversion aims to
transform images back to structured noise for recovery and editing. This paper
addresses two key tasks: (i) inversion and (ii) editing of a real image using
stochastic equivalents of rectified flow models (such as Flux). Although
Diffusion Models (DMs) have recently dominated the field of generative modeling
for images, their inversion presents faithfulness and editability challenges
due to nonlinearities in drift and diffusion. Existing state-of-the-art DM
inversion approaches rely on training of additional parameters or test-time
optimization of latent variables; both are expensive in practice. Rectified
Flows (RFs) offer a promising alternative to diffusion models, yet their
inversion has been underexplored. We propose RF inversion using dynamic optimal
control derived via a linear quadratic regulator. We prove that the resulting
vector field is equivalent to a rectified stochastic differential equation.
Additionally, we extend our framework to design a stochastic sampler for Flux.
Our inversion method allows for state-of-the-art performance in zero-shot
inversion and editing, outperforming prior works in stroke-to-image synthesis
and semantic image editing, with large-scale human evaluations confirming user
preference.