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

Text-to-image editing requires a delicate balance between two competing objectives: maintaining the structural consistency of the source image and achieving faithful alignment with a new target prompt. Existing flow-based editing methods often rely on heuristic inversion pipelines or unstable trajectory constructions that are sensitive to hyperparameters and lack a unified theoretical foundation. This paper asks: can we formulate image editing as a principled conditional generation problem to achieve robust, controllable, and decoupled editing?

The authors propose h-Flow, a framework that reformulates image editing using Doob's h-Transform. While the classical h-Transform is defined for stochastic differential equations (SDEs), rectified flow (RF) models operate on deterministic ordinary differential equations (ODEs). To bridge this gap, the authors construct an equivalent SDE that shares the same marginal distributions as the RF model.

Within this framework, they define two harmonic functions: one for source consistency (reconstruction) and one for target alignment (editing). By calculating the log-gradients of these functions, they derive closed-form guidance signals. To resolve the inherent tension between these two goals, they introduce a velocity orthogonal decomposition. This technique projects the semantic editing signal onto the orthogonal complement of the reconstruction velocity, effectively decoupling the two objectives so that they can be tuned independently without mutual interference.

h-Flow provides a rigorous, training-free, and plug-and-play solution for image editing. By using orthogonal projection, the framework allows users to adjust the strength of source preservation and target alignment via separate hyperparameters (lambda_rec and lambda_edit) without one objective degrading the other. Experiments demonstrate that this approach is more robust than existing heuristic methods, as it avoids the instability often associated with per-step noise sampling or architecture-specific inversion techniques. Because the method modifies the backward generative process, it remains agnostic to the specific forward inversion strategy used, making it highly flexible for diverse editing scenarios.