Taming Rectified Flow for Inversion and Editing
Authors: Jiangshan Wang
Junfu Pu
Zhongang Qi
Jiayi Guo
Yue Ma
Nisha Huang
Yuxin Chen
Xiu Li
Ying Shan
Venue: ICML 2025 poster (2025)
Keywords: Diffusion; Image Editing; Video Editing
Primary area: applications->computer_vision

Abstract: Rectified-flow-based diffusion transformers like FLUX and OpenSora have demonstrated outstanding performance in the field of image and video generation. Despite their robust generative capabilities, these models often struggle with inversion inaccuracies, which could further limit their effectiveness in downstream tasks such as image and video editing. To address this issue, we propose RF-Solver, a novel training-free sampler that effectively enhances inversion precision by mitigating the errors in the ODE-solving process of rectified flow. Specifically, we derive the exact formulation of the rectified flow ODE and apply the high-order Taylor expansion to estimate its nonlinear components, significantly enhancing the precision of ODE solutions at each timestep. Building upon RF-Solver, we further propose RF-Edit, a general feature-sharing-based framework for image and video editing. By incorporating self-attention features from the inversion process into the editing process, RF-Edit effectively preserves the structural information of the source image or video while achieving high-quality editing results. Our approach is compatible with any pre-trained rectified-flow-based models for image and video tasks, requiring no additional training or optimization. Extensive experiments across generation, inversion, and editing tasks in both image and video modalities demonstrate the superiority and versatility of our method. The source code is available at https://github.com/wangjiangshan0725/RF-Solver-Edit.

Taming Rectified Flow for Inversion and Editing
Jiangshan Wang 12
Junfu Pu 12 Zhongang Qi Jiayi Guo
Yue Ma
Nisha Huang'
Yuxin Chen Xiu Li Ying Shan
Task Image Inversion and Reconstruction
Task 2: Video Inversion and Reconstruction
cake, fork, beer and orange
child holding phone by laptop..."
".. vibrant train traveling through rural landscape....
"... 4 giant panda walking through SHowy environment...
Source image
Source video
RF.
RF- Solver
Solver
Vanilla
Vanilla Rectified flow
Rectified
flow
Task 3: Image Editing
(resolution: 1360 x768)
Task 4: Video Editing
(resolution: 1360 x 768; 96 frames)
"magazine"
"truck"
"plane"
"sumamer" "autumnn"
"woman"
"African woman"
Source
Source video
image
Edited
Edited
image
video
Figure 1. RF-Solver for downstream tasks image and video. We propose RF-Solver to solve the rectified flow ODE with reduced error, thereby enhancing both sampling quality and inversion-rcoosttuutiionn accuracy for petified-flow-baeee generative models (Black- Forest-Labs, 2024; Zheng et al., 2024). Furthermore, we propose RF-Edit, which utilizes the RF-Solver for editing. Our methods demonstrate impressive performance across generation, inversion, and editing tasks in both image and video modalities.
Abstract
propose RF-Solver, novel training-free sampler that effectively enhances inversion precision by mitigating the errors in the ODE-solving process of rectified flow. Specifically, we derive the exact formulation of the rectified flow ODE and apply the high-order Taylor expansion to estimate nonlinear components, significantly enhancing the precision of ODE solutions at each timestep. Building upon RF-Solver, further propose RF- Edit, a general feature-sharing shaee-g-barineeeeed based framework for image and video editing. By incorporating self-attention features from the inversion process into the editing process, RF-Edit effectively preserves the structural information of the source image video while achieving high-quality editing results. Our approach is compatible with
Dectified-flow-brie diffusion transformers like FLUX and OpenSora have demonstrated outstanding performance in the field of image and video generation. Despite their robust generative capabilities, these models often struggle with inversion inaccuracies, which could further limit their effectiveness in downstream tasks such image and video editing. To address this issue,
"Equal contribution 'Tsinghua University 2 ARCC Lab, Tencent PCG HHKUST. 'Proeect lead: Junfu Pu <jevinpu tomment.com>>. Correspondence to: Zhongang Qi <zhonganggi @ gmail.com>> Xiu Li <li.xiu@ @iu@zzzu www.ssinngu.eeuuucn.......
Proceedings of the nd International Conference on Machine Learning, Vancouver, Canada. PMLR 267, 2025, Copyright 2025 by the author(s).

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Taming Rectified Flow for Inversion and Editing
any pre-trained petified-floo-basee models for image and video tasks, requiring no additional training optimization. Extensive experiments across generation, inversion, and editing tasks in both image and video modalities demonstrate the superiority and versatility of our method. Code is available at this URL.
MSE
RF Reconstraction
043
Source Imaae
Ours Receastruction
TimeSteps
1. Introduction
125
Figure 2. Analysis of the version takes the source image latent Z, as the input and pro- gressively add noise for N timesteps, obtaining Zin E (0, I). Z is then denoised for N timestops to obtain the reconstruction z During this process, we store the latent Z. and Zr at cach timestep respectively in inversion and denoising processes. Then we calculate the Mean Squared Error (MSE) between them. The red curve represents the vanilla Rectified Flow inversion and the green curve represents RF-Solver inversion.
process. In-
Recent advancements of generation methods based on Rec- tified Flow (RF) (Liu et al., 2022a; Lee al., 2024; Wang et al., 2024b) have demonstrated exceptional performance in synthesizing high-quality images and videos. Different from traditional approaches represented by Stable Diffusion (Ho et al., 2020; Rombach et al., 2022), these methods lever- age the Diffusion Transformer (Peebles & Xie, 2023; Yang et al., 2024c; Xie et al., 2024; Tang et al., 2024) architecture and implement straight-line motion system to produce the desired data distribution. With these effective designs, FLUX (Black- 2024) and OpenSora (Zheng et al., 2024) have respectively emerged as one of the state- of-the-art (SOTA) methods in the field of Io-age (T2I) and Text-to-Videe (T2V) generation.
erably deviated output (the red curve in Figure 2). Based the definition and inference process of RF (Liu, 2022; Liu et al., 2022a), we identify that these errors stem from the Ordinary Differential Equation (ODE) solving process (Zhang et al., 2024; Wang et al., 2024a; Hong et al., 2024; Peng et al., 2024). Specifically, the essence of the inver- sion and generation process for RF to derive the solution of RF ODE (Liu et al., 2022a). Since this ODE includes terms involving complex neural networks, the solution can only be coarsely approximated by a sampler. However, the experiment in Figure 2 indicates that the sampler adopted in existing models (Black-Forest-Late 2024) lacks sufficient precision for the inversion task, caus- ing notable errors to accumulate at each timestep, finally leading to unsatisfactory reconstruction results.
Despite the remarkable success in the fundamental T2I and T2V generation tasks, few studies have explored the performance of RF-based models on various downstream tasks such as inversionnrreconstuuciioo (Song et al., 202 Mokady et al., 2023; Guo et al., 2024; Wang et al., 2023c) and editing (Hertz et al., 2022; Meng et al., 2022). When directly applying the vanilla RF for inversion, we observe that it fails to faithfully reconstruct the image or video from the source. Examples are shown in Figure Task and Task 2 (the third row). For image inversion, the positions of ob- jects (e.g., the cake) and the appearance of individuals (e.g., the child) in the reconstructed image significantly diverge from the source image. The performance of video inver- sion is even worse, with noticeable distortions present in the reconstructed video. The inaccuracies of inversion and reconstruction would severely constrain the performance of RF models other inversion-based based downstream tasks such as image editing (Hertz et al., 2022; Tumanyan et al., 2023; Nguyen et al., 2024: Duan et al., 2024; Ju et al., 2024) and video editing (Liu et al., 2024; Ku et al., 2024; Fan et al., 2024: Shin et al., 2024).
2024; Zheng et al.,
Based the analysis, we aim to improve inversion accu- racy by introducing a more effective sampler, which is more general and fundamental than designing a specific inversion method. To this end, we propose RF-Solver. Specifically, we note that the exact formulation of the RF ODE solu- tion can be directly derived using the variation of constants method. For the nonlinear component of this solution (i.e.,, the integral of the neural network), we utilize Taylor expan- sion for estimation. By employing higher-order Taylor ex- pansion, the ODE can be solved with reduced error, thereby enhancing the performance of RF models. RF-Solver is a generic sampler that can be seamlessly integrated into any rectified flow model without additional training or optimiza- tion. Experimental results demonstrate that RF-Solver not only significantly enhances the accuracy of inversion and re- construction (the green curve in Figure 2), but also improves performance on fundamental tasks such as T21 generation.
In this work, we investigate the aforementioned problem by delving into the inversion and reconstruction process of the RF. Specifically, timestep during inversion and reconstruction, calculating the Mean Square Error (MSE) between them at corresponding timesteps. We observe that significant errors are introduced at each timestep throughout the whole reconstruction pro- cess, and their accumulation ultimately results in consid-
track the latent at each intermediate
Building upon this, we propose RF-Edit to leverage RF. Solver in editing tasks. weal-world image and video edit- ing require the model to make precise modifications to a
2

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Taming Rectified Flow for Inversion and Editing
source image/video while maintaining its overall structure unchanged, presenting greater challenges than reconstruc- tion. In this scenario, it is inadequate to solely rely the inverted noises as prior knowledge for editing, which could lead to edited results being excessively influenced by the tar- get prompt, diverging significantly from the original source (Hertz et al., 2022; Tumanyan et al., 2023). Addressing this problem. RF-Edit stores the V (value) feature in the self-attention layers at several timesteps during inversion. These features are used to replace the corresponding fea- tures in the denoising process. Practically, we design two specific sub-modules for RF-Edit, respectively leveraging the DiT structure of FLUX Stack-FFrres-Labs. 2024) and OpenSora (Zheng et al., 2024) as the backbones for image and video editing. With the effective design of RF-Edit, it demonstrates superior performance in both image and video domains, outperforming various SOTA methods.
(Qi et al., 2023; Wang al., 2023b; Liu et al., 2024), motion
guidance (Cong et al., 2023; Geyer et al., 2023; Yang et al., 2024a; Wang et al., 2024c), latent manipulation (Zhang et al., 2023; Yang et al., 2023a; Kara et al., 2024; Chen et al., 2023), and canonical representation (Chai et al., 2023; Lee et al., 2023; Ouyang et al., 2024; Kasten et al., 2021). To date, the editing performance of RF-based diffusion trans- formers has remained largely under-explored. Although (Rout et al., 2024b) employs FLUX (Black-Forest-LLate 2024) for image editing, its performance is limited to simple tasks such as stylization and face editing while often failing to effectively maintain the structural information of source images. Moreover, currently there is no research exploring the video editing capabilities of RF-based models.
3. Method
In this section, we present our method in detail. First, we introduce RF-Solver, which significantly enhances the pre- cision of inversion and reconstruction. Subsequently, we present RF-Edit, an extension of RF-Solver designed to enable high-quality image and video editing.
2. Related Work
2.1. Inversion
Inversion maps the real visual data, i..., image and video, to representations in noise space, which is the reverse process of generation. The representative method, DDIM inver- sion (Song et al., 2021a;b), adds predicted noise recursively at each forward step. Many efforts (Elarabawy et al., 2022: Wallace al., 2023; Mokady et al., 2023; Rout et al., 2024a; Miyake et al., 2023; Lu et al., 2022) have been made to mitigate the discretization error in DDIM inversion. Despite the effectiveness of inversion in diffusion models, the explo- ration of inversion in SOTA rectified flow models like FLUX and OpenSora is limited. RF-prior (Yang et al., 2024b) uses the score distillation invert the image while it re- quires many optimizing steps. More recently, (Rout al., 2024b) introduces an additional vector field conditioned the source image to improve the inversion. However, the error from the original vector field of rectified flow still persists, which would limit the performance of such method on various downstream tasks. In contrast, we aim to directly mitigate the error from the original vector field in this work.
3.1. Preliminaries
Rectified Flow (RF) (Liu et al., 2022b) facilitates the tran- sition between the real data distribution To and Gaussian Noises distribution π along a straight path. This is achieved by learning a forward-simulant ODE: dZ, = v Z. t)dt, t E [0, 1], which maps Z m to Zu πu-
system defined by the
In practice, the velocity field v is parameterized by a neural network Ug. During training, given empirical observations of two distributions Xn ~ To, X, ~ T and t E [o, 1]. the forward process (i.c., adding noise) of rectified flow is defined by a simple linear combination: X, fxx, + (1 X The differential form of the equation is given by: dX. (X1 - Xo)et. Consequently, the training process optimizes the network by solving the least squares regression problem, which fits the ug with (X1 - -oo):
min / E - - wo ()1 dt. (1)
2.2. Image and Video Editing
Training-free methods for image and video editing (Huang et al., 2024a; Sun et al., 2024) have gained increasing popu- larity for their efficiency and effectiveness. Existing image editing methods focus prompt refinement (Ravi al., 2023; Wang et al., 2023a), attention-sharing mechanism (Hertz et al., 2022; Parmar et al., 2023; Cao et al., 2023; Tumanyan et al., 2023), mask guidance (Avrahami et al., 2023; Couairon et al., 2022; Huang et al., 2023), and noise initialization (Brack et al., 2023; Yang et al., 2023b). Video editing introduces additional complexities in maintaining temporal consistency, making it more challenging task. Existing video editing methods focus attention injection
In the sampling process, the ODE is discretized and solved using the Euler method. Specifically, the rectified flow model starts with Gaussian noise sample Zex E (0, T). Given a series of N discrete timesteps t = {fN,................. ..., to the model iteratively predicts Va ZZt,, 44) for i E (N, 1} and then takes a step forward until generating the images zgg with the following recurrence relation:
(2) The RF model can generate high-quality images in much fewer timesteps compared to DDPM eHoet 2020), owing
Z Z. + (4-1 - 4:)o( (Z., 4t)
3

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Taming Rectified Flow for Inversion and Editing
to the nearly linear transition trajectory established during training. With these effective designs, RF model illustrates great potential in the field of T21 and T2V generation (Black- Forest-Labs, 2024; Zheng et al., 2024).
Substituting Equation (6) and Equation (5) into Equation (3), we derive the n-th order solution of Rectified flow ODE:
(t, (1-1- - 1,) +,
Ze: Zz: +
(1)
(Zz, (i)
(k: + 1)!
K=
3.2. RF-Solver
+ (h)+)))
The vanilla RF sampler demonstrates strong performance in image and video generation. However, when applied to inversion and reconstruction tasks, we observe signifi- cant eπror accumulation at each timestep. This results in reconstructions that diverge notably from the original im- age (see Figure 2). This severely limits the performance of RF models in various inversion-basee downstream tasks (Hertz et al., 2022; Wang et al., 2024a). Delving into this problem, we identify that the errors stem from the process of estimating the approximate solution for the rectified flow ODE (Wang et al., 2024b; Liu, 2022), which is formulated by Equation (2) in existing methods (Black-Forest-Late 2024; Zheng et al., 2024). Consequently, obtaining more precise solutions for the ODE would effectively mitigate these errors, leading improved performance.
where h; := t,-1 - t.. Equation (7) indicates that to es-
timate Z we need to obtain the k-th order derivatives
(k) (mg) (Z,,,4) for E {0. n .n-1}.
Considering n = 1, the formula reduces to the standard rec- tified flow (i.e.., Equation (2)). In our experiments, we find that setting n = 2 effectively mitigates the errors, yielding:
Z Zt. + (t:-1 t, (Z..
(1) + 2 (t-1 -1) (Z., tz).
(8)
Note that Vgg in Equation (8) is the first-order derivative of the network prediction term uye which cannot be analyti- cally derived due to the complex architecture of the neural network. To estimate this term, we first obtain the network prediction ét; at the timestep 4, i.e., Dr, = (z 14). Then we step forward small timestep At (which is set to 0.01 in experiments), and update the latents to obtain Zt.+At = Zz, + At- êr Subsequently, we calculate an additional prediction of the network at the timestep t; + At, i.e., 0,+ - 0o (Z 44 + At). With é; and tt.+Ar. the first-order derivative of vg at the timestep 4 can be es- timated as: v/6 (Ze, = +,,+ae-0,, Substituting this formulation into Equation (8) results in the practical im- plementation of the RF-Solver algorithm. The complete sampling process for RF-Solver is presented in Algorithm 1.
Based on this analysis, start by carefully examining the differential form of the Rectified flow: dZz (Z f)dt. This ODE is discretized in the sampling process. Given the initial value Z,, the ODE can be exactly formulated using the variant of constant method:
Z Zi, + /.m
vo vo T).T.
(3)
At.
In the above formula, uo (Z,,,)) is the non-linear compo- nent parameterized by the complex neural network, which is difficult to approximate directly. As an alternative, we employ the Taylor expansion at & to approximate this term:
Obtaining the sampling form of RF-Solver, we further derive its inversion form. Inversion maps data back into noise, which reverses the sampling process. Following previous methods for DDIM inversion (Song et al., 2021a; Dhariwal & Nichol, 2021), the ODE process can be directly reversed in the limit of small steps. Based on this assumption, the inversion process of RF-Solver can be derived as:
Zo(Z,,
Σ k=0
11)*
O(T - t,)"), (Z V
(k)
k!
(4)
where (8) (Z.,
d' (., dez denoting the k-order
derivative of Va and O denotes higher-order infinitesimals. Substituting Equation (4) into the integral term yields:
Ztoe1 Zt. + (l++1 - ()) (2., (2,
(N) U (Ze,, ts) 1'M
(r (T-te) 1*)*
2o (Z, = Σ
dr
+ 2 (t++1 1 - (1) Z tc),
k!
0=
+ ((T - -)
(5)
where Z., and 2 (.., denotes the latents during inversion. Through the high order expansion. the error of the ODE solu- tion in each timestep is reduced from ((h)²) to ((h,))). significantly facilitating inversion and reconstruction pro- cess (see Figure 2). Beyond this, RF-Solver can also be applied to any RF-based model (such as FLUX (Black- Forest-Labs, 2024) and OpenSora (Zheng et al., 2024)) for other tasks such as sampling and editing, enhancing perfor- mance without requiring additional training.
Through the above process, the network prediction term and its higher-order derivatives are separated from the integral. Then we notice that the remaining component in the integral can be computed analytically:
(r 17-4, -() dr =
[T (T-1))+1174
= (4-11 - 11)
k!
(k + 1)! 1:
(k + 1)!
4
(6)
4

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Taming Rectified Flow for Inversion and Editing
RF--Shher Imversiox
RF-Solver Insasionx N
"jeep"
"A
Sigle Blocks
OpenSora Blocks
Double Blocks
Source Prompt
Modildion
Selr Altn
Q
R
Speial
Atta
Croes
PPN
A
Concatenated Festure
Noise
Source Image
Source Video
Noise
"Red jeap winter"
"A woman"
Doubie Blocks
Target Prompt
Modhuleloo on
V
Sponial Atn
Rempono
Adda
PPN
K
Concatenated Footure
Single Blocks
Edit Image
OpenSora Blocks
Noise
Noise
Edited
RF-Solver Denoisingx N
RF-Solver Denoisinge N
Video
(a). RF-Edit for Image
(b). RF-Bdit for Video
Figure RF-Edit pipelines for image editing and video editing. We design two sub-modules applying RF-Edit (a), Image editing with FLUX (Black-Forest-Labs. 2024) and (b). Video editing with OpenSora (Zheng et al., 2024). Note that for FLUX, there multiple Double Blocks, followed by multiple Single Blocks. For OpenSora, there are multiple OpenSora DiT blocks. simplicity. only one block of each type depicted in the figure.
3.3. RF-Edit
of RF-Solver algorithm (Algorithm I): {Vi } Extract 0g (Zi. (Zsx,tx) tu))
Incorporating higher-order terms enables RF-Solver to sig- nificantly reduce errors the ODE-solving process, thereby enhancing both sampling quality and inversion accuracy. Furthermore, extend the application of RF-Solver to the more complex real-world image and video editing tasks, which present greater challenges than reconstruction. In such scenarios, preserving the content and structure of the original image is crucial. For example, when replacing an object in a source image with another one, regions unrelated the object in this image are expected to remain unaf- fected by the editing process. However, directly applying RF-Solver during the inversion and denoising stages may cause the model to be overly influenced by the target prompt, resulting in unintended modifications in other regions of the source image or video. Similar issues are common across various existing editing methods (Rout et al., 2024b; Hertz al., 2022; Tumanyan et al., 2023).
(11)
(Tm + } Extract (vg t Atx)).
(12)
During the first n timesteps denoising, considering the mth transformer block at the timestep k; the original self- attention can be formulated as:
F Attention Q!t Km VT))
(13)
where Fm denotes the output feature of the self-attention module and Q KC Vr, represent query, key and value for attention during the denoising process, respectively.
In RF-Edit, the above self-attention mechanism modified to cross-attention where ViT is replaced by V
Fm Attentionn 21), KC M
(14)
The modified output feature F is then passed to the sub- sequent modules for further processing.
To address this problem, propose RF-Edit, which builds upon the diffusion transformer architecture. Specifically, focus on the self-attention layer in the last M transformer blocks of Ug at the last n timesteps during inversion. The self-attention operation can be formulated by:
Similarly, this feature-sharing process is also adopted in the derivative calculation process of RF-Solver:
Fmm 14:4% Attentioo
Q., k
Km K444tt Att
Dm V. (15)
F Attention TT Kmm V
(10)
The proposed RF-Edit framework enables high-quality edit- ing while effectively preserving the structural information of the source image/video. Building on this concept, design two sub-modules for RF-Edit, specifically tailored for image editing and video editing (Figure 3). For image editing, RF-Edit employs FLUX (Black-Foreet--Laee 2024) as the backbone, which comprises several double blocks and single blocks. Double blocks independently modulate
Here, E {N- - n.... NN. and m E (1) F denotes the output feature of the self-attention module and Q Km ym represent query, key and value for attention during the inversion process, respectively. We extract and store the Value feature { and (Vi++as + } in the process
5

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Taming Rectified Flow for Inversion and Editing
Source
Image &Video
RF- Solverr
Vanilla Rectified flow
(a). Image Inversion and Reconstruction
(b). Video Inversion and Reconstruction
Figure 4. Qualitative results of image and video reconstruction. compared to the vanilla rectified flow baselines (the third row).
Our method (the sccond row) demonstrates superior performance
Table Quantitative results on text-to-image generation. RE-
Table 2. Quantitative results on inversion and reconstruction.
Solver outperforms several baselines.
Our method significantly improves the accuracy of reconstruction both images and videos.
DPMSolver++
RF
RF-Heun
Ours
FID (J)
24.63
25.33
24.40
23.98
Method
MSE (4)
LPIPS (L)
SSIM (1)
PSNR (1)
CLIP Score (t)
30.62
31.01
31.03
31.09
RF 0.0268
0.6253
0.7626
28.28
image
RF-Heun
0.0117
0.4696
0.8924
29.67
text and image features, while single blocks concatenate these features for unified modulation. In this architecture, RF-Edit shares features within the single blocks, as they cap- ture information from both the source image and the source prompt, enhancing the ability of the model to preserve the structural information of the source image. For video edit- ing, RF-Edit mainly employs OpenSora (Zheng et al., 2024) as the backbone. The DiT blocks in OpenSora include spa- tial attention, temporal attention, and text cross-attention. Within this architecture, the structural information of the source video is captured in the spatial attention module, where we implement feature sharing.
Ours
0.0092
0.4239
0.9276
29.89
RF 0.0206
0,4159
0.8134
18.12
video
RF-Heun
0,0156
0.3554
0.8711
18.29
Ours
0.0134
0.3287
0,8812
18.41
quantitative (Section 4.1) and qualitative results (Figure 10) demonstrate the superior performance of RF-Solver fun- damental T2I generation tasks, producing higher-quality images that align more closely with human cognition.
4.3. Inversion and Reconstruction
We conduct experiments on inversion and reconstruction for both image and video modalities, comparing our method with the vanilla RF sampler and the Heun sampler.
4. Experiment
4.1. Setup
Quantitative Comparison. The quantitative comparisons (Section 4.3) are conducted to reflect the similarity between the source and reconstruction results. Our method demon- strates superior performance across all four metrics com- pared with the vanilla RF sampler and Heun sampler.
We implement our method respectively FLUX (Black- Forest-Labs, 2024) and OpenSora (Zheng et al., 2024). In the experiment, we adopt the guidance-distillee variant of FLUX (Black-Forest-Labby 2024) for image tasks and Open- Sora (Zheng et al., 2024) for video tasks. The derivative computation in RF-Solver requires an additional forward pass, resulting in the network needing forward twice at each timestep. As result, when comparing our method with the Rectified Flow baselines, we set the number of timesteps for the vanilla Rectified Flow to be twice that of our method to ensure a fair comparison under the same number function evaluations (NFE). More detailed infor- mation for experiment setup provided in Appendix B.
Qualitative Comparison. RF-Solver effectively reduces the error in the solution of RF ODE, thereby increasing the accuracy of the reconstruction. As illustrated in Figure 4(a), the image reconstruction results using vanilla rectified flow exhibit noticeable drift from the source image, with signifi- cant alterations to the appearance of subjects in the image. For video reconstruction, as shown Figure 4(b), the base- line reconstruction results suffer from distortion. In contrast, RF-Solver significantly alleviates these issues, achieving more satisfactory results.
4.2. Text-to-image Sampling
4.4. Editing
We compare the performance our method with DPM- Solver++ (Lu et al., 2022), the vanilla RF sampler, and Heun sampler on the sot-tto-mmage generation task. Both the
We conduct experiments to evaluate the image and video editing performance of our method. For image editing, we
6

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Taming Rectified Flow for Inversion and Editing
Source
Image
horse cameel
dog
car > motorbike hiking stick rose + sunflowers couple family violin - cello cartoon style
Our
RF Inversion
P2P
DiffEdit
SDEdit
PnP
Instruct
pix2pix
Figure 5. Qualitative comparison of image editing. With RF-Solver and Seature-sharing mechanism in RF-Edit, our method can successfully handle various kinds of image editing cases, outperforming the previous SOTA methods.
Table Quantitative results of image editing. RF-Edit effec- tively edits the images according to the prompts while preserving the integrity of unrelated regions.
Table 4. Quantitative results of video editing. RF-Edit outper-
forms several previous SOTA video editing methods.
FateZero
Flatten
COVE
RAVE
Tokenflow
Ours
P2P
DiflEdit
SDEdit
PnP
Pix2Pix
RF-Inv
Ours
SC (t)
0,9382
0,9420
0,9433
0.9292
0.9439
0.9501
LPIPS (1)
0.419
0.157
0,394
0,080
0.155
0,318
0.149
MS (*)
0.9611
0.9528
0.9697
0.9519
0,9632
0,9712
CLIP Score
30.70
32.68
31.61
30.58
32,33
33.02
33,66
AQ (1)
0,6092
0.6329
0.6717
0.6586
0.6742
0.6796
11)
0.6898
0.7024
0.7163
0.6917
0.7128
0.7207
compare our method with P2P (Hertz et al., 2022), DiffEdit (Couairon et al., 2023), SDEdit (Meng et al., 2022), PnP (Tumanyan et al., 2023), Pix2pix (Parmar et al., 2023) and RF-Inversion (Rout et al., 2024b). For video editing tasks, we compare our method with FateZero (Qi et al., 2023),
consistency while demonstrating superior quality.
Qualitative Comparison. For image editing, compare the performance of our method with several baselines across different types of editing requirements including adding, replacing, and stylization (Figure 5 and Figure 8). The baseline methods often suffer from background changes or fail perform the desired edits. In contrast, our method demonstrates satisfying performance, effectively achieving balanced trade-off between the fidelity to the target prompt and the preservation of the source image.
FLATTEN (Cong et al., 2023), COVE (Wang et al., 2024c), RAVE (Kara et al., 2024), Tokenflow (Geyer et al., 2023).
Quantitative Comparison. In image editing, Our method outperforms all other methods in CLIP score (Section 4.4), indicating that the edited images align well with the user- provided prompts. For LPIPS, it is noted that PnP (Tu- manyan et al., 2023) has much lower value than all other methods. Based on the qualitative results (Figure 5), it can be seen that PnP is only suitable for editing cases that do not significantly modify the structure or shape of the source image (such as changing red roses into yellow sunflowers). It fails in the case of shape editing, resulting in image very similar to the source. Consequently, although PnP has the lowest LPIPS score, its CLIP score is the lowest. For video editing, RF-Edit achieves higher scores on VBench (Huang et al., 2024b) metrics (Section 4.4). The results illustrate that our method successfully maintains temporal
The qualitative results for video editing are shown in Fig- ure 6. RF-Edit illustrates impressive performance in han- dling complicated editing cases (e.g.. modifying the leftmost lion among three lions into a white polar bear and changing the other two small lions into orange tiger cubs), whereas all other baseline methods fail in this scenario.
Besides, Hunyuan Video (Kong et al., 2024) has recently demonstrated strong performance in text-to-video gener- ation. Thanks to the generality of our method, it can be implemented on Hunyuan Video for video editing. More
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Taming Rectified Flow for Inversion and Editing
3 lions + left: 2 tiger cubs; right: 1 polar bear
autuma
Source Video
Ours
FateZero
Flatten
COVE
RAVE
TokenFlow
Souree Video
OUES
FateZero
Flaten
COVE
RAVE TokenHow
Figure Qualitative comparison of video editing. The first video comprises 200 frames with a resolution of 512 x 512, while the second video contains 60 frames with resolution of 1024 x 768 (frames compressed for neat layout).
qualitative results are shown in Figure
output being overly similar to the source image, ultimately undermining the intended editing objectives (Figure 7). To investigate the impact of feature-sharing steps on editing results, we incrementally increase the number of feature- sharing steps applied to the same image. Due to the vary- ing levels of difficulty that different images presented to the model, the optimal number of sharing steps may differ across cases. Experimental results reveal that setting the sharing step to 5 effectively meets the editing requirements for most images. Additionally, we can customize the sharing step for each image identify the most satisfying outcome.
4.5. A Ablation Study
We conduct ablation studies to illustrate the effectiveness of RF-Solver and RF-Edit. Without loss of generality, these ablation studies are performed on the image tasks using FLUX (Black-Forest-Latee 2024) as the base model.
Taylor Expansion Order of RF-SSoler. We investigated the impact of the Taylor expansion order in RF-Solver (Sec- tion 4.5) under the same NFE across different orders. Com- pared to the first-order expansion (i.e., the vanilla rectified flow), the second-order expansion demonstrates significant improvement across various tasks. However, higher-order expansions do not yield further enhancements. We speculate that this primarily due to higher-order Taylor expansions requiring more inference steps per timestep. With a fixed NFE, this results in reduced overall number of timesteps compared to lower-order expansions, leading to suboptimal performance. Moreover, computing the higher-order deriva- tives of tn (2tt,,4) 4;) substantially increases the complexity of the algorithm, posing challenges for practical applica- tions. Consequently, we employ second-order expansion (i.e., RF-Solver-2 in Section 4.5) for various downstream tasks due its effectiveness and simplicity.
Swidin golden retriever + dalmatiin glasses
school bus fire truck
Source Image
Feature Shartnn Step
Figure 7. Ablation study of feature-sharing step in RF-Edit. The second row is the results produced solely by RF-Solver, with- out the proposed feature-sharinn mechanism. Feature-sharing can significantly enhance the consistency between source and target images, while too-large feature-sharing step may lead to the failure of editing.
Table Ablation study the Taylor Expansion order. Here, RF implics the vanilla Rectified Flow without the proposed RF- Solver algorithm. All of the experiments for editing in the tahle apply the proposed feature-sharing mechanism for better results.
Metric
RF
RF-Solver-2 RF-Solver-a
FID (1)
25.33
23.98
23.94
5. Conclusion
Sampling
CLIP Score (t)
31.01
31.09
31.09
In this paper, we propose RF-Solver, a versatile sampler for the rectified flow model that solves the rectified flow ODE with reduced error, thus enhancing the image and video generation quality across various tasks such sampling and reconstruction. Based on RF-Solver, we further propose RF. Edit, which achieves high-quality editing performance while effectively preserving the structural information in source images or videos. Extensive experiments demonstrate the versatility and effectiveness of our method.
MSE (1)
0.0268
0.0092
0.0131
Inversion
LPIPS (L)
0.6253
0.4239
0.4817
I.PPSS CLIP Score (1)
0.1524
0.1494
0.1503
Editing
32.97
33.66
33.18
Feature Sharing Steps of RF-Edit. RF-Edit leverages fea- ture sharing to maintain the structural consistency between original images and edited images. However, an excessive number of feature-sharing steps may result the edited
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Taming Rectified Flow for Inversion and Editing
Acknowledgments
optical flow-guided attention for consistent text- to-video editing. arXiv preprint arXiv:2310.05922. 2023.
Flatten:
This work was partly supported by Shenzhen Key Labora- tory of next generation interactive media innovative tech- and National Key Laboratory of Human-Machin Hybrid Augmented Intelli- gence, Xi' an Jiaotong University (No. HMHA1202410),
Couairon, G., Verbeck, J., Schwenk, H., and Cord, M. Diffedit: Diffusion-basee semantic image editing with mask guidance. arXiv preprint arXiv:2210. 1427, 2022.
nology
Couairon, G., Verbeek, J., Schwenk, H., and Cord, M. Diffedit: Diffusion-based semantic image editing with mask guidance. In ICLR 2023 (Eleventh International Conference on Learning Representations), 2023.
Impact Statement
This paper presents work whose goal advance the field of Machine Learning. There are many potential societal consequences of our work, none which feel must be specifically highlighted here.
Dhariwal, P. and Nichol, A. Diffusion models beat gans on image synthesis. Advances in neural information processing systems, 34:8780-8794, 2021.
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Taming Rectified Flow for Inversion and Editing
Appendix
ing, we use over 300 images for quantitative comparison, which both include real images (obtained from public social media and the DIV2K dataset) and generated images. For each image, we use GPT-4o to generate the source prompt and manually refine the generated prompt. There are 2 3 target prompts for different requirements of editing in- cluding adding. replacing, and stylization for each source image. We compare our methods with RF-inversion and several diffusion-basee editing methods. For RF-inversion, we adopt the implementation in ComfyUI (com). For other baselines, we use their implementation from diffuser and adjust the relevant hyper-parametee to achieve optimal re- sults. For video editing, the data preparation mainly follows previous works COVE (Wang et al., 2024c). We use the official codes of all the baseline methods and tune the hyper- parameters to achieve satisfactory results.
A. Pesudo Code of RF-Solver Algorithm.
Algorithm 1 Sampling process of RF-Solver
Input:
Up
> Velocity function Time steps
t [tN ta]
Z 10.
Initial Gaussian Noise
For: i N to 1 do
b1 val (z,,(i))
Ze, c Ze, + Ar.d:
01 + vol + + At.)
vi, + (i1;+
(1)
At Calculating the Derivatives
Z 4- Zı; + (11-1 - u) + (1411 - -,,)" (1)
Output: Zo
B. Experimental Settings
B.2. Evaluation Metries
B.1. Baselines and Implementation Details
For text-to-image sampling, we report Fréchet Inception Distance (FID) and CLIP Scores. The FID is a metric used to evaluate the quality of generated images by assessing the similarity between the distributions of real and generated image features, typically extracted using a pre-trained In- ception network. The CLIP Score evaluates the alignment between generated images and textual descriptions by mea- suring the similarity of their embeddings within a shared multimodal space using the CLIP model.
Text-fo-lmage Generation. We compare our methods with the following baselines: FLUX with the vanilla sampler, Heun Solver, and DoMve.. The Heun Solver is a second- order ODE solver that can be applied to pretrained rectified flow to solve the ODE more precisely. DPM-Solver a high-order sampler for diffusion ODE, which not suitable for RF-based models like FLUX. As alternative, we apply the DPM-Solver on Stable Diffusion to evaluate its performance. For FLUX with the vanilla sampler and the Heun Solver, we randomly select 10000 images from the MS-COCO validation dataset and use their caption as the prompt for generation. The resolution of generated images is x024x 1024. For DPM-Solver, we adopt the implementation from the diffuser, adopting its default setting to generate images. The total NFE for generating one image is set to 10 for both our method and baselines.
For Inversion tasks, our evaluation metrics include MSE, LPIPS, SSIM, and PSNR. MSE measures the average squared difference between predicted and ground-truth val- ues, quantifying the overall error in pixel intensity. LPIPS assesses perceptual similarity between images by comparing deep feature representations extracted from neural networks, aligning with human perception. SSIM evaluates image quality by comparing luminance, contrast, and structure to measure the similarity between the reference and recon- structed images. PSNR quantifies the ratio between the maximum possible signal value and the power of noise, commonly used to assess image reconstruction quality.
We compare the performance of our methods among RF with the vanilla sampler and the Heun sampler. For image inversion, similar to Text-to- Image generation, use images and captions from the MS-COCO valida- tion set. For video inversion, we select about 40 videos from social media platforms such as TikTok and other pub- licly available sources. We have observed the quality of the text prompts significantly influences the quality of inver- sion. Consequently, we employ GPT-4o to generate detailed captions for both images and videos, which are then used in the inversion tasks. The total NFE for generating one image/video is set to 50 for both our method and baselines.
Inversion.
For video editing, we adopt the VBench Metrics. The evalu- ation criteria include Subject Consistency, Motion Smooth- ness, Aesthetic Quality, and Imaging Quality. Subject Con- sistency measures whether the subject (e.g., a person) re- mains consistent throughout the video by computing the similarity of DINO features (Caron et al., 2021) across frames, which is similar to the CLIP Score for images. Mo- tion Smoothness assesses the smoothness of motion in the generated video using motion priors from the video frame interpolation model (Li et al., 2023). Aesthetic Quality evaluates the artistic and visual appeal of each frame as perceived by humans, leveraging the LAION aesthetic pre- dictor (LAION-AI, 2022). Imaging Quality examines the
Editing. For image editing, we share the features of the last 19 single blocks in FLUX. For video editing, we share the features of the last 14 blocks in Open-Sora. We adjust the hyper- prper-parameter of shauuig steps to achieve better results for both image and video editing. For image edit-
13

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Taming Rectified Flow for Inversion and Editing
Refferncce Style
"Statue of Liberty"
"A cat"
"A couple"
"A dwarf"
"A dwarp"
"Trump"
f Stylized Generation
"A piggy in flying pose"
"Eiffel Tower"
"A couple and baby"
piano"
"A piano"
"Biden"
"Iron Man in flying pose"
"A couple and a cat"
"A cat"
"A boat"
"A boat"
"Elon Musk"
Figure Stylized Generation.
level of distortion in the generated frames (e.g., blurring or flickering) based on the MUSIQ image quality predictor (Ke et al., 2021).
stream blocks. We implement the RF-Solver and RF-Edit on Hunyuan Video, where the RF-Edit shares the feature in the single-stream block. The results are shown in Figure 9.
C. Qualitative Results for Text-to-image Sampling
F. More Potential Applications
RF-Solver is universal sampler for rectified flow. Besides image and video editing, it is also potential on image video generation (Xiao et al., 2025; Ma et al., 2024b;a; Lin et al., 2025) and other diffusion- based tasks (He et al., 2024; Fang et al., 2024; Guo et al., 2022). Furthermore, our proposed feature-sharing method in RF-Edit can also be applied other image and video editing methods (Zhu et al., 2024b;a).
Qualitative results for Text-to-image Sampling are shown in Figure 10. Experimental results demonstrate that com- pared vanilla Rectified Flow, the RF-Solver sampler can generate higher-quality images that better align with human perception.
D. More Qualitative Results for Image Editing
Here we provide more qualitative results for image editing and stylization (Figure 8).
E. More Qualitative Results for Video Editing
Hunyuan Video (Kong et al., 2024) has recently demon- strated strong performance in text-to-video generation. The backbone of Hunyuan is similar to FLUX, which also contains several double-strean blocks, followed by single-
14

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Taming Rectified Flow for Inversion and Editing
Source
Video
"jeep"->"" pink Porsche"
"parrot" ->" dragon"
Edited
Video
Source
Video
"Santa hat"
"rabbit" Tom cat"
Edited
Video
Source
Video
" "rabbit" cat"
"heart " ">.>>"elloww car"
Edited Video
Figure 9. More video editing results.
bathroow with collet and scale floor
A banana that resting something
Two wild zebra eating safari
A bedroomm with bunk beds and the bathwanks
RF-S Sot-Solver
Vanilla RF
Figure 10. Qualitative results of text-to-image generation. By employing the RF-Solver, the model is able to generate images with higher quality than baselines.
15


Reviews:
[{"review_id": "PavA5mRVvq", "reviewer": "Reviewer_n1SC", "summary": "This paper introduces RF-Solver, a training-free, high-order solver to improve inversion and reconstruction in rectified flow models, and RF-Edit, a feature-sharing mechanism for image and video editing. The method states improvements in inversion accuracy and editing quality compared to vanilla rectified flow and several baselines.", "questions": "", "limitations": "", "rating": 2, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Dear Reviewer n1SC,\n\nThanks for your time and thoughtful review! We appreciate your recognition of the effectiveness of our methods. Here is our feedback:\n\n## More Explanations about Our Methods\n### RF-Solver\nIf we substitute the formulation of derivative into Equation 9, then the formulation becomes \n\n$Z_{t_{i+1}} = Z_{t_{i}} \n    + ({t_{i+1}} - {t_{i}}) v_\\theta (Z_{t_{i}}, t_{i}) \n    + \\frac{1}{2} (t_{i+1} - t_{i})^2 \\cdot \\frac{v_\\theta (Z_{t_{i} + \\Delta t}, t_{i} + \\Delta t) - v_\\theta (Z_{t_{i}}, t_{i})}{\\Delta t}.$\n\nIn the above formula, $\\Delta t$ is required to be set to a **sufficiently small value** to estimate the derivative with less error (as specified in Line 187~188 in paper), which **is not equivalent to** $t_{i+1} - t_{i}$. As a result, RF-Solver exhibits a clear difference from the Heun method. RF-Solver also outperforms Heun method (Table 1).\n\nWhat's more, RF-Solver is not limited to 2nd order expansion. We derive the **general form** (Equation 7) by firstly deriving the exact formulation of the solution for RF ODE and then applying the high-order Taylor expansion. **This has not been explored by previous works.** If we apply 3rd order expansion, the performance can be further improved ([Table5](https://postimg.cc/4mxRLZNc)).\n### RF-Edit\nThe methods you mentioned are based on U-Net. Among them, Dragdiffusion and Style Inject target point-based editing and style transferring, which is not the core focus of our work. Due to the time limit, we would like to further explore the potential of RF-Edit on these tasks in future work.\n\nOur work focuses on **prompt-based editing using DiT** (such as FLUX and OpenSora). Given DiT's distinct architecture from U-Net and larger parameter count, designing an effective and efficient feature sharing method is non-trivial and underexplored. Addressing this, we thoroughly explore the different choices of feature sharing in DiT (more results are shown in the \"More Experiments\" Section), proposing RF-Edit. RF-Edit is a unified feature-sharing-based framework which can be applied to various DiT architectures. Achieving satisfying results, we believe RF-Edit is insightful for further work.\n\n## More Experiments\nThanks for your valuable and insightful advice! More experiments are provided as follows: \n- Step-vs-quality analysis: Shown in [Table5](https://postimg.cc/4mxRLZNc). \n- Alternative metrics for image editing: Shown in [Table6](https://postimg.cc/XB6kzVb0). At the same time, we would like to kindly point out that LPIPS is also a widely-used metric for measuring the image consistency in previous works of image editing such as PnP (CVPR 2023), Null-Text-Inversion (CVPR 2023). \n- Choices for feature sharing: Further analysis is shown in [Figure11](https://postimg.cc/p5QJNgW5), [Figure12](https://postimg.cc/9rVBPFbd), [Figure13](https://postimg.cc/CdbNffGM), [Figure14](https://postimg.cc/F7ZVT5C2). We finally choose to share the V feature in last 20 single-stream blocks of FLUX in the timesteps near to noise, which is proved to be the most effective choice.\n- Comparisons on more baselines: Results about MasaCtrl are shown in [Table6](https://postimg.cc/XB6kzVb0) and [Figure15](https://postimg.cc/5X2qG7Zj). Results about SANA are shown in [Table8](https://postimg.cc/8F3HLRXc). \n## Detailed Experiment Setup\nFor image editing task, our evaluation dataset consists of about 300 images, following previous works such as PnP (CVPR 2023), InstructPix2Pix (CVPR 2023), Null-Text-Inversion (CVPR 2023) and SmartEdit (CVPR 2024). For the image generation task, we conducted experiments on MS-COCO validation dataset, following previous works such as Stable Diffusion (CVPR 2022). For video inversion and editing tasks, we mainly follow the dataset construction process in COVE (NeurIPS 2024). \n\nFor image generation task, the NFE is set to 10 for both RF-Solver and Vanilla RF. The timestep for DPM-Solver++ is set to 20 according to their official github repo. For editing tasks, the hyperparameters for all the baseline methods follow their official github repo for best results. We will add more detailed information in the main paper.\n \n## Other Questions\n> Doubling baseline solver ... pareto-optimality in lower number of steps.\n\nAs illustrated in [Table5](https://postimg.cc/4mxRLZNc), with the increase of timesteps, the performance of both baseline and our methods becomes better. In low timesteps scenarios such as 3 steps for RF-Solver-2 (6 NFE) and 7 steps for Vanilla RF (7 NFE), our methods also illustrate better performance. \n> Discuss potential failure ... computational cost.\n\nThe inversion prompt is **optional** and does not significantly impact editing results (you can also see from some examples provided in the supplementary materials) and our method can edit a high-resolution image (1360\\*768) with less than 1 minute on a single A100 GPU. The failure case is shown in [Figure16](https://postimg.cc/5XKqM5Vg). We will add these discussions to the main paper！", "claims_and_evidence": "The paper claims that RF-Solver improves inversion accuracy by reducing the error in solving the rectified flow ODE through a high-order Taylor expansion, and that RF-Edit enhances image and video editing by transferring self-attention value features from the inversion process to the denoising process. The authors support these claims with quantitative results (e.g., lower MSE, LPIPS, and higher CLIP scores in the inversion and editing tasks) and qualitative comparisons against several baselines.\n\nHowever, some details affecting the strength of these claims remain unclear. For instance, the evaluation lacks complete descriptions of dataset selection, the exact number of solver steps used by baseline methods, and a detailed step-vs-quality analysis. In addition, the editing evaluation relies primarily on LPIPS, which may not fully capture semantic consistency; alternative metrics such as CLIP-I or DINO could offer more insight. Finally, the derivation presented in Eq (9) appears equivalent to Heun's method, and it is not fully clear how the proposed method differs from standard second-order approaches.", "methods_and_evaluation_criteria": "The evaluation method and clarity could be improved. The paper does not explain how the evaluation data were chosen or how large each set was. The authors also do not describe in detail how many solver steps are used by the baseline models. They claim a faster solver but do not show a thorough step-vs-quality analysis. Feature-sharing for editing is described, but it is similar to ideas in works like DragDiffusion or MasaCtrl. The paper does not include direct comparisons or discussions that clarify how this method stands out.\n\nTable 3 depends strongly on LPIPS, known to be uninformative in some editing tasks. Authors do not attempt alternative metrics (CLIP-I, DINO, or MDINO) that better capture semantic consistency.\n\nDoubling baseline solver steps to match function evaluations is not necessarily fair since most baseline methods achieve pareto-optimality  in lower number of steps.", "theoretical_claims": "The derivations (e.g., on Taylor expansion) are technically solid. Same for the attention sharing.\n\nBut if I understand it correctly your step update in Eq(9) is equivalent to Heun's method:\n$\nZ_{t+\\Delta t} = Z_t + \\Delta t u_t + \\frac{1}{2} (\\Delta t)^2 \\frac{u_{t+\\Delta t}- u_t}{\\Delta t}\n= Z_t +  \\Delta t u_t + \\frac{1}{2} \\Delta t (u_{t+\\Delta t}- u_t)\n= Z_t +  \\frac{\\Delta t }{2} \\Delta t (u_{t+\\Delta t}+ u_t)\n$\nCould you please explain how your method differs from other 2nd order methods?", "experimental_designs_or_analyses": "The authors valuate image editing with LPIPS, but that metric often fails to measure fine-grained editing fidelity. They do not include widely used metrics like CLIP-I or DINO, which may capture semantic changes more precisely. \n\nThe effect of solver order 2 vs 3 is briefly mentioned, yet the explanation for 3rd order being worse remains superficial (“less timesteps overall”). More thorough ablations or error analyses would help.", "relation_to_broader_scientific_literature": "They cite SANA 2025 for diffusion-based high-resolution image synthesis, and mention DragDiffusion, MasaCtrl, and Style Injection for attention-based editing. But the paper itself does not seriously compare with those or situate how its approach truly diverges from known feature-sharing or other inversion techniques.", "essential_references_not_discussed": "Some very related papers are cited but not discussed:\n\n[1] Xie et al, SANA: EFFICIENT HIGH-RESOLUTION IMAGE SYNTHESIS WITH LINEAR DIFFUSION TRANSFORMERS (2025)\n[2] DragDiffusion: Harnessing Diffusion Models for Interactive Point-based Image Editing\n[3] Can et al., MasaCtrl: Tuning-Free Mutual Self-Attention Control for Consistent Image Synthesis and Editing\n[4] Chung et al, Style Injection in Diffusion: A Training-free Approach for Adapting Large-scale Diffusion Models for Style Transfer", "other_strengths_and_weaknesses": "N/A", "other_comments_or_suggestions": "- Please confirm if eq(9) is indeed identical to Heun. If there is novelty, show a direct comparative formula.\n- Provide more data on number of steps vs. final image quality.\n- Include key experimental details (datasets, NFE, hyperparameters) in the main text to improve reproducibility.\n- Consider more robust metrics (e.g., CLIP-I, DINO) for evaluating editing quality to complement LPIPS.\n- Clarify and justify choices in feature-sharing (number of layers and timesteps) with further ablations or discussion.\n- Discuss potential failure cases or limitations, especially regarding inversion prompt dependency and computational cost.\n- Show comprehensive experiments against stonger baslines (i.e. SANA) to highlight improvement.", "questions_for_authors": "**I am adding here extra questions for the authors because there is an issue with the visibility of my comments.**\n\n\n## New questions April 8th\n\nI thank the authors for their response. The extra experiments are welcome.\n\nIn light of your response, the method you propose is part of the well known family of Taylor series integrators. To my understanding this type of integrator **have** been extensively studied for diffusion models in the probability flow ODE setting [1-3] . Could provide further clarifications about the novelty of your method and how it differs from previous work?\n\nIn Table 5 does the number of steps indicate the same number of NFE?\n\n[1] [DEIS](https://arxiv.org/abs/2204.13902)\n\n[2] [DPM-Solver](https://arxiv.org/abs/2211.01095)\n\n[3] [DPM-Solver++](https://arxiv.org/pdf/2206.00927)", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "tz6xjjFJu7", "reviewer": "Reviewer_eQrG", "summary": "This paper aims to leverage Rectified-flow-based generative models for unified image and vide editing. Specifically, this paper proposes RF-Solver, which uses high-order Taylor expansion to eliminate the errors in the inversion and reconstruction process. The paper further proposes RF-Edit, which use value feature-sharing for editing. Extensive experiments illustrate the effectiveness of the proposed methods.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Dear Reviewer eQrG,\n\nThanks for your comprehensive review and insightful comments on our paper. We appreciate that you recognize the motivation and performance of our methods. The response to your concerns is shown below.\n\n> Implementation Details about HunyuanVideo\n\nThanks for your advice! For video editing on HunyuanVideo, total timesteps are set to 25, and the feature-sharing step is between 1 to 5 for different cases. We will add these implementation details in the main paper. What's more, we have provided the code in the supplementary materials and planned to release it in the future.\n\n> The authors should provide qualitative and quantitative results to demonstrate the benefits of RF-Solver without feature-sharing.\n\nThanks for your advice, we have provided the qualitative results of feature-sharing in RF-Edit in [Table7](https://postimg.cc/dky96hgB). The quantitative results are provided in Figure 7 in the paper. \n\nWhat's more, we also provide a more detailed analysis about the feature sharing strategy in [Figure11](https://postimg.cc/p5QJNgW5), [Figure12](https://postimg.cc/9rVBPFbd), [Figure13](https://postimg.cc/CdbNffGM), [Figure14](https://postimg.cc/F7ZVT5C2). We finally choose to share the V feature in the last 20 single-stream blocks of FLUX in the timesteps near to noise, which is proved to be the most effective choice.\n\n> Qualitative comparisons between RF-Edit and previous methods such as MasaCtrl and PnP.\n\nThanks for your advice! The results are provided in [Table6](https://postimg.cc/XB6kzVb0) and [Figure15](https://postimg.cc/5X2qG7Zj). The qualitative comparisons between our method and PnP are shown in Figure 5. Our method outperforms the baselines both qualitatively and quantitatively.\n\n> Additional ablation studies using the same number of timesteps\n\nThanks for your advice. We have provided more detailed experiments on both image generation tasks and reconstruction tasks in [Table5](https://postimg.cc/4mxRLZNc). \n\nThe results illustrate that with the increase of Taylor Expansion order, our method illustrates a better performance at various timesteps. Although the comparison is conducted with the same number of timesteps (rather than the same NFE), we notice that under similar NFE, a higher order expansion sometimes also illustrates a better performance. For example, considering the 20 timesteps for Vanilla RF, 10 timesteps for RF-Solver-2, and 7 timesteps for RF-Solver-3, the NFE for them is similar (20, 20, 21, respectively), while RF-Solver-3 illustrates the best performance among them.", "claims_and_evidence": "1.\tThe paper primarily contributes in two aspects: the RF-Solver sampler and the RF-Edit framework. The RF-Solver sampler is novel and effective. The RF-Edit framework is somewhat similar to existing U-Net-based methods, while this paper explores its application on the mainstream Diffusion Transformer architecture.\n\n2.\tThe research area of this paper is very active and interesting. Given the performance of rectified-flow-based models in image and video generation, exploring their performance on various downstream tasks is meaningful and promising.\n\n3.\tThe paper is well-written and easy to follow. The authors provide a theoretical derivation of the high-order expansion for RF-Solver.", "methods_and_evaluation_criteria": "1. The paper proposes using a high-order Taylor expansion to reduce errors during the inversion and reconstruction processes. Then, it proposes the RF-Edit framework, which uses a feature-sharing mechanism to further preserve unintended modifications, i.e., the background.\n\n2. Extensive experiments from both qualitative and quantitative perspectives illustrate the effectiveness of the methods. The authors explore performance across various backbones, including FLUX and OpenSora, demonstrating the universality of the proposed methods.", "theoretical_claims": "The theoretical derivation provided in this paper is comprehensive, offering theoretical justification for both sampling and inversion processes.", "experimental_designs_or_analyses": "Overall, the experiment is extensive and thorough.", "relation_to_broader_scientific_literature": "The paper aims to achieve satisfying editing outcomes using the recent rectified-flow based DiT. There are extensive works about image and video editing based on diffusion and UNet architecture such as PnP [1] and Masactrl [2]. More recently, there are also some works using FLUX to achieve image editing [3].\n\n[1]. Plug-and-Play Diffusion Features for Text-Driven Image-to-Image Translation\n\n[2]. MasaCtrl: Tuning-free Mutual Self-Attention Control for Consistent Image Synthesis and Editing\n\n[3]. Semantic Image Inversion and Editing using Rectified Stochastic Differential Equations", "essential_references_not_discussed": "No", "other_strengths_and_weaknesses": "The paper exhibits several strengths, introducing novel aspects and presented in a clear and well-structured manner. My main concerns are listed below:\n\n1. Some implementation details are unclear, particularly regarding experiments conducted on HunyuanVideo. The authors are expected to provide a more thorough specification of the implementation.\n\n2. The authors should provide qualitative and quantitative results to demonstrate the benefits of RF-Solver without feature-sharing. Additionally, to further validate the superiority of RF-Edit, the authors could include qualitative comparisons between RF-Edit and previous methods such as MasaCtrl and PnP, implemented on the U-Net architecture.\n\n3.  The ablation study in Table 5 maintains the same total number of function evaluations (NFE) across different orders, leading to suboptimal performance for higher-order expansions (e.g., the row labeled 'RF-Solver-3'). The authors should conduct additional ablation studies using the same number of timesteps (instead of total NFE) to better illustrate whether higher-order expansions can further enhance performance.", "other_comments_or_suggestions": "No", "questions_for_authors": "See \"Other Strengths and Weaknesses\"", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "cO9DrcrHDN", "reviewer": "Reviewer_1xw9", "summary": "This paper proposes a flow inversion method based on the improved higher order ODE, which simply extracts the first order derivative from the volatility prediction for more accurate model denoising generation. this method can be applied to accurate image or video inversion based on the pre-trained image or video flow diffusion models. To keep more consistency, the author also proposes the reuse the \"Value\" from the attention for image or video editing, which results in better consistency on text-guided editing.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Dear Reviewer 1xw9,\n\nWe sincerely thank for your recognition of the methods and experiments in our work!\n\n> I saw there is a hunyuan video editing code; is there any results on this?\n\nWe provided some video editing results produced by HunyuanVideo in Figure 9 in the Appendix. We also provide the code for video editing in the supplementary. \n\nThe quantitative results are shown in the table below, where the experimental settings follow Table 4 in the main paper. We will also add this to the main paper.\n\n**Table 9. Quantitative results about HunyuanVideo**\n| |SC|MS|AQ|IQ|\n|-|-|-|-|-|\n|RF-Edit (HunyuanVideo)   | **0.9573** | **0.9749** | **0.6880**| **0.7298** | \n|RF-Edit (OpenSora)   | 0.9501 | 0.9712| 0.6796 | 0.7207 |", "claims_and_evidence": "yes", "methods_and_evaluation_criteria": "yes, it makes sense to me", "theoretical_claims": "yes", "experimental_designs_or_analyses": "The experimental comparison is fair and sufficient.", "relation_to_broader_scientific_literature": "DDIM inversion would be the most related literature.", "essential_references_not_discussed": "Most of the references are discussed.", "other_strengths_and_weaknesses": "Strengths: This paper proposes an effective flow diffusion inversion method, and it is training-free, which achieves pretty accurate image and video inversion. Based on the proposed method, we can have more consistent content editing.\n\nWeakness: No significant weakness found.", "other_comments_or_suggestions": "Nice work, I saw there is a hunyuan video editing code; is there any results on this?", "questions_for_authors": "Please refer to above.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "AhbY4qsrjJ", "reviewer": "Reviewer_5wXG", "summary": "The paper points out the problem of in accurate reconstruction for regular inversion method on flow models, and proposed to methods for inversion and editing. For Inversion, the authors introduced a new ODE by employing higher order with Taylor expansion, and found the second-order expansion is already helpful for better inversion. Though intriducing more computation when approximating the second order term, the authors cut half of the NFE for a fair comparision. The second contributions is to manipulate the self attention layers during the reverse process. The authors applied editing for both image and videos to demonstrtate its effeciveness.\n\n## update after rebuttal\nI increased score to accept since the authors addressed my concern on the ablation studies.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Dear Reviewer 5wXG,\n\nThank you for your comprehensive and detailed review of our paper and the recognition of our work's effectiveness. We provide our feedback as follows. \n\n> Experiment to demonstrate the effectiveness when increasing the order using Taylor expansion, which is the key idea of the paper.\n\nThanks for your advice! We have provided experiments on both image generation and reconstruction in [Table5](https://postimg.cc/4mxRLZNc). \n\nThe results illustrate that under various timesteps, our methods outperform the baseline significantly. With the higher order expansion (RF-Solver-3), the performance becomes even better. Although the comparison is conducted with the same number of timesteps (rather than the same NFE), we notice that under similar NFE, a higher order expansion sometimes also illustrates a better performance. For example, considering the 20 timesteps for Vanilla RF, 10 timesteps for RF-Solver-2, and 7 timesteps for RF-Solver-3, the NFE for them is similar (20, 20, 21, respectively), while RF-Solver-3 illustrates the best performance among them. \n\n> Hyperparameter robustness for feature sharing\n\nWe have provided a more detailed analysis about the choice of feature sharing in [Figure11](https://postimg.cc/p5QJNgW5), [Figure12](https://postimg.cc/9rVBPFbd), [Figure13](https://postimg.cc/CdbNffGM), [Figure14](https://postimg.cc/F7ZVT5C2). In our work, solely tuning the hyperparameter of the feature-sharing step is enough to obtain a satisfying result. What's more, editing a high-resolution image (1360 \\* 768) using our methods only takes a short time (less than 1 minute). As a result, we believe that the parameter-tuning is acceptable for most users.\n\n> What happens if you only have RF-solver but not RF-edit for editing\n\nAs mentioned in Line 242~258 in the main paper, only using RF-Solver for editing sometimes cannot maintain the consistency between the source image and the target image. Figure 7 illustrates some results produced solely by RF-Solver. We also provide a quantitative ablation study about this in [Table7](https://postimg.cc/dky96hgB).\n\n\n> What's the memory for storing Vs? Why not storing/sharing Ks or attention maps?\n\nFor editing a 1360\\*768 image, the total memory needed to store the feature is about 18G. We store the feature in the CPU, rather than GPU Memory. In practice, this would not significantly reduce the efficiency of inversion and editing. \n\nWe also add the qualitative results about sharing K or attention maps in [Figure13](https://postimg.cc/CdbNffGM). Experimental results demonstrate that, compared to K or the attention map, V contains the richest information regarding the original image. Sharing V can effectively preserve the source image's details in a relatively small number of feature-sharing steps, whereas sharing K and the attention map under the same number of steps yields less satisfactory outcomes. Therefore, we choose to share V for its effectiveness and efficiency.", "claims_and_evidence": "Mostly yes, please see experiment section below for more questions.", "methods_and_evaluation_criteria": "yes", "theoretical_claims": "The equations in the paper look correct to me.", "experimental_designs_or_analyses": "1. One important contribution of the paper is to use higher order RF ODE for better inversion/reconstruction. I would like to see how much of improvement it brings up. Though Table 5 compares under the same NFE, it does not show the advantage of the proposed higher-order ODE as it increases. I understand that RF-Solver-2 might be a good sweet spot for tradeoff performance and latency, but there’s no experiment to demonstrate the effectiveness when increasing the order using Tyler explosion, which is the key idea of the paper. Specifically, I’m mainly looking for the proof of the intuition behind the methods, e.g., you find higher order ODE brings better preformance but more computations expensive, and then you figure out using less NFE to resolve it and fair comparison, or, on the other hand, increase the steps used in regular inversion/editing with same NFE for fair comparison.\n\n2. An important problem in many inversion-based editing methods are the tuning of hyperparameters. It's mentioned in the last section that  sharing step 5 is a good choice, do you have more studies on it? e.g., when to apply to early stage of later, what's the hyperparameter robustness for different editing (e.g. stylization, adding object, changing object)?\n\n3. what happen if you only have RF-solver but not RF-edit for editing? this mean you only have RF-solver to better preserve the original construction of the image and use prompt for editing without changing the attention modules. This would better demonstrate the advantage of RF-edit.\n\n4. What's the memory for storing Vs? Why not storing/sharing Ks or attention maps?", "relation_to_broader_scientific_literature": "The method proposed in this paper differs from other works by emplying taylor expansion to construct a higher order ODE for flow model inversion. The editing part is good but less significant because attention-based editing has been explored a lot in previous works.", "essential_references_not_discussed": "no", "other_strengths_and_weaknesses": "refer to the other secions", "other_comments_or_suggestions": "refer to the other secions", "questions_for_authors": "refer to the other secions", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: This paper proposed rectified flow to editing and inversion.

The most of reviewers admits the novelty of this work (eQrG, 1xw9, 5wXG). One contribution is using higher order Taylor expansion to solve ODE resulting in robust preserving unintended mofications (eQrG & 5wXG). Significant experiments support the proposed method (eQrG). On the other hand, reviewers n1SC, 5wXG & eQrG  asked unclear points : dataset selection, solver steps, distinction from baselines, and ablation studies. After rebuttal phase, most of queries from reviewers (5wXG & eQrG) were adequately answered and satisfied by reviewers. Raised concerns from n1SC were not answered properly because of issue with the visibility to authors. However, except the additional queries from n1SC, rebuttals by authors answered previous questions to be made by n1SC and it addressed properly. I believe in resolving the rest of the extra questions in camera-ready process by the authors.

I agreed that this paper will have the positive impact and presents a timely topic to ICML conference. Therefore, I would like to recommend this paper for publication.
Decision: Accept (poster)