h-Flow: Flexible Flow-based Image Editing via Doob's h-Transform

2026-07-12

AI Summary

Existing editing methods based on pretrained text-to-image flow models struggle to simultaneously preserve alignment with target prompts and consistency with the original image. Inspired by Doob’s h-transform, this work introduces the first training-free conditional generative editing approach by extending the transform from the stochastic differential equation (SDE) framework to the deterministic rectified flow (RF) paradigm. The method leverages closed-form reconstruction guidance and velocity-based semantic editing signals, and incorporates an orthogonal decomposition of the velocity field to decouple editing and reconstruction directions. This enables joint control over source-image consistency and target-semantic alignment. Extensive experiments demonstrate that the proposed approach achieves superior efficiency, robustness, and flexibility across diverse image editing tasks, significantly outperforming current state-of-the-art techniques.

Abstract

Editing images with pre-trained text-to-image flow models typically requires carefully balancing target alignment with the desired prompt and source consistency with the original image. Existing approaches either rely on inversion-based pipelines or heuristic source-to-target trajectory constructions, which often depend on architecture-specific designs or are sensitive to hyperparameters. In this paper, we propose h-Flow, a training-free and theoretically grounded flow-based editing framework. Inspired by Doob's $h$-Transform, we reformulate image editing as conditional generation under multiple terminal events corresponding to source consistency and target alignment. We first extend the classical $h$-Transform from SDE-based models to the deterministic RF framework by constructing an equivalent SDE with identical marginals. Within this formulation, we design dedicated $h$-functions for source consistency and target alignment, yielding closed-form reconstruction guidance and velocity-based semantic editing signals. We further introduce a velocity orthogonal decomposition to decouple reconstruction and editing directions, enabling a controllable trade-off between the two objectives. Extensive experiments demonstrate that h-Flow achieves effective, robust, and flexible editing across diverse scenarios. The code will be released soon.

Problem

• image editing
• flow-based models
• source consistency
• target alignment
• text-to-image generation

Innovation

• Doob's h-Transform
• flow-based editing
• rectified flow
• velocity decomposition
• training-free image editing