# SlerpFlow: Spherical Trajectory Correction for Rectified Flow Inversion

arXiv: https://arxiv.org/abs/2607.21326 · HTML: https://mlsanity.com/paper/2607.21326/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Image generation, text-to-image and editing, one of 14 directions in Diffusion models.
- Builds on 28 of its 39 references that are in the map.
- First posted on arXiv 23 Jul 2026.

## Placed in

- Diffusion models / [Image generation, text-to-image and editing](https://mlsanity.com/diffusion/image-generation-text-to-image-and-editing/)

## Builds on (most cited first, 28 of 28)

- [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)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [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)
- [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)
- [MasaCtrl: Tuning-Free Mutual Self-Attention Control for Consistent Image Synthesis and Editing](https://mlsanity.com/paper/2304.08465/) (2023)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [EDICT: Exact Diffusion Inversion via Coupled Transformations](https://mlsanity.com/paper/2211.12446/) (2022)
- [Taming Rectified Flow for Inversion and Editing](https://mlsanity.com/paper/2411.04746/) (2024)
- [Negative-prompt Inversion: Fast Image Inversion for Editing with Text-guided Diffusion Models](https://mlsanity.com/paper/2305.16807/) (2023)
- [Improving the Training of Rectified Flows](https://mlsanity.com/paper/2405.20320/) (2024)
- [Prompt Tuning Inversion for Text-Driven Image Editing Using Diffusion Models](https://mlsanity.com/paper/2305.04441/) (2023)
- [Beyond First-Order Tweedie: Solving Inverse Problems using Latent Diffusion](https://mlsanity.com/paper/2312.00852/) (2023)
- [FireFlow: Fast Inversion of Rectified Flow for Image Semantic Editing](https://mlsanity.com/paper/2412.07517/) (2024)
- [TextCtrl: Diffusion-based Scene Text Editing with Prior Guidance Control](https://mlsanity.com/paper/2410.10133/) (2024)
- [Add-it: Training-Free Object Insertion in Images With Pretrained Diffusion Models](https://mlsanity.com/paper/2411.07232/) (2024)
- [Geometric Understanding of Deep Learning](https://mlsanity.com/paper/1805.10451/) (2018)
- [UniEdit-Flow: Unleashing Inversion and Editing in the Era of Flow Models](https://mlsanity.com/paper/2504.13109/) (2025)
- [Lightning-Fast Image Inversion and Editing for Text-to-Image Diffusion Models](https://mlsanity.com/paper/2312.12540/) (2023)
- [Visual Text Processing: A Comprehensive Review and Unified Evaluation](https://mlsanity.com/paper/2504.21682/) (2025)
- [Invertible Consistency Distillation for Text-Guided Image Editing in Around 7 Steps](https://mlsanity.com/paper/2406.14539/) (2024)
- [FreeInv: Free Lunch for Improving DDIM Inversion](https://mlsanity.com/paper/2503.23035/) (2025)
- [StyleTextGen: Style-Conditioned Multilingual Scene Text Generation](https://mlsanity.com/paper/2605.14708/) (2026)

## Abstract (arXiv)

Rectified-flow-based diffusion transformers, particularly FLUX, have demonstrated outstanding performance in high-quality image generation. However, achieving fast and accurate inversion--transforming images back to latent noise for faithful reconstruction and editing--remains a challenging bottleneck due to the discretization errors of linear solvers. This paper introduces SlerpFlow, a straightforward yet highly effective zero-shot approach that unlocks the full potential of FLUX for high-fidelity inversion and editing. Unlike existing approaches (e.g., RF-Solver) that rely on complex numerical approximations such as high-order Taylor expansions to correct trajectory errors, we present a geometric view based on the Manifold Hypothesis: the empirically observed trajectory curvature is not a numerical artifact, but rather serves as a necessary "centripetal force" that constrains the flow to remain on the data manifold. Guided by this insight, SlerpFlow integrates Spherical Linear Interpolation (Slerp) to rectify flow velocity directions on the hypersphere, strictly adhering to the intrinsic curvature of the latent space. Crucially, by caching the corrected velocity for subsequent steps, SlerpFlow achieves high-precision inversion while maintaining the computational efficiency of a first-order Euler solver. Extensive experiments on FLUX-based reconstruction and editing tasks demonstrate that SlerpFlow improves reconstruction fidelity and achieves stronger semantic alignment in editing without requiring additional training. Code is available at https://github.com/0answer0/SlerpFlow.