FlowAlign: Trajectory-Regularized, Inversion-Free Flow-based Image Editing
Authors: Jeongsol Kim
Yeobin Hong
Jonghyun Park
Jong Chul Ye
Venue: ICLR 2026 Poster (2026)
Keywords: flow models
image editing
inversion-free
Primary area: generative models

Abstract: Recent inversion-free, flow-based image editing methods such as FlowEdit leverages a pre-trained noise-to-image flow model such as Stable Diffusion 3, enabling text-driven manipulation by solving an ordinary differential equation (ODE). While the lack of exact latent inversion is a core advantage of these methods, it often results in unstable editing trajectories and poor source consistency. To address this limitation, we propose {\em FlowAlign}, a novel inversion-free flow-based framework for consistent image editing with principled trajectory control. FlowAlign introduces a flow-matching loss as a regularization mechanism to promote smoother and more stable trajectories during the editing process. Notably, the flow-matching loss is shown to explicitly balance semantic alignment with the edit prompt and structural consistency with the source image along the trajectory. Furthermore, FlowAlign naturally supports reverse editing by simply reversing the ODE trajectory, highliting the reversible and consistent nature of the transformation. Extensive experiments demonstrate that FlowAlign outperforms existing methods in both source preservation and editing controllability.

FLOWALIGN: TRANECTORYREGGULARZED, INVERSION-FREE FLOW-BASED IMAGE EDITING
Jeongsol Kim*, Yeobin Hong*, Jonghyun Park, Jong Chul Ye KAIST
[jenngsel, yeobin34, jhpark99, jong - yel @kaikt..aa
Equal contribution
Source
Edited Image
Source
Edited
Source
Edited Image
..monley..
m_mon..
...0lods..
".eggg..."
b.bird."
buutterfln
"..beor, shees, apple.." '_./abbit, goot, carrot.."
m._mttol ley.."
"_wooden ley.."
...onuss...
T..cookees...
"..plone.."
"e.hlloppper...
"..brown...
"..blu..."
m_mouse..
"_cot...
Figure 1: Representative editing results produced by FlowAligg, where the red portion of the prompt replaced with the green portion. Samples are drawn from EditBench and PIEBench.
ABSTRACT
Recent inversion-free, flow-based image editing methods such as FlowEdit lever- ages pre-trained noise-to-image flow model such Stable Diffusion 3, enabling text-driven manipulation by solving an ordinary differential equation (ODE). While the lack of exact latent inversion core advantage of these methods, it often results in unstable editing trajectories and poor source consistency. To address this limitation, we propose FlowAlign, novel inversion-fres flow-based frame- work for consistent image editing with optimal control-based trajectory control. Specifically, Flow Align introduces source similarity at the terminal point as a regularization term to promote smoother and more consistent trajectories during the editing process. Notably, our terminal point regularization is shown to explicitly balance semantic alignment with the edit prompt and struetural consistency with the source image along the trajectory. Furthermore, FlowAlign naturally supports reverse editing by simply reversing the ODE trajectory. highliting the reversible and consistent nature of the transformation. Extensive experiments demonstrate that FlowAlign Align outperforms existing methods both source preservation and editing controllability.

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INTRODUCTION
In text-based image editing (Meng et al. [021] Mokady et al. 2023 Tumanyan et al. 2023 Hertz et al. 2023 Kim et al. 2024 Kulikov al. 2024. Brooks et al., 2023). the goal is transform a source image into a target based on either textual descriptions of the images or specific editing instructions. From distributional perspective, the image editing task can be interpreted as continu- ous normalizing flow (CNF) (Papamakarios et al. (022)) that pushes forward source distribution to a target distribution. Specifically, we parameterize a velocity field, that uniquely determines the flow, using a neural network. Then, the generative process corresponds to solving an ordinary differential equation (ODE) governed by the trained velocity field. To reduce the computational cost of simulating ODEs during training for likelihood evaluation, flow matching has been proposed (Lipman et al. 2023). Its conditional variant enables direct supervision by computing the target velocity, allowing efficient training of flow models between arbitrary distributions. These flow models includes score-based diffusion models (Song et al. 202 1b Ho et al., 2020 Song et al.) 2021a) as
well as rectified flow models (Liu et al. 2023b Esser et al. 2024).
Recently, within the framework of flow-based models, text-to-image generation has achieved signif- icant advancements through improved time discretization, loss weighting, and model architecture, notably based on DiT (Peebles & Xie 2023). While these foundational models are trained to map samples from normal distribution to clean data distribution, additional training- eether from scratch or via tin-ttnnng--aa is necessary to establish a flow between two arbitrary distributions.
To mitigate this additional cost for constructing approaches such as SDEdit (Meng et al. 202I) and Dual Diffusion Implicit Bridge (DDIB) (Su et al., 2023) have leveraged pre-trained noise-to-image diffusion models. However, SDEdit requires careful selection of an appropriate initial noise level for editing, while DDIB relies on an inversion process that is prone errors arising from discretization and an approximated velocity field for subsequent timesteps.
flow between image distributions, several
Recently, RF-inversion (Rout al. 2025a) proposes an optimal-control based inversion for flow models, in which a guiding vector field steers the dynamics toward high-likelihood samples via velocity interpolation. Unfortunately, it still involves computational overhead due to the ODE inversion. To address this, FlowEdit (Kulikov et al. 2024)) proposed simulating an ODE between two image samples without inversion. However, empirical results showed that the method is quite sensitive to the hyperparameters and often fails to retain the source consistency. Moreover, the method heuristically applies classifier-free- frre-guidance (CFG) to the both source and target velocity fields with different scaling factor and relies skipping early timesteps of the ODE to enhance editing quality. These design choices introduce multiple hyperparameters to be searched and compromise the deterministic nature of ODE (see Section 4)
Motivated by the observation that these limitations of FlowEdit arise from nonsmooth and unstable editing majectories-party due to the lack of explicit latent inversion-wer introduce FlowAlign, an optimal control-based inversion-free approach for consistent and controllable text-driven image editing through trajectory regularization. In contrast to RF-inversion that requires an ODE inversion, we introduce a structural similarity at the terminal point as our trajectory regularization term to overcome the instability caused by the absence of the inverted latent. Although the regularization is primarily enforced at the terminal point, we further observe that it also naturally enforces source consistency along the trajectory by penalizing unnecessary deviations from the original image.
In contrast to methods like FlowEdit, which require four times the NFE due to the reliance on classifier-free guidance on both source and target sides, our approach is more computationally efficient. FlowAlign introduces minimal overhead of only one additional function evaluation (NFE) per ODE step to apply its regularization term. Despite this efficiency, FlowAlign achieves superior source preservation and competitive or improved editing quality compared to FlowEdit and also other existing approaches in image, video, and 3D editing. Finally, FlowAlign supports editing through backward ODE with the learned flow field, enabling accurate reconstruction of the original image from the edited output. This highlights the reversible and deterministic nature of the learned transformation, made possible by our explicit trajectory regularization.
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2 BACKGROUNDS
Suppose we have access to samples from two distributions X1 p and Xo ~ q that forms inde- pendent coupling, no, (Xo, X1) = p(X))(((()))))) (XX)). We can define a time-dependent function called flow (x) [0. 1] Rd + Rd, which is diffeomorphism and satisfies (X1) a continuous transform between X1 and Xy- Specifically, for 0 S < t S 1, we can sequentially transfer the sample X, to X, (X,) = (,, (X,)) (X,,. Here, the th is uniquely
Xt, to describe
characterized by a flow ODE
deh (x) = (e(b
where U2 represents velocity field. Here, V, is approximated by neural network of with the parameter I to construct a flow generative model. The training objective for the parameterized velocity field is called flow matching, which is expressed as
LFM = -EE (xx) of (x)))l?
Unfortunately. we cannot access (a:)) due to intractable integration over all To- To address this, Lipman al. (2023) proposes conditional flow matching:
CCFM = Eeg[0.1].tu0qgll0 (zo) - oi (2)
where (ar is conditional velocity field given by
(x(2) ( (zx =o)) = (22 (zu).
where the last equality is due the definition of æ; (x) (zo)). One of the most important contribution Lipman et al. (2023) is that the trained velocity field uy (xx)) from the conditional flow matching Eq. (3) can also approximate the unconditional velocity field vy (2x) in Eq. ( Accordingly,
after training of the velocity field using Eq. (3), we can generate a sample by solving the following ODE:
dæ of (xt)dt.
(5)
Among various flows, the affine conditional flow defined as (1) (azo) a,a0 b,30 is widely used, where ag = b1 = 1 and a1 = bo = O. The resulting conditional velocity field derived from the rectified flow for Eq. then given by
(v (m)) = via ( (x0) 0g + b,
(6)
In case of linear conditional flow (or rectified flow) (Liu et al.. 2023b). a = t and by = 1 - t,, the conditional velocity field derived from the rectified flow for Eq. 3 is (,(x,
x1 Zg-
Without loss of generality, the problem formulation could be extended to a flow defined in latent space. Accordingly, we will use a, to denote both images and latent codes.
FLOWALIGN
3.1 TEXT-BASED IMAGE EDITING USING PRE-TRAINES FLOW MODELS
In text-based image editing using flow models, we aim to translate a source image Ter at (- = 1 to a target image Figt at f based on text description of each image or editing instruction. In particular, such translation can be represented through linear conditional flow between two image distributions,
(x (Rtgt) == (1 l)atgt + I.c.re-
Note that the associated flow ODE described by Eq. (5) requires training between two image
distributions using the conditional flow matching of Eq. (3) with Eq. 77. To bypass the additional training, consider two generative flows that transfers the same noise ~ N/O, Ia) to each image,
(e = q: = (1 t)xere + te,
(8)
1/! ggt (c(xrget) pt (1 t)x te,
(9)
3

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(e)
Inverted Noise 4: Pi
[b)
Rendom Noise (0..)))
[c]
Random Noise ((.
d. Vil Gare)
fh OPee Gras)
Rc
X Pt 4r
Pe
+yR(quP)
Source Image
Target Image
Source Image K2
Edited Image
Source Image
Edited Image
Po
Figure 2: Overview. (a) Starting from the inverted latent, the ODE from source to target images can be obtained. (b) In contrast, existing inversion-fic -fre approaches suffer from nonsmooth trajectories, as qi is sampled with random noise at each step, often resulting in editing artifacts. (c) FlowAlign uses the regularized velocity of from the similarity regularization smoother and more consistent trajectories between the source and target images. Prompt: "... white and red sign that reads CAFE"
the terminal point (R), producing
white and red sign that reads ICLR".
and the associated ODEs:
dq: = (q:) dp: = vi (p:)dt
(10)
with Pi e, Tarcs and Dtgt- Since both flows are accessible without additional
training by using pre-trained coise-to-imaaee flow mode [1] it is beneficial if we can leverage Eq. (8)
and Eq. (9) to simulate the ODE for the flow in Eq.
Importantly, the system of equations (Eq. Fq. and Eq. (9) lead to the following key equality:
Et
+ Esrc:
where
21
-src: Ligt
(11)
Consequently, simulate the ODE for image editing by
dæ: = dp: - dq: [ (p:) u, (qt where
P: = 2t Esre
(12)
without additional training of flow models (see Figure 2 2a)). In case of text-conditional pre-trained flow models, can leverage the same neural network oy with text embeddings Care and Ctgt to approximate the o! (p:), (q))(q:) respectively, leading to
day, [v. (pe, Cegt) vg (qi, Care)]dl.
(13)
3.2 TRAJECTORY ERRORS FROM INVERSION- FREE APPROACHES
In Eq. 13
P: and q are first computed at each discrete time step f. If an inverted latent einv is obtained ODE inversion from the source image Ese along the trajectory qe (as illustrated in Figure 2 ()), then Pt and can be further updated as:
(14) with the initialization condition P1 = 91 = Gjav- However, ODE inversion increase the overall computational cost. Thus, interested in avoiding the ODE inversion process. Toward this aim, FlowEdit (Kulikov et al. 2024) proposed the following update for pt and q:
dq: v. (q:; Cara)dl, dp: of (pt, Ctgt)
4: with the initialization condition P1 = =Q = for randomly sampled e at each I, where the second equality stems from Eq. (TT). i.e. P: = +
1) wre + Le, dp: of (g: 3t &sres Ctgt dtt
(15)
Mrre-
Unfortunately, one of the critical limitations of FlowEdit using Eq. 15) is that qe trajectory is not sufficiently smooth due to the random sampling of (Figure 2())). This leads to the inaccuracy of using simulated ODE Eq. (13) for He. To mitigate this, we propose an explicit trajectory regularization method using the structural similarity at the terminal point.
In this paper, use Stable Diffusion 3.0 (medium), a foundational pre-trained flow model for the main experiments.
4

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3.3 TRAJECTORY REGULARIZATION USING SIMILARITY AT TERMINAL POINT
Given that the trajectory of 2e in Eq. [3 is not necessarily smooth due to the random sampling of e, our objective is to simulate an ODE that explicitly penalizes deviations from a smooth trajectory as form of regularization. Inspired by the recent advances of the optimal control approaches for flow models(Rout et al. 2025a b). we consider the following time-reversal optimal control problem
Bt = u(x+),, 21 Dare
(16)
v(u,)= = -f¹ E(xz, ue t)dt + mm(x)
(17)
In this paper, we use the following loss:
{ar, ue, 1) := 1 - (v. (pt, Ctge) v. (qt: Care)) 11?
(18)
thereby enforcing the similarity of the optimal control u, to the original velocity field in Eq. 13 Unfortunately, this is shown not sufficient for regularizing the trajectory deviation owing to the lack of inverted latent. Therefore, our goal is utilize the terminal loss m(x1) to enforce the trajectory smoothness.
One of the most important contributions of this work is showing that a similarity regularization the terminal point serves the goal. Specifically, we introduce a 12-based terminal point regularization:
m(xx) - ano Øsrel"
(19)
This implies that the ODE evolution from from = to t = 0 ultimately converges to a terminal solution that closely resembles the starting point, i.e. Vtgt aare. While this might raise concerns about convergence to a trivial solution where I; = Dare for all t, the crucial distinction lies in our use of finite 7) opposed to taking the limit 17 - oo as done in RF- (Rout al.) (025a). In what follows, we show that this terminal point regularization lead to the balance between the semantic guidance and structural preservation.
Proposition 1. For the linear conditional flow with a₂ = 1 and b, where 0 S t $ ODE that solves the optimal control problem with Eq. 477). Eq. (78) and Eq. (19 is given by
1, the
dx.;" Vi (pt; qt Po, 2o ddt
(20)
with the initial condition I1 = Esre. where
0. (Pr, qu Po: qo) :~ ve(p:, Ctgt)) - ve velq,, Carc) + (Elpolpil ] Elgolde))
(21)
. where 7 I- is positive for sufficiently large and E[golle [tol = qr - -tv, Carc), Blpoolppp....
P:- tv, (Pt, Ctgt) are Tweedie's 's denoising estimates.
Note that the resulting velocity field can be decomposed as of (Pc, qo> Po, qo) [Pr Ctgt) Ve Ve(gi, Carc)] +7 (L |p:]
E (g)))
(22)
Semantic Guidance
Source Consistency(Pe)
The final velocity in Eq. 22 needs more discussion. Similar to the drift term in Eq. 13 the first term in Eq. (22) serves the directional signal from the source the target semanties. On the other hand, the second term becomes a source consistent regularization gradient based on the distance between the clean estimates of Pt and q:, computed using Tweedie formula. This regularization gradient keeps the trajectory pt close to the source-consistency direction represented by Elgo q:), thereby implicitly regulating Zt.
Another byproduct of trajectory regularization is the robustness to the classifier- free guidance (CFG). Unlike recent work (Kulikov et al. (024) that uses CFG to both estimated noises with null-text embedding and different scales, we use the CFG as for the ODE trajectory P: only,
n (Pt, Cure; Cttt) = (pt, Care) + w [o" (Pt: Ctgt) v (pr, Care)]
(23)
where w 2 0 is the CFG scale factor. We find that commonly used CFG values (such as 7.5) are effective. For further analysis of the effect of w, Section 4 Accordingly, the proposed method is presented as time-reversal regularized trajectory:
dx:- = (pt, Cigt, Care) vz(gt. Core) >dt [E (o q:1 Eppol
21 Dare
(24)
The complete algorithm is presented in Algorithm [
Our approach introduces two hyperparameters w and ( = -ydtt > O. We find that using constant values yields stable results and provide detailed analysis of their effects in Section 4
5

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Algorithm 1 Algorithm of Flow on Latent Space
Require: Source image Pare. Pre-trained flow model v", VAE encoder and Decoder &, D,
Souree/Target text embeddings Cares Cages CFG scale w. source consistency scale Ç
1: Zare + [Zerr)
2: at f- D'rre
3: for :: + 0 do
4:
~~ (0,1)
5:
qt + (1 t)xaree + te
6:
Pr + H; Egre + q:
7:
p'())) v" (pt, Csrc)
(pt, v (pt, Carc)
8:
(q:):) = ra Cerc)
9:
E(polpt] t - -t (p)) Elgol qi) t qi tto
10: 3t + 8z + (p:) v (q:)] dt C1Elgol -Elpolp:)
end for
12: Zedit - ((x()
(6) 28
(b)
Baseline
No preference
Our method preferred
Ours
preferred
26
FlowEdit
Batkground PSNR
SDEdit
RF-lnwersion
24%
58%
Ri-imv
22
FlowEdit
37%
20
18
27%
62%
16
SDEdR
37%
35%
405
14
50
10
50
similarity
Preference Ratio
Figure 3: Quantitative and human preference evaluation. (a) Trade-off between CLIP similarity background PSNR. The darker the blob, the larger CFG scale. (b) User preference results.
Each bar shows the proportion of responses favoring the baseline (red), showing no preference (gray), or favoring our method (green). Bars are centered at emphasize directional preference. Across all comparisons, our method is preferred.
EXPERIMENTAL RESULTS
Dataset, Baseline and Compute Resource. To verify the editing performance, we perform multiple analysis using PlE-Benchh (Ju et al.) (023) that contains 700 synthetic and natural images with paired original and editing prompts. For baseline algorithms, we focus on comparing with methods that establish trajectory between two samples. For the methods that utilizes noisy sample distribution to connect two trajectories, the method that improves the inversion process. we use RF inversion (Rout et al. 2025a). For the inversion-free method, select FlowEdit (Kulikov et al. 2024). Note that all these methods training-fic free text-based image editing algorithms. For a fair comparison, we use the same flow model and 33 NFEs by following FdowEdit. In case of methods that involves inversion process, use 17 NFEs for each inversion and sampling process. We conduct experiments using NVIDIA GeForce RTX 4090 (24GB VRAM). For runtime analysis, see Appendix D
SDEdit (Meng al. 2021) and DDIB (Su et al.) 2023). For
Semantic alignment and Structure Consistency. Image editing quality should be evaluated from two complementary perspectives: semantic alignment and source structure consistency. An effective editing method should achieve a balance between these two objectives, improving both simultancously. To assess our method, we follow prior works and report CLIP similarity as a measure of semantic alignment and background PSNR as proxy for structural consistency. We evaluate performance across various that modulates the trade-off between semantic fidelity and structure consistency in flow-based, text- guided image editing. Figure 3 presents the quantitative evaluation results. For the complete results, please refer to Appendix W While the trade-off between semantic alignment and structure consistency remains, the proposed method consistently achieves higher structural preservation compared to all other methods. In terms of semantic alignment, measured by CLIP similarity, the proposed method
(CFG) scales (5.0, 7.5, 10.0, 13.5), as CFG a key parameter

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SDEdit
RF-inversion
FlowEdit
"an opened eyes cat sitting on wooden floor" wooden,ffoor" > "a closed eyes cat sitting on wooden floor"
"o woman in black hoiding on umbrella walks through a field" + "a womon in block holding on umbreilo wolks through a forest"
sitting mirrrr" "a silver sculpture mirror"
white table with four choirs and flowers" "a white table with four choirs and dog"
"a with glasses sitting wall" fa sitting wall"
Figure 4: Qualitative comparison text-based image editing methods. Insets provide zoomed-in views of regions highlighted by red and blue rectangles. Our method achieves better semantic alignment and structure consistency across a diverse set of prompts.
outperforms SDEdit and DDIB, while FlowEdit and RI-Inversio achieves higher scores. However, these baselines tend to increase CLIP similarity at the cost of source structure consistency. In many cases, their high CLIP scores result from over-expression of target prompt objects, often distorting the original image as shown in Figure
Human evaluation. Due to limitations of current metrics, such as CLIP similarity (as discussed the previous section), additionally conduct human preference study. From pool of 700 validation samples, we randomly select 100 images along with their corresponding original and editing text prompts. For each participant, by the proposed method and that of a randomly selected baseline. Participants are asked to indicate which result they prefer, that is defined one with accurate reflectance of editing prompt with source structure preservation. For more detailed description of the human evaluation protocol, refer to Appendix C Figure summarizes the preference ratio of out method against each baseline. Across all comparisons, the proposed method is more preferred. These results demonstrates that our method achieves improved editing fidelity and superior source structure consistency, as intended.
present pairwise comparison between the edited image produced
Table 1: Quantitative comparison for backward editing results. Bold represents the best.
Metric
PSNR 1
DINO Dist |
LPIPS L
MSE +
SDEdit (Mng et al. 2021
13.83
0,078
0.419
0.043
DDIB Su et 2023
18. 18
0.041
0.190
0.019
RF-Inv Rout et al 2025a
12.14
0.113
0.502
0.065
FlowEdit Kultiko el al 2024
19.88 98.88
0.037
0.147
0.012
Ours
27.42
0.025
0.085
0.006
Backward Editing. this work, we proposed a flow matching regularization to make smoother trajectory between two image samples. Thus, investigate whether the proposed trajectory Eq. (24) behaves deterministically between two samples. To test this, we solve Eq. (24) in backward direction starting from the edited image. By evaluating the similarity between the source image and recon-
7

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(a)
(c)
Circle Rectangle
Rectongle > Circle
Tulip >
Lion > Tulip
Bird Origami
Origami Bird
Torch >
Flower
Lion
Flower
Torch
Figure 5: Qualitative comparison of editing (odd columns) and backward editing (even columns) results. Align (the 2nd row) achieves better reconstruction quality compared to the baselines. (a) Source image, (b) FlowAlign, (c) FlowEdit, (d) RF-inversion, (e) DDIB, and (f) SDEdit.
structed image, we can evaluate whether the editing method indeed shows behavior like an ODE, We compute both pixel-wise metries (PSNR, MSE) and perceptual metrics (LPIPS, DINO structural distance) and report the results in Table Across all metrics, the proposed method outperforms the baselines. These results suggest that reverse editing using the proposed method nearly reconstructs the source image, supporting the effectiveness of the proposed trajectory regularization. Figure 5 shows a qualitative comparison for the edited image and reconstructed image. For example, in last column, the proposed method uniquely reconstruct the torch of the statue to match the source image, whereas the baselines fail to reconstruct accurately and instead convert it into a real torch. Importantly, the edited image obtained the proposed method faithfully reflects the intended editing direction. This implies that the observed reconstruction ability stems from the smooth trajectory, rather than simply reducing changes during the editing process.
Ablation Study. The proposed method introduces two hyperparameters, and Ç, which control the relative strength of each regularization term in Eq. (22). These parameters govern the trade-off be- tween semantic alignment with the target prompt and structural consistency with the source image.
Eursimlaryy
To evaluate their impact, we conduct an ablation study under various settings. As shown in Figure we observe that setting Ç = 0.01 consistently achieves a favorable balance between semantic alignment and structure preservation. Notably, the framework without any additional gradients (i.e. ( 0, block dot) results in insufficient edit-
20
Voluee
Se5
50
Structuaa Distance
Figure 6: Ablation study for and Ç. Top-left points represent to balanced performance.
8

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Source
Edited
(b)
'A photo of hamboo" + photo of christmas tree"
A photo of man" > "A photo of Joker
Source
Edited
"A silver car driving down curvy road" > "A blue car driving down a curvy rood"
Figure 7: Editing results for (a) 3D Gaussian splatting rendered from four different viewpoints, and (b) video sequence edited frame-by-fraine by-frame.
ing, which appears at the left-hottom position. This result emphasizes the effectiveness of the proposed CFG.
Further Applications. Figure 7 demonstrates the application of FlowAlign to 3D editing via Gaussian splatting, highlighting its effectiveness in editing Gaussian parameters using FlowAlign in place of standard score distillation-the thus extending its utility beyond 2D image editing. Figure 7p illustrates the application of Alogn to video editing, where is applied independently each frame. A Although temporal consistency is not explicitly enforced, the strong source consistency of Flow Align results in visually coherent backgrounds across frames. Additional details and results for these applications are provided Appendix G
5 CONCLUSION
In this paper, propose flow matching regularization, that leads to smooth and stable editing trajectory, for inversion-free flow-based image editing algorithm. By defining differentiable optimal control problem with similarity regularization at the terminal point, explicitly balance semantic alignment with editing text and structural consistency with the source image. As result, the proposed method achieves comparable better editing performance while showing superior source consistency and better computational efficiency. Notably, we demonstrate that the simulated ODE exhibits a deterministic property by performing the reverse editing experiments. In summary, this work provides a novel design space for approximating ODEs between two samples without requiring additional training.
Limitation and Potential Negative Impacts. While the proposed method offers efficient training-fri freee image editing algorithm, requires multiple diffusion timesteps for inference. The proposed method leverages noise-to- maise-to-image flow-based models for image editing, it inherits potential shortcomings of the underlying voise-to-image flow-based models, such as biased generation. In addition, image editing techniques may be misused for harmful applications, and research addressing these societal risks should be considered alongside technical advances.
ACKNOWLEDGMENTS
This work was supported by the National Research Foundation of Korea under Grant RS-2024- 00336454, the Institute of Information & Communications Technology Planning & Evaluation(IITP) grant funded by the Korea (oV)) (RS-2025-0230499 AI Star (ellowship(KAIST), No. RS RS-2024-00457882 AI Research Hub Project), the AT Computing Infrastructure Enhancement (GPU

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Rental Support) User Support Program funded by the Ministry of Science and ICT (MSIT), Republic of Korea (ROT-25-120217).
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A OPTIMAL CONTROL FORMULATION TO PROVE PROPOSITION
The following lemma is required for the proof.
Lemma 1. Consider the sollowing lime-reversal optimal control problem:
V(u,)= = {/' E( ue t) m(xo)) a; = =(xx)) Fto Estarts
(25)
where
1
(1 uc, 1)
1t arl?
(26)
2
m m(xo)
17
100 xarell
(27)
Then, the optimal solution trajectory given by
+ a2
(28)
where Pt is given by
") Pt nyt
Ut := f( at
(at + 0. Esrc)
where
(29)
Proof. The Hamiltonian for the given optimal control problem can be represented by
H( un Pt. t) == 2 ail1 + p 4
(30)
The optimal control un that minimizes the Hamitonian is then given by
u a2 Ps
(31)
This leads to the following
H (a us Pt, 1) =
|pll1 + p a2
(32)
Then, the minimum principle (Basar et al. pair (z,, P:) should satisfy the following:
2020: Fleming & Rishel 2012 informs that the optimal
2; ui a: P:
(33)
OH (1, ui Pt. t)
p.
0
(34)
Ōx
with the additional boundary conditions
am((); ()
Trg. Estart,
Po
=1(200 x.rc))
(35)
Oæ, (==
From Eq. 34 we can see that pt is time-invariant constant, i.e. P: = P for all / E [0, 1]. Accordingly, we have
3y = 1io +
-p + agdl
(36)
t0
= top + Ito + Uto
(37)
where
Uto = L anll
(38)
By plugging this in Eq. 35 with Po p. we have
7 p (1 + Uto B.rce)
p= n (fop + It + Uio Esrc)
1 ton
Therefore, the optimal control iz given by
u at + 1pt -
7/
(xt, + v2 - B.rc))
(39)
13

---

Now ready to prove main results.
Proposition 1. For the linear conditional flow with 0, 1 and b, where 0 S L S 1, the
ODE that solves the optimal control problem with Eq. 177. Eq. 18 and Eq. 19 is given by
dæ: = Dt (pt: Qc Po, yo
(20)
with the initial condition æ1 = Dare. where
ot (pt, Po. qo) = Ve(ps, Ctgt)) ve Carc) + (Blpolpii) -
(21)
where Y n is positive for sufficiently large n, and E [ogolg.) = qr - (ge Care), C.po)_
q-- Ps bv (Pr, Cegt) are Tweedie's 's denoising estimates.
Proof.
We can now use Lemma 1 with the following modification
a of (pt. Cegt) v. (qt. Carc)
(40)
This leads to the following first order approximation:
01 = S. a = {.¹ ((v(pp) "x(pi) - (el
(41)
(m)( + (1t)
(42)
Accordingly, we have
Et V2 Esre
Pt q: 12
~ Pt q: + (-tv; + tw, (q:))
Pt] Elgol q:l
where we use 2g - Øsre = Pt Qe from Eq. for the first equality. Thus, the optimal control uz given by
at +
1/l (x: + v2 - Barc)
at + nt - (E(polpe) E[goll:))
17
(43)
Therefore, we have
x = ve (pt, Cigt)) Cttt) - 17 Carc) +
nt --1 (E(polp:) [[golg])
(44)
Vy (Pe, Ctgt) - ve Carc) + (Elpolpid) - B[golg:]]
(45)
B IMPLEMENTATION DETAILS
In this section, provide implementation details of baseline methods and the proposed method. For the proposed method, we will release the code to lttts:://gttttti com/ c.om/Flowwe FlowAlign/ FlowAlign
Backbone model While various text-to-image generative models exist, we leverage a flow-based model defined in latent space, specifically using Stable Diffusion 3.0 (medium) (Esser et al. 2024) provided by the diffusers package. Given the significantly improved generative and text alignment performance of this backbone compared to earlier versions, baselines to establish fair comparison. For the time discretizations, we set the shift coefficient to 3.0, which is default option of the Stable Diffusion 3.0
the same backbone model for all
14

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Baseline methods
1. DDIB (Su al. 2023) DDIB involves an inversion process followed by a sampling process. For inversion, we adopt the backward flow ODE. Regarding classifier-free guidance (CFG), we use only the null-text embedding during inversion and both target text and null-text embeddings during the sampling. This choice motivated by the instability observed when applying standard CFG (i.e., using the source text and null-text embeddings) during inversion. We set the number of ODE timesteps to 17 for both the inversion and sampling processes, to conduct a comparison under similar number of total ODE timesteps.
2. SDEdit (Meng et al. 2021): SDEdit requires specifying the initial SNR (i.c. timestep), and performance can vary significantly depending on this choice. In this work, our main focus is to address the limitations of inversion- free editing methods. To fairly demonstrate the effectiveness of our approach in comparison alternative methods that also can mitigate this issue, we adopt the same initial SNR setting FlowEdit (Kulikov et al., (024), determined by the starting timestep of the ODE. Specifically, we use the 18th timestep as the starting point in our experiments.
3. RF-inversion (Rout et al. 2025a) II-Inversion introduces an optimal-control- control-based guid- ance mechanism that ensures the inverted representation aligns with a target terminal state, resuling in sampling process that is more likely under predefined terminal distribution. We follow the official implementation, setting 7 0.5, 7 = 0.9, the starting time & = and the stopping time 0.25, RF-Inversion uses only the null-text embedding during inversion, while both the target text and null-text embeddings are used during the sampling phase.
4. FlowEdit (Kulikov et al. 2024
We follow the official implementation of FlowEdit, setting the CFG scale to 3.5 for the source direction. Additionally, we solve the flow ODE starting from the 18th timestep out of 50, resulting in 33 ODE timesteps.
Evaluation Metrics For the quantitative comparison, we evaluate following metrics using the official evaluation code P from PIEBench (Ju et al. 2024):
1. Background PSNR: PlEbench (Ju et al. 2024) provides masks that cover the object to be edited. Accordingly, we compute the PSNR by excluding the masked region, resulting in the background PSNR.
2. Background LPIPS : We measure the LPIPS (Blau Michaeli 2018 which is defined distance between feature maps of pre-trained VGG network, by excluding the masked region.
3. Background SSIM We compute the structural similarity (Wang et al. 2004) by excluding the masked region.
4. Background MSE we compute pixel-wise mean-squared-erro by excluding the masked region.
5. CLIP-score: We report the similarity between features embedded by pre-trained CLIP (Rad- ford et al. 2021 image encoder and text encoder.
6. HPS : We measure the Human Preference Score (HPS) (Wu et al., 2023), a metric trained large-scale dataset of human feedback to predict the aesthetic quality and text-image alignment.
C HUMAN PREFERENCE TEST PROTOCOL
To evaluate the quality of image editing, we conduct human preference study in the form of an AB- test. Specifically, we randomly sample 100 images from the 700 validation samples of PIEBench (Ju ct al. 2024). The study follows the protocol below for each participant:
1. Randomly select one sample from the 100-image pool.
htttps:/gittiii com cure- I onttreeemain//vee htt.//ealllaiiooooo We use CL.PP pathhe and ViT-large-patch14,
15

---

1/20
Soure
1. Change the cat from real one to silver sculpture
Which better reflects the editing instruction?
Please consider both of the following:
Whether instruction
Whithhr instrcttdd parta changed
Image
Image
sure Both simler
St. Submit
Back
Figure 8: User interface for AB-test.
2. Randomly choose one baseline method from the four.
3. Randomly assign the baseline and the proposed method to gruops A and B.
4. Display AB-test user instruction with editing instruction, source image, and edited results from both methods.
5. The participant selects one of the following options: "A is better", "B is better", or "Not sure".
6. The participant clicks "Submit", and the response is recorded.
7. Step 1-6 are repeated until 20 cases are completed.
8. If more than half of the responses are "Not sure", an additional comparisons is presented following the same protocol.
Although the editing methods utilize cource-targed text pairs, we present the editing instructions from PlEBench participants instead, aiming improve readability and reduce cognitive load. The AB-test interface is shown Fig. 8 and was implement using Google Script. We recruited 25 participants and collected a total of 505 responses (with one participant receiving additional cases due to frequent "Not sure" selections). These responses were used to compute the final human preference results.
D RUN-TIME COMPARISON
Table Runtime comparison (unit: seconds). Averaged time for samples is reported.
DDIB
SDEdit
RF-inv
FlowEdit
FlowAlign
Stable Diffusion 3.0
4.06
5.26
4.06
10.64
7.14
In this section, report the wall-clock time for each editing method evaluated in the main paper, specifically focusing on the runtime for solving ODE in latent space. We use single RTX 4090 to measure the runtime. All experiments the sample x, updated.
conducted with the similar number of ODE timesteps where For inversion- based methods, we update sample with 17 ODE timesteps for inversion and 17 ODE timesteps for the sampling, and for inversion-free free methods, ODE timesteps
16

---

Distribution
(b)
Sampling
(d)
10
(b')
Tamsport
(c')
Tansport
(d')
Tranpprt
(d"))
Figure 9: Results of inversion- transformation, FlowEdit and FlowAlign on 2D toy dataset.
set to 33. Table shows the averaged runtime (in seconds) measured across 50 editing cases. For SDEdit, the runtime corresponds to standard reverse sampling with CFG. In comparison, DDIB and RF inversion achieve slightly shorter runtime, as set the CFG scale 0 during inversion. This is because applying CFG in the inversion stage often amplifies errors and disrupts the sampling process. FlowEdit requires computing CFG twice per ODE timestep once for the source direction and once for the target which results in approximately double the runtime of SDEdit. In other words, when using the same discretized ODE schedule, FlowEdit incurs similar computational cost to inversion-bast baadd methods. In contrast, the proposed method achieves faster runtime compared to FlowEdi due its efficient CFG, which computed only for (p:)). Importantly, this computational efficiency is achieved without sacrificing performance.
E ANALYSIS ABOUT EDITING TRAJECTORY
To provide empirical evidence for the efficacy the proposed regularization term, we validate our algorithm using a controlled 2D toy experiment. As illustrated in Fig. (a), the toy experiment utilizes Gaussian Mixture Models distributed uniformly 2D space to represent the source data (green), target data (blue), and noise (red) distributions. Since direct source and target prompt conditioning infeasible in this setting, separate Rectified Flow models were trained for the noise-to- to-s-tt-souree and noise-to-target data mappings. We compare the transport performance across three methodologies:
Inversion and Sampling: Fig. (b) and (bb)) demonstrate that the sequential application of source-to-noise inversion followed by noise-to-target sampling successfully transports data from the source domain to the target domain along clear trajectories.
FlowEdit: As FlowEdit samples random noise at every time step, this random noise selection frequently leads to out-of-domain outputs (Fig. (c)) and results in non-straight transport trajectories (Fig. (c)).
Flow FlowAlign: Figures (d) illustrates the effect of incorporating regularization term, which is derived from the first-order approximation of the optimal control solution. This regularization significantly reduces the prevalence of out-of-domain samples (Fig. 9d(d))
compared to FlowEdit. Crucially, FlowAligr yields straighter transport paths (Fig. "'d") and effectively ensures that source data is transported close target data, simplifying the complex trajectory in Fig. (b)).
The reliance on the first-order velocity approximation and the multi-step nature of the flow-based model introduces some failure cases. As depicted in Fig. (d'", when the predicted velocity field
17

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Table 3: Quantitative results for image editing PIEBench, compared identical ODE timesteps.
(CFG scale 13.5)
Source Cenentency
Semantic Aligument
metlad
Serustual Distnne
Backgronnd PSNR
Background LPIPS
Buckgrounal MSE
Background SSIM
CLIP HPS(x10")
DDIB
ST0 PX03
0.12
13:22
0,312
0,065
0,672
24.17
19.727
506
0,077
22.17
121
0,008
0.740
24:84
20.537
RF-4ax
0.111
15.12
0.308
0.038
0.633
27.67
21.289
FlowBun KaRIeo 2024
0.41
21.44
EL108
0,009
0.814
26.45
21.106
FlowAlian
0.031
24.21
[.009
0,005
0.864
25.63
20,550
Table 4: Quantitative results for image editing on PlEBench, compared using an identical Neural Function Evaluations (NFEs). (CFG scale 13.5)
Sounce Consitency
Setuantic Aligameut
method
Streotural Distace
Background PSNK
Backgronnd LPMSS
Bockkgrund MSE:
Background SSIM
CLIP 1
DDIB
St 2X23 Tooon P0N
FlowAlian
0.009
0.864
25.63
points in an incorrect direction during the initial timesteps (low signal-to-noise ratio), the generated sample trajectory can diverge, leading out-of-domain samples. Although this occurrence is observed less frequently in FlowAlign (Fig. (d)) compared to FlowEdit (Fig. (c)).
We provide additional visualization in Fig. 21 comparing the velocity vector field (dx) and the resulting trajectory (xt) of FlowEdit and Flow Align the same timestep t. Without an explicit regularization term for source consistency, the velocities generated by FlowEdit appear noisy and dispersed. In sharp contrast, the velocities generated by Flogn are clean and concentrated near the specified editing target. Consequently, the accumulated change from the source image in FlowEdit's s editing results is significant and widespread, whereas the results produced by FlowAlign remain close to the source while only applying the desired edit.
F ADDITIONAL EVALUATION RESULTS ON PIEBENCH
F.1 QUANTITATIVE AND QUALITATIVE RESULTS
We provide the complete evaluation result on PlEBench in Table which includes metrics described in Section B As discussed in the main paper, the proposed method outperforms all baselines in source consistency metrics while achieving both CLIP (ViT-L/14) and HPS scores comparable to FlowEdit. inversion-basee editing algorithm, exhibit higher semantic alignment
Although RF-Inversion, scores, they tend to overemphasize the target concept at the expense of preserving the source structure (see more examples in Fig. I0 and TT.. We also illustrate more qualitative results of the proposed method on text-based image editing task. Specifically, Fig. 10 and TT present additional qualitative comparison between baselines and the FlowAllggn. For diverse editing categories and objects, the proposed method shows better editing capability with better source structure preservation.
We additionally provide a comparison under fixed computational budget in Table 4 All methods benchmarked at approximately 99 Neural Function Evaluations (NFEs) to match the computational cost of our approach. For the inversion-based method, we used 33 ODE timesteps for inversion without CFG and 33 for sampling. For SDEdit and FlowEdit, which require a specified initial Signal-to-Noise Ratio (SNR), we selected starting timesteps that align with the noise levels proposed in FlowEdit (Kulikov et al.) 2024), initiating them at timestep 26 (out of 76) and 13 (out of 37), respectively, totaling 100 NFLs. The results under this equalized budget are consistent with our previous findings regarding source consistency and HPS. However, this analysis also reveals that while baseline methods can achieve higher CLIP scores with more function evaluations, it leads to significant degradation in source preservation. This reveals fundamental inability of these approaches to maintain structural fidelity when striving for better semantic alignment, a limitation method successfully overcomes.
18

---

Table 5: CLIP score all PIEBench Categories
Category
DDIB
FlowEdit
RF-Inversion
SDEdit
Ours
O-random
26.72
25.48
24.77
26.08
27.41
1-change object
23.95
26.44
27.33
24.81
25.30
2-add object
25.46
27.18
28.25
25.87
26.42
3-delete object
22.50
24.82
26.50
23.46
23.69
4-change attribute content
23.44
26.28
26.63
24.32
25.20
5-change attribute pose
23.66
26.21
26.96
25.24
25.75
6-change attribute color
24.89
26.52
28.70
24.66
26.19
7-change attribute material
24.13
26.39
27.81
24.88
25.98
8 8-change background
24.03
25.98
27.16
24.45
25.47
9- 9-change style
25.30
28.14
29.59
26.83
27.22
F.2 ABLATION
The proposed method includes typer--arameters: w, which controls efficient CFG, and which weights the source consistency term derived from the flow-matching regularization. As discussed in Section of the main paper, there trade-off between semantic alignment with the target text and structural consistency with the source image. Fig. I2 presents qualitative examples from the ablation study, focusing on the effect of Ç with fixed w 10.0. While the editing results may vary across samples even for the same Ç. we find that Ç 0.01 consistently yields robust and balanced performance, effectively satisfying both the editing instruction and source structure preservation across diverse cases.
Additionally we compare robustness of the proposed hyperparameters FlowAlign and FlowEdit in Fig. 13 In FlowAlign (Fig. (a)) Ç 0.01 shows robust performance the trade-off between CLIP similarity and structural distance across various values of w. In contrast, the original FlowEdit formulation (Fig. 13 (b) lacks clear Pareto optimal curve when evaluating the impact of its signal to noise ratio N. This suggests a non-robust relationship between and the editing outcomes. FlowEdit relies heuristically determined value (e.g., N 0.34 in 50 timesteps) for early stopping, which is not systematically optimized for balancing these two objectives.
F.3 FAILURE CASES
While FlowAligg achieves competitive performance across most PIEBench categories, it exhibits its lowest CLIP score in the "3-delete object" category (Tab. F.3 Detailed qualitative examples illustrating these limitations are provided in Fig. 22 The challenge precise object deletion often results in Flogn generating unwanted replacement in the original object's 's location. This issue not unique to our approach; both FlowEdit and SDEdit exhibit similar failure modes. Furthermore, FlowEdit frequently compromises overall image fidelity by introducing unintended transformations to regions outside the specified editing area. In contrast, while RF-Inversio and DDIB more closely adhere to the textual editing instructions for deletion, they fail maintain satisfactory source image consistency, leading to significant content deviation from the original image.
G ADDITIONAL RESULTS ON VIDEO AND 3D EDITING
As we demonstrated in the last section of the main paper, Flow Align can be extended beyond text- based image editing. In this section, we provide details and additional examples for video editing and 3D editing via Gaussian splatting.
G.1 FURTHER APPLICATIONS VIDEO EDITING
Flow Align is fundamentally a text-based image editing method built on an image flow-based model. In contrast, video editing typically relies generative models trained on video datasets with temporal
attention mechanisms to enhance temporal consistency (Jeong et al., 2024b) Liu et al. 22224 Jeong
al. 2024a Park et al. 2025). However, video editing also be viewed sequence of image
19

---

Table 6: Quantitative Comparison video editing
FlowEdt
Flow Align
FlowDirector (FE+mask)
FlowAlign + mask
Background PSNR
26.73
27.19
25.39
26.46
Background LPIPS
0.0719
0.0662
0.0765
0.0702
Background MSE
0.0032
0.0028
0.0043
0.0037
Background SSIM
0.8167
0,8286
0,8197
0.8340
Overall Consistency
0.2164
0.2209
0.2386
0.2276
CLIP
24.18
24.22
25.41
24.85
editing tasks. Extending the applicable range of image editing methods to video could offer practical benefits, such as reduced training and inference costs.
While the proposed method does not explicitly enforce temporal consistency, can still apply it independently to each video frame. For this experiment, we use the DAVIS dataset (Caclles et al.) 2019) and extract the source text prompt using LLaVA (Liu et al. 2023ah, conditioned the middle frame of each video. For the hyperparameter X, we use a constant 0.01, consistent with the main experiments. For w, vary it over [5.0, 7.5, 10.0, 13.5] and qualitatively select the best pest-performing value.
Figures 14 and 13 present examples of edited video frames, focusing texture and object editing tasks. Due to the strong source structure consistency of the proposed method, the video background remains well-preserved However, temporal consistency for the edited object is limited, constraint is imposed- for example, the head of the swan in Figure [4] Nonetheless, these results highlight the potential of the proposed method lightweight solution for video editing.
explicit
G.1.1 QUANTITATIVE COMPARISON ON VIDEO EDITING
We evaluate Align against FlowEdit and Flow Director Li et al. (2025) on 125 cases (25 videos with 5 different editing prompts). All methods were tested on the DAVIS dataset Pont-Tuset et al. (2017) utilizing the latent video model, WAN2.1-T22 Wan et al. 20255) We also include results for FlowAlign combined with attention masking introduced in Flow Director. Tab, demmonstrats that FlowAlign achieves superior source consistency compared to baselines while maintaining comparable text alignment results.
G.1.2 QUALITATIVE COMPARISON ON VIDEO EDITING
In Fig. 16 FlowAligg demonstrates improved text-to-video alignment compared to FlowEdit, which relies on an carly-stopping mechanism. Furthermore, FlowAlign exhibits superior source consistency when compared to FlowDirector (e.g., observe the preservation of the subject's 's face in the frame on the right).
G.2 FURTHER APPLICATIONS GAUSSIAN SPLATTING EDITING
Recall that one of the main contributions of Flow is introducing a regularization term for inversion-free image editing method, which has goal of simulating the flow ODE between two image samples. Accordingly, we can apply Flow Align for a 3D editing via Gaussian splatting. The basic idea is distill the knowledge of text-conditioned image prior of flow model update Gaussians.
The common way to distill the prior knowledge to parameters of generators, such as NeRF or Gaussian Splatting, is to optimize those parameters with score distillation gradients. More generally, it involves guiding the parameters through the use of a pre-trained denoiser acting critic. From the result of Proposition 1, we construct a regularized trajectory between source and target images and the drift term Eq. 445) corresponds to gradient reflecting the editing direction. Specifically, can define a editing loss function that satisfies
V LFA : ve(pt, Ctyt) velgs Care) (E [p.] E[go (:))
(46)
20

---

Table 7: Quantitative Comparison 3DGS editing
(bg) LPIPS
CLIP Dir. Sim.
CLIP
Aesthetic Score
SDS
0.33
0.10
0.27
4.94
DDS
0.33
0.18
0.27
4.76
PDS
0.23
0.12
0.24
4.12
IGS2GS
0.10
0.07
0.23
5.48
FlogAlign
0.06
0.18
0.26
5.52
where we assume that the Jacobians @0,(g.)
dan; are identity matrices. Then, by using LF as critic for updating Gaussians, we can guide them toward target Gaussian whose rendered views are high likely sample in perspective of flow model. The only one we should consider is extending FF to contain parameters & differentiable generator g.
Bm, and (vy(Pe)
flow model defined in latent space, we compute the loss function using Qt.c s) fe, Pt.c = qt.c + Tt,c &src.c. Here, с denotes sampled camera view, &arc.c E(g(veree c)) denotes the latent code of rendered view from initial Gaussian, 2t.c E(g c)) denotes the latent code rendered vidw from current Gaussian, denotes the pre-trained encoder of VAE and NO0 I). By using the chain rule, obtain the following gradient for flow-based 3D
Because
editing:
dx,
V.LFA [v,LFAl
(47)
Orp
da:
[Iv((rt,r Cagt) Ve Vel Cerc) + 7Blpulpp E[golad)]
(48)
and use gradient descent to update the a/ as
ー Ne V Cr
(49)
For the semantic guidance term in this gradient. we only apply CFG for p, by setting Care as null- text embedding, same as the image editing algorithm. The pseudocode for the 3D editing with FlowAlign is in Algorithm and additional qualitative results are Fig. 18
G.2.1 QUANTITATIVE COMPARISON ON VIDEO EDITING
We perform Gaussian Splatting optimization for 3, 000 iterations using a classifier-free guidance (CFG) weight w set to either 70 100. Experiments
conducted real-world scenes using datasets from IN2N (Haque et al.) 2023) and PDS (Koo et al. 2024). For comparison, we benchmark
against existing distillation methods, including SDS (Poole al. 2022), DDS (Hertz al. 2023). and
PDS (ooo et al.) 2024). as well as the non-distillation baseline IGS2GS (Vachha & Haque
2024 For
baselines using distillation methods
used Stable Diffusion 3.0 and for IGS2GS (Vachha & Haque
2024), we use UltraEdit (Zhao et al. 2024) in replacement of Instruct- Nerfueerr (Haque et al.
2023) for flow-based models. Across 15 scenes (6 distinct scenes with varying prompts), FlowAlign demonstrates superior performance not only in source consistency (measured by background LPIPS) but also 3D consistency (measured by CLIP directional consistency) and human preference
(measured by LAION aesthetic score) (Tab. 7).
G.2.2 QUALITATIVE COMPARISON ON VIDEO EDITING
Qualitative comparison of our method against score distillation methods (SDS, DDS, PDS) and IGS2GS are provided Fig. 17
H FURTHER VARIANTS FLUX
Our main experiments are conducted using by leveraging pre-trained flow model, Stable Diffusion 3.0. Since the proposed method regulates the sampling ODE via flow matching cost, it is also compatible
21

---

Algorithm 2 Algorithm of Flow for 3D editing
Require: Source parameter V'rre Pre-trained flow-based model vg. VAE encoder &, Source/Tareet text embeddings Care, Cigt, CFG scale w, camera views Cams, Noise Schedule os, differentiable generator 9, min and max timestep T min, T max
1: V- f- Ware
2: // Freeze VAE encoder and flow model 10g
3: Bsrce < ( c))
4: for :: :ort:Tmar 7 Tiin do
5: E~ N~,0 o c~ U(Cams)
6: Ft.c + ())
7:
qtcc (1 -1-60 -0t))asreee dzC
8:
Pte t It.c - Barr.c + qr.c
9:
(Pr.c) = =v (pici Cara) tw [v0 (pr.c: Ctge) - (pr,os Care]] (gt,e) = v (gt,err Carc)
10:
E(polpt] -Pic - -too E(golq) qi] t qt.c to (qtc))
11: VoLFA + [(vo(rr.)) (t..) + (Elpolpp Elgo (1:)
12: 1 Φ TA CFA
13: end for
14: return &b
Algorithm 3 Algorithm of Alonn with FLUX (Guidance distilled model)
Require: Source image Tarcs Pre-trained flow model v", VAE encoder and Decoder E, D,
Source/Target text embeddings Cares Ctgt, CFG scales Wares wigt, source consistency scale
1: 2t f E(2sre)
2: for prt:: + 0 do
3: e IOO
4:
Gt - (1 -laaare Le
5:
Pr Dr Bere + 9:
6:
(pt) == (pt Cigt, Wegt),
v" (q:) == v (g:: Cares Ware)
7: Elpolpr] + Pt -ttt to (pr).
Elgo q: t q: to (q:)
8: De f xt + (p)(pt) v (q:)] + <(Elgull q:l E(polp
9: end for
10: Zedit <- D(x..)
with other flow-based models, such as FLUX. Following the setup in FlowEdit (Kulikov et al. 2024), additionally evaluate method using FLUX the backbone model. We incorporate the source consistency term derived from optimal control with flow matching regularization, as described in Algorithm 3 As FLUX.. 1-dev is guidance-distilled model that directly takes the CFG scale input, there is no need to apply the modified CFG strategy used in Stable Diffusion 3.0 case. Therefore, we simply provide the CFG scale to both vp.)) and v(g:). following the approach used in Flow Edit. Figure 19 illustrates edited results generated by the proposed method implemented with FLUX. I Ideev Similar the results with Stable Diffusion 3.0, the outputs effectively reflect the intended editing direction specified by the text prompts while preserving source structures. These results imply that proposed method broadly applicable to flow-based models for image editing.
H.O.1 QUANTITATIVE COMPARISON ON FLUX
We provide additional comparison against methods that rely on source image inversion RF-Edit Wang al. (2025), FluxSpace Dalva et al. (2024) and FireFlow [eng al. (2024). Our results show that AlogAligg achieves more faithful and controlled edits than the inversion-based baselines. Inversion- based methods inherently suffer from reconstruction errors, which lead to significant deviations from the source image. To mitigate this, RF-Edit, QK-Edit, and FireFlow inject attention-layer features (Q/K/V) extracted during the inversion process back into the generation process. FluxSpace leverages an ceiting-directio attention shift. However, shown in Tab. all remain highly sensitive to inversion errors; even with higher-order ODE solvers, flow inversion IS imperfect and computationally expensive. FlowEdit and FlowAlign bypasses inversion altogether, avoiding these errors without
22

---

Table 8: Quantitative Comparison additional image editing baselines on FLUX (transposed)
FireFlow
FluxSpace
RF-Solver-Edit
Flon
Structure
0.0456
0.1647
0.0451
0.0414
Background PSNR
20.37
11.69
20.34
20.75
Background LPIPS
0.1824
0.3914
0.1824
0.1314
Background MSE
0.0136
0,0971
0,0136
0.0122
Background SSIM
0.7584
0.5747
0.7589
0.8123
CLIP
26.69
24.41
26.75
26.97
adding computational overhead, while FlowAlign further enhances source consisteney with optimal control formulation and source consistency regularization.
H.0.2 QUALITATIVE COMPARISON ON FLUX
In Fig. 20 we illustrate qualitative comparison on Flux. While additional baselines FireFlow Deng
al. 2024). FluxSpace Dalva et al. (2024) and RF-Solver-Edie Wang et al. (2025) result in saturated images, FlowAlign shows superior source preservation with better editing capability.
23

---

Source
SDEdit
DDIB
RF-inwersion
FlowEdit
Ours
"Elephant in the forest" "Elephant in the forest and man riding it"
"A girl with pink umbrella in the rain" "A girl with yellow umbrella in the rain"
"An anime painting of house on hill" >> "Kids crayon drawing of an anime painting of house on hill"
"An empty with view of the beach" "Black and white ink painting empty..."
"A white kitten sitting leopord print blonket" >> "A yellow kitten sitting leopard print blanket"
MAM
"A woman sitting in cove light coming from light" "A pen ink sketch of.."
"An angel with wings standing in field > "An angel with wings standing in river"
Figure 10: Additional qualitative comparison results.
24

---

Source
SDEdit
DDIB
RF-inwersion
FlowEdit
Ours
"a cartoon giraffe sitting down white background" > "a watercolor giroffe
"A woman in hood holding a fire" > "Chinese wotercolor of woman in hood holding fire
"A woman in jacket standing in the rain" -> "A woman in blouse standing in the rain"
"A wotercolor pointing white bunny in cup of flowers" > pink bunny in cup of flowers"
"Sunset at the rock by jomes mccormick" > "Black and white ink painting of sunset..."
"Illustration of cup and lamp on table by window" > "... crystal lamp on table by window"
"A cartoon man" >> "A cartoon and bird"
Figure 11: Additional qualitative comparison results.
25

---

Source
0.005
0.0075
0.01 (Ours)
0.03
0.05
"Photo of a goot and a cat standing on rocks near the ocean" horse and a cat
cute dog holding red heart" > cute dog holding a pink heart"
"A tiger swimming in pond of green algae" > "A dog swimming in pond of green olgae"
"A cake with pink and blue icing" -> "A icecream with pink and blue icing"
"A white buildog is walking on the grass" > "A white rot is walking on the grass"
"A water droplet hangs from string of lights" > "A water droplet hangs from string of red lights"
Figure 12: Ablation results for Ç.
26

---

(a) Ours
(b) FlowEdit
CUP Similerity
CLiP Similantt
52
vallee
value
value
value
Se-3
0.24
5.0
7,5e-
7.5
0.29
7.
1e-2
10.0
31
Structural Distance
Structural Distance
Figure 13: Ablation study for hyperparameters of FlowAlign and FlowEdit.
Source Fraees
Edited Frames
"A black swan is swimming" >> "A statue of swan floating"
Source Frames
Edited Frames
"A duck swimming in body of water" >> 'A wooden duck swimming a body of water"
Figure 14: Additional results for video editing: texture change.
27

---

Source Frames
Edited Frames
"A boy riding BMX over bump" + "A boy is riding motorcycle over bump"
Source Frames
Edited Frames
"A womon wearing black dress is walking" "A womon wearing black T-shirts is walking"
Figure 15: Additional results for video editing: object change.
Source
ROVEdE
Durs
Ouz-F3
"a small boot traveling through the water ..." > "a groy seal ..."
"o little girl holding a kitten in her arms" > teddy bear
Figure 16: Qualitative Comparison on video editing.
28

---

Source
SDS
DDS
PDS
IGS2GS
Ours
"A photo of a bambao" >> photo of an orange tree with oranges"
"A photo of a face" >> "A photo of face with glasses"
Figure 17: Additional results for 3D editing.
Figure 18: Video results of 3D editing. Click each image to play the video in Acrobut Reader.
29

---

Source
Edited
Source
Edited
Source
Edited
Three people people
Metollic strap - leather strop
Cat dog
Young woman > old woman
White - purple
Women - men
Tiger > cat
Three sandwiches
Plastic chair - wooden chair
Women >
girl
Bed > grassy meadow
Vose plant
Cat + tiger
Closed mouth >> open mouth
Metalic spoon wooden spoon
Front a toilet > forest night
Men
Cot dog
Meerkat puppy >> lion puppy
+ar
Figure 19: Qualitative image editing results using FLUX.
30

---

Durk
standing
"shata racks
"smobe" "Jo""
sitting the cat sitting in the rocis."
To pointing of fairy with green wings holding a plawing jes "a pointing of foey with green wings holding cryonal jact
photo of white and black photo of tride and groom emérace the woods. colorful and phote
bride and groam embroce the woods."
young wortn holding dog." old women & holding dog."
"dogs running in the grass" Trabaits ronning the grars"
Figure 20: Qualitative Comparison with baseline methods on FLUX.
31

---

dx
FlowEdit
FlowAlign
"a bird standing on clods" > "a bird standing on eggs*
FlowEdit
FlowAlign
"gold buddha statue in the temple" >> "stone buddha statue in the temple"
Figure 21: Visualization of FlowEdit and FlowAlign editing trajectories.
32

---

Source
SDEdit
DDIB
RF-inversion
FlowEdit
""a cat wearing headphones on a gray background" >> ""a cat on gray background"
"a cheetah walking across grassy field >> "a cheetah walking across field
gray polar bear on an iceberg with plane flying overhead" >> ".. gray polar bear on an iceberg"
Figure 22: Failure cases of FlowAlign on "3-delete object" category in PIEBench.
33


Reviews:
[{"review_id": "EPErF84ZaZ", "reviewer": "Reviewer_2ckP", "summary": "This paper introduces FlowAlign, an inversion-free, flow-based framework for text-guided image editing built on pre-trained rectified flow models such as Stable Diffusion 3. It formulates editing as an optimal control problem and derives a modified velocity field that combines FlowEdit-style semantic drift with a source-consistency term expressed via Tweedie denoising of source and target latents. The resulting ODE is training-free, adds only a small computational overhead, and aims to produce more stable and deterministic editing trajectories. Experiments on PIEBench with SD3 show improved background preservation metrics and human preference over SDEdit, DDIB, RF-Inversion, and FlowEdit, while keeping CLIP and HPS scores competitive.", "questions": "How closely does the approximated drift in the implemented ODE track the exact optimal-control solution on simple toy problems, and did you observe regimes where the approximation qualitatively breaks down?\n\nAre there characteristic failure modes (e.g., multi-object insertion, strong domain shifts) where FlowAlign underperforms FlowEdit or RF-Inversion, and could you provide concrete examples or diagnostics?\n\nTo what extent can the core idea be ported to non-rectified-flow backbones e.g. standard diffusion models, and what modifications would be required?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- The optimal-control formulation leads to a drift that explicitly combines semantic editing and source-consistency terms, offering a clear interpretation of how FlowAlign stabilizes trajectories.\n\n- Using a shared SD3 backbone and comparable NFEs, FlowAlign consistently improves background PSNR/SSIM/LPIPS/DINO over SDEdit, DDIB, RF-Inversion, and FlowEdit while maintaining competitive CLIP and HPS scores.\n\n- Reconstructing the original image by integrating backward yields much better fidelity with FlowAlign than with FlowEdit, reinforcing the claim of more stable, ODE-like behavior.\n\n- Applying the trajectory regularizer as a guidance signal in these settings suggests that the idea could generalize beyond 2D image editing and inspire further work on structured generative representations.", "weaknesses": "- The optimal-control derivation relies on linear assumptions and a first-order approximation to the integrated drift, so the implemented ODE is not tightly characterized by theory and functions more as a guided heuristic.\n\n- The paper positions FlowAlign mainly against multi-step ODE/SDE editors and does not clearly situate it relative to recent fast or one-step editing approaches that optimize for speed–quality trade-offs.\n\n- Results on video and 3D Gaussian splatting are purely qualitative, without metrics for temporal or multi-view consistency, making it hard to assess robustness in these scenarios.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "7diq7PChBW", "reviewer": "Reviewer_GZwn", "summary": "The paper proposes FlowAlign, an inversion-free image editing method for rectified flow models. Through terminal point regularization, the balance between semantic alignment and structural consistency can be improved. Extensive experiments illustrate the superior performance of the proposed method.", "questions": "See weakness.", "limitations": "", "rating": 2, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "- The method is training-free and inversion-free, which can be applied on various off-the-shelf flow-based models.\n- Compared to the baseline methods such as FlowEdit, the proposed method is more computationally efficient.\n- The paper is well-written and easy to follow.", "weaknesses": "- The motivation of this paper is not clear.  Authors claim that 'these limitations of FlowEdit arise from non-smooth and unstable\nediting trajectories' (Line 86). However, there is no experimental analysis in the paper to support this, making this claim unpromising.\n- Authors claim that FlowEdit is sensitive to the hyperparameters. However, there are also many hyperparameters need to be tuned in the proposed method (including but not limited to the ω and ζ ). Could FlowAlign perform better than FlowEdit in terms of hyperparameter sensitivity?\n- A comprehensive discussion of the related work is missing, there has emerged a number of image editing methods recently, such as RF-Edit [1], QK-Edit [2], FluxSpace [3], FireFlow [4]. Authors are highly suggested to discuss and compare the performance between the proposed method and these baselines.\n- Authors say that 'FlowAlign achieves superior source preservation and competitive or improved editing quality compared to FlowEdit and also other existing approaches in image, video, and 3D editing.' However, they do not compare the performance of their method with any baselines of video editing. By the way, the prompt in Figure 13 ( A black swan is swimming...) does not match the video.\n\n[1]. Taming Rectified Flow for Inversion and Editing\n\n[2]. QK-Edit: Revisiting Attention-based Injection in MM-DiT for Image and Video Editing\n\n[3]. FluxSpace: Disentangled Semantic Editing in Rectified Flow Transformers\n\n[4]. FireFlow: Fast Inversion of Rectified Flow for Image Semantic Editing", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "wOoYLn3HRQ", "reviewer": "Reviewer_TFck", "summary": "This paper introduces FlowAlign, a flow-based image editing framework that builds upon a prior inversion-free approach, FlowEdit. While this method demonstrated that direct editing without inversion is feasible, FlowAlign focuses on improving the smoothness and consistency of the editing trajectory. To achieve this, it introduces source similarity at the terminal point as a regularization term, encouraging trajectories that preserve structural consistency with the source image while following the intended semantic edits.", "questions": "I raised question in the weaknesses section.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Good results with clear qualitative comparisons – the paper presents convincing visual examples that highlight the differences between FlowAlign and baselines. The figures clearly show improved source structure preservation and accurate semantic edits.\n2. Human preference study – beyond quantitative metrics, the authors conduct a user study showing that participants consistently prefer FlowAlign’s outputs over baselines. As far as I know, this is the first time human preference is reported for these low-based editing methods.\n3. Demonstrated across multiple settings – The method is evaluated on 2D image editing, video editing, and 3D Gaussian splatting, showing versatility and robustness across different tasks.", "weaknesses": "1. Trajectory regularization intuition – while trajectory regularization appears effective, the paper could provide a deeper explanation of why smoother trajectories improve editing outcomes. It seems intuitive that smoother trajectories help preserve the original image structure, but it is unclear what trade-offs or costs this introduces. For example, could this regularization limit the strength or flexibility of edits, or bias the model toward minimal changes? \n\n2. Figure 2 clarity – figure 2 is somewhat confusing. It is not clear which panels correspond to FlowEdit versus FlowAlign. What does “R” represent? This term does not appear in the text. Additionally, the velocity field mentioned in the caption is not visually represented in the figure, making it difficult to interpret the intended trajectory differences. Clarifying these points would improve readability and understanding of the proposed method.\n\n3. It is unclear whether the paper uses the same early-timestep skipping as FlowEdit.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "CXmJZNd3Oc", "reviewer": "Reviewer_JBzF", "summary": "FlowAlign is a flow-based approach for text-guided image editing that operates without additional training or inversion. Unlike prior methods such as FlowEdit, which suffer from unstable trajectories and source degradation, FlowAlign introduces trajectory regularization using terminal structural similarity to address these issues. This allows the method to achieve a balanced trade-off between semantic alignment and structural consistency, resulting in smooth and deterministic transformations. Moreover, FlowAlign achieves computational efficiency by requiring only one additional function evaluation (NFE) per ODE step and enables near-perfect reconstruction of the source image via backward ODE integration.", "questions": "1.The most important point is the comparison with FlowCycle. FlowCycle demonstrates superior performance compared to FlowAlign — can the authors explain why FlowAlign performs better than FlowCycle?\n\n2.As mentioned in the Weaknesses Section, there are several questionable aspects in the presented results. The main ones are as follows:\n\n2-1. In Figure 3(a), did the authors indeed set the CFG scales to {5.0, 7.5, 10.0, 13.5}? If so, were the source CFG and target CFG values identical for the baselines? If they were the same, this does not match the baseline settings described elsewhere (in other tables, figures, or the Implementation Details section). In particular, for FlowEdit, if the source CFG values were set to {5.0, 7.5, 10.0, 13.5}, as far as I know, this is not a standard setting.\n\n2-2. While it is reasonable to point out the limitations of CLIP scores, the Human Evaluation results in Figure 3(b) and the CLIP scores in Table 3 are highly inconsistent. The discrepancy is too large to attribute merely to the limitations of CLIP score. Why does FlowAlign show better Human Evaluation results but lower CLIP scores?\n\n3.The key idea of FlowAlign seems to be its improved efficiency by computing CFG only for 'v'. However, to convincingly demonstrate superior performance over the baselines, more comparisons involving 'source CFG' and 'target CFG' variations should be provided. How does the performance vary across baselines depending on the source and target CFG values?", "limitations": "", "rating": 2, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "1.FlowAlign performs efficient editing without requiring inversion or additional training. In addition, FlowAlign is more efficient than FlowEditing.\n\n2.FlowAlign achieves smooth and stable trajectories through trajectory regularization.\n\n3.FlowAlign It balances semantic alignment and structural consistency effectively.", "weaknesses": "1.My main concern is the comparison with FlowCycle [1]. FlowCycle presents a more advanced approach than the proposed FlowAlign.\n\n2.There are some questionable aspects in the figures and tables presented by the authors. Please refer to the \"Questions\" Section for specific details.\n\n3.The diversity and explanation of CFG settings appear insufficient. Although the authors acknowledge that CFG is a highly critical parameter, they provide limited experimental results, using only fixed CFG settings for the baselines.\n\n[1]FLOWCYCLE: PURSUING CYCLE-CONSISTENT FLOWS FOR TEXT-BASED EDITING", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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:

Decision: Accept (Poster)