FireFlow: Fast Inversion of Rectified Flow for Image Semantic Editing

Yingying DengXiangyu HeChangwang MeiPeisong WangFan Tang

article2025ICML55 citations

Introduces a training-free numerical solver for rectified flow models that achieves second-order inversion precision with first-order computational efficiency, enabling high-fidelity image semantic editing in only eight steps with a three-fold speedup.

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Generative artificial intelligence models have become central tools for automated image synthesis and editing. In practical applications, modifying an existing image requires an inversion process that transforms the observed image back into a structured latent representation before applying target edits. While modern generative frameworks based on ordinary differential equations—known as Rectified Flow models—offer straighter paths and faster sampling than earlier stochastic diffusion techniques, existing inversion methods remain computationally expensive, require dozens of iterative steps, or introduce severe reconstruction errors that distort non-edited image areas.

The article introduces FireFlow, a zero-shot, training-free numerical framework designed to evaluate and demonstrate whether image inversion and prompt-guided editing can achieve high reconstruction precision with significantly reduced computational overhead in as few as eight steps.

To overcome the computational trade-offs of existing techniques, the authors designed a modified numerical solver that reinterprets the generation dynamics through higher-order ordinary differential equation principles. Higher-order methods typically demand multiple network evaluations per step, doubling computational cost. FireFlow resolves this by caching and reusing intermediate velocity approximations from preceding steps, effectively retaining second-order mathematical accuracy while requiring only a single network evaluation per iteration. The authors verified their solver through theoretical convergence proofs, synthetic 2D distribution benchmarks, standard generation datasets such as CIFAR-10 and MS-COCO, and specialized editing and reconstruction benchmarks, including the Densely Captioned Images and PIE-Bench datasets.

The experimental findings show substantial improvements in both operational speed and visual fidelity. First, FireFlow achieves an approximate 3× runtime speedup over state-of-the-art Rectified Flow inversion techniques, completing 1024×1024 image edits in about 24.5 seconds compared to over 71 to 78 seconds for baseline approaches. Second, the solver reduces reconstruction errors by over 70% relative to standard baselines, demonstrating faster and more stable convergence. Third, during text-guided semantic editing across hundreds of complex benchmark prompts, FireFlow achieves superior background preservation and text alignment in eight steps (requiring 18 total network evaluations), outperforming both diffusion-based models and competing flow solvers that require 28 to 50 steps.

These findings indicate that high-fidelity generative image manipulation does not require costly fine-tuning, complex multi-network architectures, or slow inference pipelines. For enterprise systems, deploying efficient solver dynamics directly reduces graphics hardware resource requirements and latency, making real-time, interactive image editing commercially viable within production pipelines.

Organizations developing or deploying image editing workflows should consider adopting velocity-reusing solvers like FireFlow to lower operational compute costs and accelerate turnaround times. When implementing attention feature replacement for editing, teams should utilize FireFlow's standard value-feature configuration for general edits, while evaluating key-feature blending strategies if handling substantial color changes or unusual compositional modifications.

The article notes certain limitations: the basic value-replacement strategy occasionally struggles with severe color shifts or atypical visual descriptions, and alternative feature-blending adjustments introduce modest trade-offs in background preservation. Nevertheless, supported by rigorous numerical proofs and empirical validations across diverse benchmarks, confidence in the primary efficiency and reconstruction improvements is high.

Institute of Automation, Chinese Academy of Sciences Institute of Computing Technology, Chinese Academy of Sciences Nanjing University of Science and Technology University of Science and Technology Beijing image semantics FireFlow image semantic editing rectified flow

arXiv: 2412.07517

Paper: Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow, Xingchao Liu et al. (2023). This seminal work establishes the foundational Rectified Flow ODE framework that FireFlow directly adapts and accelerates for image inversion and editing.
Paper: Flow Matching for Generative Modeling, Yaron Lipman et al. (2023). It introduces continuous normalizing flows and velocity field regression via Flow Matching, providing the essential dynamical principles underlying flow-based generative solvers.
Paper: Scaling Rectified Flow Transformers for High-Resolution Image Synthesis, Patrick Esser et al. (2024). It establishes large-scale rectified flow transformers for high-resolution image synthesis, providing the modern flow architecture context on which fast inversion methods operate.
Paper: Null-text Inversion for Editing Real Images using Guided Diffusion Models, Ron Mokady et al. (2022). It defines pivotal inversion and latent trajectory optimization for text-guided semantic editing, establishing core inversion concepts improved upon by FireFlow's training-free flow approach.
Paper: Denoising Diffusion Implicit Models, Jiaming Song et al. (2021). It introduces deterministic ODE sampling and inversion for generative models, which provides the mathematical motivation for high-order trajectory inversion in flow models.
Paper: Elucidating the Design Space of Diffusion-Based Generative Models, Tero Karras et al. (2022). It formalizes higher-order ODE numerical integrators for generative dynamics, directly inspiring FireFlow's multi-step velocity reuse strategy.

Paper: Variational Flow Maps: Make Some Noise for One-Step Conditional Generation, Abbas Mammadov et al. (2026). This work explores variational noise adapters to solve conditional inverse problems and image editing in minimal steps, extending the pursuit of fast flow inversion.
Paper: Mean Flows for One-step Generative Modeling, Zhengyang Geng et al. (2025). It advances flow-based generative modeling to direct one-step evaluations by learning average velocities, providing a logical continuation for accelerating flow trajectories.
Paper: Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Control, Carles Domingo-Enrich et al. (2025). It develops optimal control formulations to fine-tune continuous flow matching dynamics, offering an advanced downstream direction for steering flow paths.
Paper: UniReal: Universal Image Generation and Editing via Learning Real-world Dynamics, Xi Chen et al. (2025). It extends text-guided manipulation across unified generative tasks by learning physical dynamics, broadening the application scope of fast generative image editing.

Cover for FireFlow: Fast Inversion of Rectified Flow for Image Semantic Editing

Abstract

Though Rectified Flows (ReFlows) with distillation offer a promising way for fast sampling, its fast inversion transforms images back to structured noise for recovery and following editing remains unsolved. This paper introduces FireFlow, an embarrassingly simple yet effective zero-shot approach that inherits the startling capacity of ReFlow-based models (such as FLUX) in generation while extending its capabilities to accurate inversion and editing in 8 steps. We first demonstrate that a carefully designed numerical solver is pivotal for ReFlow inversion, enabling accurate inversion and reconstruction with the precision of a second-order solver while maintaining the practical efficiency of a first-order Euler method. This solver achieves a 3× runtime speedup compared to state-of-the-art ReFlow inversion and editing techniques while delivering smaller reconstruction errors and superior editing results in a training-free mode. The code is available at this-URL.

Topics

image semantics

Keywords

FireFlow image semantic editing rectified flow image inversion structure background preservation Null-Text Inversion FLUX-dev model CLIP similarity image reconstruction generative models

1. Introduction
2. Preliminaries and Related Works
2.1. Rectified Flow
2.2. Inversion
2.3. Editing
3. Motivation
4. Method
5. Experiment
5.1. Implementation Details
5.2. Text-to-image Generation
5.3. Inversion and Reconstruction
5.4. Inversion-based Semantic Image Editing
6. Conclusion
Acknowledgement
Impact Statement
References
A. The Pseudo-code for Inversion and Editing
B. Technical Proofs
B.1. Proof of Proposition 3.1
B.2. Proof of Proposition 4.1
B.3. Proof of Theorem 4.2
C. Empirical Convergence Rate
D. Python-style Pseudo-Code
E. Ablation Study
F. Limitations

Knowls

Knowl 1 — Modified midpoint solver with one new function evaluation per step
model/method
FireFlow solves the ReFlow probability-flow ODE $\frac{dX(t)}{dt}=v_\theta(X(t),t)$ using a modified midpoint scheme. Here, $X(t)\in\mathbb{R}^d$ is the latent state, $t$ is continuous time, and $v_\theta$ is the pretrained ReFlow drift model. For a discretization point $t_i$ and step size $h_i=t_{i+1}-t_i$ , FireFlow reuses the midpoint velocity computed at the preceding step:
$\hat v_i=v_\theta\left(\widetilde X_{i-\frac12},t_{i-\frac12}\right),$
where $\widetilde X_{i-\frac12}$ is stored in memory from the preceding iteration. It then computes
$\widetilde X_{i+\frac12}=X_i+\frac{h_i}{2}\hat v_i,$ $v_{i+\frac12}=v_\theta\left(\widetilde X_{i+\frac12},t_i+\frac{h_i}{2}\right),$ $X_{i+1}=X_i+h_i v_{i+\frac12}.$
At the first step, FireFlow evaluates $v_\theta(X_0,t_0)$ to form the initial midpoint state and evaluates the model once more at that midpoint; every subsequent step loads the previous midpoint velocity and requires only one new evaluation of $v_\theta$ . The same update works for inversion with $h_i>0$ and denoising with decreasing time and typically $h_i<0$ . Thus, the method has the per-step cost of Euler integration while using midpoint information to obtain second-order behavior.
Knowl 2 — Training-free inversion and semantic editing pipeline
algorithm
FireFlow performs zero-shot image inversion and editing with a pretrained ReFlow model, a prompt-embedding network, and no auxiliary editing model. The inversion process maps a reference image to structured noise while storing self-attention value features; the denoising process uses an edited prompt and reuses those stored features to preserve source content.
Input: Reference image $X_0$ , source and edit prompts, inversion time grid $t_0<\cdots<t_N$ , pretrained drift model $v_\theta$ , prompt encoder, and self-attention feature storage
Output: Edited image $X_0^{edit}$
Inversion:
  Evaluate $v_\theta(X_0,t_0)$ and take a half-step to obtain the first midpoint state.
  Evaluate the drift at that midpoint, save its self-attention value features as $V^{inv}_0$ , and take a full midpoint update.
  For each remaining inversion interval:
    Load the previously saved midpoint velocity.
    Use it to form the current half-step state.
    Evaluate $v_\theta$ once at the current midpoint.
    Save the new midpoint velocity and its self-attention value features.
    Take the full midpoint update.
  Return the structured noise $X_N$ and all stored inversion features $V^{inv}$ .
Editing and denoising:
  Initialize the state at $X_N$ and traverse the time grid backward from $t_N$ to $t_0$ using the edit prompt.
  At every drift evaluation, replace the denoising self-attention value features with the stored inversion features at the corresponding time.
  Reuse the preceding midpoint velocity, evaluate the model once at each new midpoint, and apply the full midpoint update.
  Return the final state as the edited image $X_0^{edit}$ .
For a trajectory with $N$ intervals, initialization uses two drift evaluations and each later interval uses one, so the inversion and denoising trajectories together require approximately $2(N+1)$ function evaluations. With eight editing intervals, FireFlow uses 18 evaluations in total and does not require a separately trained auxiliary model.
Knowl 3 — Second-order accuracy of the modified midpoint method
theoretical result
Consider the ReFlow ODE $\frac{dX}{dt}=v_\theta(X,t)$ on a finite interval, where $v_\theta$ is smooth and bounded. Let $\widehat v_\theta(X_t,t)$ be the velocity reused by FireFlow instead of the exact velocity $v_\theta(X_t,t)$ . If the reuse error satisfies
$\left\|\widehat v_\theta(X_t,t)-v_\theta(X_t,t)\right\|\leq O(h),$
where $h$ is the integration step size, then FireFlow has the same local truncation error as the standard midpoint method, $O(h^3)$ , and the same global truncation error, $O(h^2)$ . The result holds because the $O(h)$ velocity-reuse error is multiplied by the half-step factor before it affects the midpoint evaluation. Consequently, FireFlow retains second-order numerical accuracy while requiring only one new drift-model evaluation per step after initialization.
Knowl 4 — Bound on the velocity-reuse error
theoretical result
For FireFlow's reused velocity $\widehat v_\theta(X_t,t)=v_\theta(X_{t-1}+\frac{h}{2},t-1+\frac{h}{2})$ , assume that the ReFlow drift $v_\theta(X,t)$ is smooth in time and has bounded spatial derivative $\frac{\partial v_\theta}{\partial X}$ . The difference between the reused velocity and the exact velocity at the current state obeys
$\left\|\widehat v_\theta(X_t,t)-v_\theta(X_t,t)\right\|\leq O(h).$
The bound contains a temporal contribution proportional to the half-step time displacement and a spatial contribution controlled by the bounded Jacobian of $v_\theta$ ; recursive reuse does not amplify the error beyond first order in $h$ . This bound supplies the condition required for FireFlow to achieve the standard midpoint method's second-order global accuracy.
Knowl 5 — Propagation of inversion error through reverse denoising
theoretical result
Let a numerical inversion produce an endpoint perturbation $\Delta_T$ at time $T$ relative to the exact inverted state. Suppose the reverse dynamics are governed by $\frac{dX}{dt}=-v_\theta(X,1-t)$ and are Lipschitz continuous in $X$ with constant $L\geq0$ over the reverse interval $[0,T]$ . The perturbation at the reconstructed image satisfies
$\|\Delta_0\|\leq e^{-LT}\|\Delta_T\|.$
Therefore, reverse denoising does not increase the endpoint inversion error under the stated Lipschitz condition. If a $p$ -th-order ODE solver creates inversion error of order $O(h^p)$ , the reconstructed image also has asymptotic error $O(h^p)$ , up to the Lipschitz-dependent factor.
Knowl 6 — Efficiency and formal order compared with existing ReFlow editing solvers
data/table
The paper compares training-free FLUX/ReFlow inversion-editing methods along four dimensions: number of integration steps, total number of drift-model evaluations for inversion plus editing, local truncation-error order, and whether a pretrained auxiliary editing model is needed. FireFlow reaches the second-order local error of RF-Solver while using substantially fewer evaluations and no auxiliary model.
Could not parse LaTeX table
Here, NFE denotes the total number of forward evaluations of the drift model during inversion and editing. The comparison demonstrates the intended trade-off: FireFlow combines an eight-step editing trajectory, 18 total evaluations, and third-order local truncation error without requiring an additional pretrained model.
Knowl 7 — Few-step image generation with preserved or improved quality
data/table
FireFlow was evaluated as an ODE solver for both unconditional CIFAR-10 generation using open-source 1-Rectified-Flow-distill weights and text-to-image generation with FLUX-dev on 10,000 MSCOCO validation images. FID measures distributional image quality, with lower values preferred; IS measures unconditional generation quality, with higher values preferred; CLIP Score measures text-image alignment, with higher values preferred.
Could not parse LaTeX table
Could not parse LaTeX table
On CIFAR-10, FireFlow obtains the lowest FID, 5.35, while using six evaluations, compared with 10 evaluations for the five-step standard midpoint solver. On FLUX-dev, FireFlow obtains the lowest FID, 25.16, with 11 evaluations and maintains a CLIP Score of 31.42, comparable to the 20- and 40-evaluation baselines.
Knowl 8 — Lower-error inversion and reconstruction at both high and low budgets
data/table
Inversion and reconstruction were evaluated on the first 1,000 images of the Densely Captioned Images dataset with FLUX-dev. NFE includes both inversion and reconstruction evaluations, and reconstruction does not use latent features saved during inversion. Lower LPIPS is preferred, while higher SSIM and PSNR are preferred.
Could not parse LaTeX table
At 30 steps, FireFlow has the best reconstruction metrics in every listed quality column: LPIPS 0.1579, SSIM 0.8160, and PSNR 23.87, while using 62 evaluations versus 120 for RF-Solver. At approximately the same low computational budget, FireFlow also outperforms the competing ReFlow inversion methods, achieving LPIPS 0.4111, SSIM 0.5945, and PSNR 16.01 with 18 evaluations. Reconstruction-error convergence experiments further report up to a 2.7-times speedup and more than 70% error reduction relative to the compared ReFlow solvers.
Knowl 9 — Semantic editing quality and inference speed on PIE-Bench
data/table
FireFlow was tested on PIE-Bench, which contains 700 images and 10 edit categories. The evaluation measures structural distance and background preservation using PSNR and SSIM, together with CLIP similarity for the whole image and the edited region. Lower structural distance is preferred; higher PSNR, SSIM, and CLIP similarity are preferred.
Could not parse LaTeX table
With eight editing steps and 18 evaluations, FireFlow reaches structural distance 0.0271, PSNR 23.03, SSIM 0.8249, whole-image CLIP similarity 26.02, and edited-region CLIP similarity 22.81. With eight steps it also preserves background structure better than the compared ReFlow methods at their listed settings while maintaining competitive text alignment.

Per-image inference time was measured on an RTX 3090. FireFlow is substantially faster than the ReFlow baselines at both tested resolutions:
Could not parse LaTeX table
Knowl 10 — Empirical validation of velocity reuse and eight-step editing
empirical result
Experiments support the assumptions behind FireFlow's solver. On a two-dimensional synthetic 2-Rectified-Flow problem whose source and target distributions are Gaussian mixtures, FireFlow with NFE $=20$ produces samples whose density and structure more closely match the target distribution than Euler integration at the same NFE, while its transport trajectories are straighter and closer to ideal linear motion than the compared numerical trajectories.

On FLUX-dev, the average velocity-reuse error during both inversion and reconstruction grows approximately linearly with the step size, following $C\Delta t$ for an empirical constant $C$ . Although occasional spikes occur, the error remains controlled across most integration steps; the plotted variability is represented by approximately one standard deviation.

An editing-step ablation varied the number of steps from 2 to 12. Two steps do not incorporate the editing prompt effectively, whereas quality improves as the step count increases. Eight steps produce results comparable to 10 or 12 steps, motivating the use of eight editing steps in the main experiments.
Knowl 11 — Editing limitations and the preservation–editability trade-off
limitation
FireFlow's default editing rule replaces the self-attention value features of the edited trajectory with values recorded during inversion:
$\operatorname{SelfAttn}_{edit}=\operatorname{Softmax}\left(\frac{Q_{edit}K_{edit}}{\sqrt d}\right)V_{inv},$
where $Q_{edit}$ and $K_{edit}$ are the edited trajectory's query and key features, $V_{inv}$ is the inversion trajectory's value feature, and $d$ is the attention-key dimension. This rule preserves source structure and background well, but the paper empirically finds that it can fail when an edit changes an object's color or describes an uncommon natural-image scenario, such as an image with an occluded head or an unusual character description.

A proposed remedy adds the inversion key feature to the edited key feature while using the edited value feature:
$\operatorname{SelfAttn}_{edit}=\operatorname{Softmax}\left(\frac{Q_{edit}(K_{edit}+K_{inv})}{\sqrt d}\right)V_{edit},$
where $K_{inv}$ and $V_{edit}$ are the inversion key and edited value features, respectively. This variant can resolve some failed color and uncommon-scene edits, but it reduces preservation of the original structure and background. Thus, FireFlow's simple value-replacement strategy offers strong preservation and efficiency at the cost of limited robustness for difficult semantic changes.

Coverage note — The appendix derivations and full qualitative image grids were omitted because the stated error guarantees and quantitative outcomes capture their standalone contribution; the attention-feature ablation is summarized in the limitation knowl rather than reproduced in full.

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Citation

MLA

Deng, Y., et al. “FireFlow: Fast Inversion of Rectified Flow for Image Semantic Editing”. arXiv, 2024, http://arxiv.org/abs/2412.07517v1.

APA

Deng, Y., He, X., Mei, C., Wang, P., & Tang, F. (2024). FireFlow: Fast Inversion of Rectified Flow for Image Semantic Editing. arXiv. http://arxiv.org/abs/2412.07517v1

Chicago

Deng, Y., X. He, C. Mei, P. Wang, and F. Tang. 2024. “FireFlow: Fast Inversion of Rectified Flow for Image Semantic Editing”. arXiv. http://arxiv.org/abs/2412.07517v1.

Harvard

Deng, Y. et al. (2024) “FireFlow: Fast Inversion of Rectified Flow for Image Semantic Editing”, arXiv [Preprint]. Available at: http://arxiv.org/abs/2412.07517v1.

Vancouver

1. Deng Y, He X, Mei C, Wang P, Tang F (2024) FireFlow: Fast Inversion of Rectified Flow for Image Semantic Editing. arXiv

BibTeX

@article{deng2024fireflow,
  title = {FireFlow: Fast Inversion of Rectified Flow for Image Semantic Editing},
  author = {Deng, Yingying and He, Xiangyu and Mei, Changwang and Wang, Peisong and Tang, Fan},
  year = {2024},
  journal = {arXiv},
  url = {http://arxiv.org/abs/2412.07517v1},
  eprint = {2412.07517}
}

Metadata:arXiv

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FireFlow: Fast Inversion of Rectified Flow for Image Semantic Editing

Abstract

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Table of Contents

Knowls

Knowl 1 — Modified midpoint solver with one new function evaluation per step

Knowl 2 — Training-free inversion and semantic editing pipeline

Knowl 3 — Second-order accuracy of the modified midpoint method

Knowl 4 — Bound on the velocity-reuse error

Knowl 5 — Propagation of inversion error through reverse denoising

Knowl 6 — Efficiency and formal order compared with existing ReFlow editing solvers

Knowl 7 — Few-step image generation with preserved or improved quality

Knowl 8 — Lower-error inversion and reconstruction at both high and low budgets

Knowl 9 — Semantic editing quality and inference speed on PIE-Bench

Knowl 10 — Empirical validation of velocity reuse and eight-step editing

Knowl 11 — Editing limitations and the preservation–editability trade-off

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