Semantic Image Inversion and Editing using Rectified Stochastic Differential Equations (2410.10792v1)

Abstract: 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.

Semantic Image Inversion and Editing Using Rectified Stochastic Differential Equations

The paper "Semantic Image Inversion and Editing using Rectified Stochastic Differential Equations" addresses the intricate challenges associated with image inversion and editing via generative models, specifically focusing on the application of rectified flows (RFs). This paper explores both practical and theoretical applications of RFs, presenting efficient methodologies to invert and edit real images without necessitating additional parameter training, latent optimization, or complex attention mechanisms.

Key Contributions and Methodology

This research explores two primary tasks: the inversion of real images and their subsequent editing using stochastic equivalents of rectified flow models. The authors introduce a novel method for RF inversion, which employs dynamic optimal control derived from a Linear Quadratic Regulator (LQR). The key idea is to construct a controlled forward ODE starting from a given image, designed to generate initial conditions for a reverse ODE. The authors prove that the resulting vector field aligns with a rectified stochastic differential equation (SDE), representing a significant extension of traditional rectified flows.

A distinguishing feature of this methodology is its capability to achieve state-of-the-art zero-shot inversion and editing, surpassing prior models, notably in stroke-to-image synthesis and semantic image editing. This advancement in performance is corroborated through extensive qualitative results and large-scale human evaluations which highlight user preference for outputs generated using this approach.

Theoretical Insights

The paper explores the theoretical underpinnings by establishing a connection between rectified flows and optimal control theory through LQR. It demonstrates that the adaptation of the vector field, interpolating between efficiency and edit fidelity, results in robust image transformations. In crafting the new SDE formulation, the authors open avenues for interpreting RF inversion through a probabilistic lens, contributing a stochastic sampling mechanism suitable for modern generative models like Flux.

Empirical Evaluations

The authors conduct rigorous empirical evaluations across multiple benchmarks, including LSUN-Bedroom, LSUN-Church, and SFHQ datasets. The results underline the method’s superiority in terms of faithfulness to the reference image and realism in the generated outputs. Their inversion approach improved realism by up to 89% when compared with other state-of-the-art methods and featured significant gains in user preference metrics.

Implications and Future Directions

The developed methodology holds substantial implications for advancing the efficiency of generative models in processing high-dimensional data. The innovations in inversion and editing processes are particularly applicable in scenarios requiring rapid image manipulation without degrading output quality.

While the paper does not focus on the direct applications of these advancements, it hints at potential future directions, such as extending the framework to incorporate more complex generative tasks, refining the stochastic sampling methods, and enhancing robust real-world deployments. As this field evolves, a continual exploration of the balance between computational efficiency and fidelity in generative modeling will likely spur further breakthroughs.

This work is a promising contribution to the ongoing development and deployment of generative models, especially in scenarios that demand fast, reliable, and high-quality inversion and editing capabilities.