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

• URL: http://arxiv.org/abs/2607.10800v1
• Date: Sun, 12 Jul 2026 15:14:37 GMT
• Title: h-Flow: Flexible Flow-based Image Editing via Doob's h-Transform
• Abstract summary: h-Flow is a training-free and theoretically grounded flow-based editing framework.<n>Inspired by Doob's $h$-Transform, we reformulate image editing as conditional generation.
• Score: 24.50633587117889
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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