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

arXiv: https://arxiv.org/abs/2607.10800 · HTML: https://mlsanity.com/paper/2607.10800/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 35 of its 43 references that are in the map.
- First posted on arXiv 12 Jul 2026.

## Builds on (most cited first, 30 of 35)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Prompt-to-Prompt Image Editing with Cross Attention Control](https://mlsanity.com/paper/2208.01626/) (2022)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Null-text Inversion for Editing Real Images using Guided Diffusion Models](https://mlsanity.com/paper/2211.09794/) (2022)
- [Plug-and-Play Diffusion Features for Text-Driven Image-to-Image Translation](https://mlsanity.com/paper/2211.12572/) (2022)
- [Human Preference Score v2: A Solid Benchmark for Evaluating Human Preferences of Text-to-Image Synthesis](https://mlsanity.com/paper/2306.09341/) (2023)
- [Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMC](https://mlsanity.com/paper/2302.11552/) (2023)
- [FlowEdit: Inversion-Free Text-Based Editing Using Pre-Trained Flow Models](https://mlsanity.com/paper/2412.08629/) (2024)
- [Splicing ViT Features for Semantic Appearance Transfer](https://mlsanity.com/paper/2201.00424/) (2022)
- [Taming Rectified Flow for Inversion and Editing](https://mlsanity.com/paper/2411.04746/) (2024)
- [Denoising Diffusion Bridge Models](https://mlsanity.com/paper/2309.16948/) (2023)
- [Semantic Image Inversion and Editing using Rectified Stochastic Differential Equations](https://mlsanity.com/paper/2410.10792/) (2024)
- [The probability flow ODE is provably fast](https://mlsanity.com/paper/2305.11798/) (2023)
- [FireFlow: Fast Inversion of Rectified Flow for Image Semantic Editing](https://mlsanity.com/paper/2412.07517/) (2024)
- [UniEdit-Flow: Unleashing Inversion and Editing in the Era of Flow Models](https://mlsanity.com/paper/2504.13109/) (2025)
- [Unveil Inversion and Invariance in Flow Transformer for Versatile Image Editing](https://mlsanity.com/paper/2411.15843/) (2024)
- [FlowAlign: Trajectory-Regularized, Inversion-Free Flow-based Image Editing](https://mlsanity.com/paper/2505.23145/) (2025)
- [FreeTuner: Any Subject in Any Style with Training-free Diffusion](https://mlsanity.com/paper/2405.14201/) (2024)
- [DNAEdit: Direct Noise Alignment for Text-Guided Rectified Flow Editing](https://mlsanity.com/paper/2506.01430/) (2025)
- [h-Edit: Effective and Flexible Diffusion-Based Editing via Doob's h-Transform](https://mlsanity.com/paper/2503.02187/) (2025)
- [ReFlex: Text-Guided Editing of Real Images in Rectified Flow via Mid-Step Feature Extraction and Attention Adaptation](https://mlsanity.com/paper/2507.01496/) (2025)
- [SplitFlow: Flow Decomposition for Inversion-Free Text-to-Image Editing](https://mlsanity.com/paper/2510.25970/) (2025)
- [Bidirectional Diffusion Bridge Models](https://mlsanity.com/paper/2502.09655/) (2025)

## Abstract (arXiv)

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.