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REVIEW 4 major objections 6 minor 5 cited by

FlowAlign: Trajectory-Regularized, Inversion-Free Flow-based Image Editing

T0 review · 4 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read By adding a terminal-point similarity term to the inversion-free editing ODE, FlowAlign keeps the edited image structurally close to the source while following the edit prompt, and makes the edit trajectory reversible.

desk verdict FlowAlign is a practical inversion-free editing method with strong empirical results and a heuristic theory that has a sign inconsistency; worth refereeing, but the derivation needs repair. read the letter →

arxiv 2505.23145 v4 pith:Q6F5PTGB submitted 2025-05-29 cs.CV cs.AIcs.LG

Jeongsol Kim , Yeobin Hong , Jonghyun Park , Jong Chul Ye This is my paper · ORCID
classification cs.CVcs.AIcs.LG
keywords flow-basedimageeditinginversion-freeoptimalcontroltrajectoryregularizationsourceconsistencyTweediedenoisingestimateflowmatchingtext-guided
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper proposes FlowAlign, a method for editing images with a pre-trained flow-based text-to-image model without first recovering the exact noise latent that produced the source image. It adds a terminal-point regularization term to the editing ODE that penalizes the final latent from drifting away from the source latent, and derives that term from an optimal-control formulation with a structural similarity cost. The result separates the update into a semantic-guidance component and a source-consistency component, so the two objectives are explicitly balanced along the trajectory. The paper claims this improves source preservation while staying competitive on edit-prompt alignment, and that running the same ODE backward nearly reconstructs the original image.

What carries the argument

The central object is the regularized velocity field $v_x^t = v_t(p_t,c_{tgt}) - v_t(q_t,c_{src}) + \gamma(E[p_0|p_t] - E[q_0|q_t])$ obtained from the optimal-control problem whose terminal cost penalizes squared distance to the source latent. The terms $E[p_0|p_t] = p_t - t v_t(p_t,c_{tgt})$ and $E[q_0|q_t] = q_t - t v_t(q_t,c_{src})$ are Tweedie denoising estimates, and their difference supplies the source-consistency gradient. The proof uses a first-order approximation of the velocity integral over the remaining time interval, which converts the terminal cost into an instantaneous pull during the ODE solve.

What would settle it

Compute the regularized ODE update with the exact integral of the velocity difference over the remaining time interval instead of the first-order approximation, then run backward editing; if source reconstruction quality worsens materially or the trajectory deviates from the claimed update, the load-bearing approximation fails.

Watch

Extended reading notes

Core claim

The central claim is that the inversion-free editing ODE can be stabilized by appending a terminal-point similarity term. Concretely, the velocity field becomes $v_x^t = [v_t(p_t,c_{tgt}) - v_t(q_t,c_{src})] + \gamma(E[p_0|p_t] - E[q_0|q_t])$, where $E[p_0|p_t]$ and $E[q_0|q_t]$ are Tweedie denoising estimates of the target-clean and source-clean latents. The first bracket is the semantic guidance that moves the sample from the source distribution toward the target distribution; the second bracket is the source-consistency gradient that pulls the trajectory back toward the source along the way. The paper proves this velocity solves a time-reversal optimal-control problem whose terminal cost penalizes the squared distance between the final latent and the source latent, and shows experimentally that the regularized trajectory yields higher background preservation and near-perfect backward reconstruction compared with prior inversion-free and inversion-based editing baselines.

Load-bearing premise

The derivation assumes the velocity difference between the source and target flows stays roughly constant over the remaining time interval, letting the integral be replaced by an instantaneous Tweedie estimate; if that approximation fails, the claimed regularization term is not justified.

Editorial extensions

If this is right

  • FlowAlign preserves source structure better than the inversion-free baseline and inversion-based methods under the same number of function evaluations.
  • Backward editing with FlowAlign nearly reconstructs the source image, indicating the regularized trajectory behaves close to a deterministic ODE.
  • The method extends to editing video frames independently and to 3D Gaussian splatting scenes without retraining the flow model.
  • Classifier-free guidance is applied only to the target-direction velocity, keeping the per-step cost to roughly one extra function evaluation instead of doubling it.
  • The two hyperparameters controlling semantic guidance and source consistency have a clear trade-off, with a constant default value giving balanced performance across samples.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same terminal-cost construction could be adapted to regional edits by weighting the Tweedie-difference term with a spatial mask, letting an editor suppress regularization outside the edited object.
  • Because the regularized trajectory is reversible, one could compute the implied edit direction as a vector field in latent space and use it for smooth interpolation between source and target prompts.
  • A natural portability test is to apply the same regularization with a different flow backbone; if a constant default weighting transfers across models, the method is less dependent on the specific velocity model.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper proposes FlowAlign, an inversion-free flow-based image editing method. Building on FlowEdit's idea of simulating an editing ODE without latent inversion, FlowAlign adds a terminal-point regularization term derived from an optimal control problem, which penalizes deviation of the final output from the source image. The resulting velocity field decomposes into a semantic guidance term and a source-consistency term involving Tweedie denoising estimates. The method also applies classifier-free guidance only to the target trajectory, reducing computational cost. Experiments on PIEBench report improved source-consistency metrics (PSNR, LPIPS, DINO distance) and competitive CLIP scores, with additional evidence from a human preference study, backward-editing reconstruction, and applications to video and 3D Gaussian splatting editing.

Significance. If the theoretical derivation were sound, FlowAlign would be a simple and efficient extension of inversion-free editing, requiring only one additional function evaluation per step while improving source preservation. The empirical results are promising and the applications to video and 3D editing show potential breadth. However, the central Proposition 1, which motivates the method, relies on an uncontrolled approximation and contains a sign inconsistency with the algorithm. The terminal regularization also makes some of the reported source-consistency gains unsurprising. The work therefore has clear potential, but the current manuscript does not fully establish the claimed optimal-control justification.

major comments (4)
  1. [Appendix A, Eq. (41)-(42)] The proof of Proposition 1 replaces the integral ∫_t^0 (v_s(p_s)−v_s(q_s))ds with −t v_t(p_t)+t v_t(q_t), assuming the velocity difference is constant on the interval [0,t]. For a nonlinear learned velocity field this is not an equality, and the paper provides no error bound or empirical validation of the approximation. Since this step is what allows the Tweedie estimates E[p0|pt]−E[q0|qt] to appear in the final velocity field, the derivation is load-bearing. Please either justify the approximation (e.g., under a Lipschitz or linearity assumption), provide a numerical check of its accuracy over the edit trajectory, or explicitly reframe Proposition 1 as a heuristic construction rather than a derived optimal control.
  2. [Section 3.3 and Algorithm 1 (Eq. (21), Eq. (24), line 10)] There is a sign and coefficient inconsistency between the derived update and the implemented algorithm. Equation (21) gives dxt = [v_t(pt)−v_t(qt)]dt + γ(E[p0|pt]−E[q0|qt])dt with γ = −η/(1−ηt), while Algorithm 1 line 10 implements xt ← xt + [vθ(pt)−vθ(qt)]dt + ζ(E[q0|qt]−E[p0|pt]), i.e., a positive constant ζ multiplying the negative of the derived term. As γ(t) changes sign over t∈[0,1] for η>1 (negative for t<1/η, positive for t>1/η), a single constant ζ>0 cannot equal −γ(t)dt for all steps. The text states ζ = −γdt > 0 without addressing this sign variation. This means the implemented trajectory is not, step-by-step, the optimal-control solution of Eq. (17)-(19). Please reconcile the theory and algorithm, for example by redefining γ, using a schedule-dependent ζ, or clarifying that the algorithm uses a deliberate approximation.
  3. [Section 4, Backward Editing and Table 1] The backward-editing experiment measures how well the source is recovered by reversing the forward trajectory. Since the terminal regularization m(x0) = (η/2)||x0−xsrc||^2 explicitly penalizes deviations of x0 from xsrc, the forward trajectory is pulled toward the source, making high backward reconstruction fidelity expected even without a genuinely smooth or invertible trajectory. The paper argues that the edited image 'faithfully reflects the intended editing direction' and therefore the reconstruction is not trivial, but this claim would be stronger with an ablation that includes a baseline using only the terminal penalty (or a simple post-hoc projection toward the source) without the full optimal-control term. Please add such a comparison to isolate the contribution of the proposed gradient form.
  4. [Section 4, Table 1, Table 3, Figure 3a] The main quantitative results are reported as point estimates without error bars, confidence intervals, or significance tests. Given that some differences (e.g., CLIP scores in Table 3) are small, and that PIEBench contains 700 images, the paper should report standard deviations or standard errors across samples, and ideally a paired significance test for the key source-consistency metrics. This is important for assessing whether the improvements over FlowEdit and DDIB are robust rather than driven by a few outlier cases.
minor comments (6)
  1. [Abstract] The word 'highliting' should be 'highlighting'.
  2. [Figure 3b caption] 'out method' should be 'our method'.
  3. [Appendix D, first sentence] 'resuling' should be 'resulting' in 'resuling in a sampling process'.
  4. [Appendix F.2, last paragraph] 'vidw' appears to be a typo for 'view' in 'rendered vidw'.
  5. [Algorithm 1 and Section 3.3] The definition of ζ is given only in the text after Eq. (24) as ζ = −γdt > 0, but Algorithm 1 uses ζ as a tunable hyperparameter; please state explicitly that ζ is treated as a constant hyperparameter in practice and explain how this relates to the (potentially time-dependent) γ.
  6. [Figure 6] The legend mentions a 'block dot' that should probably be 'black dot'.

Circularity Check

1 steps flagged · score 3.0 of 10

Mild self-definitional circularity: the terminal regularizer is literally source-distance, so reported source-consistency gains reflect the objective; the optimal-control derivation itself is not circular.

  1. self definitional [Section 3.3, Eq. (19)-(22); Table 1]
    "Specifically, we introduce a l2-based terminal point regularization: m(x0) = η/2 ∥x0 − xsrc∥^2 (19) ... the second term becomes a source consistent regularization gradient based on the distance between the clean estimates of pt and qt, computed using Tweedie formula."

    The 'source consistency' that FlowAlign claims to achieve is defined by the same distance to the source image that is minimized by m(x0): Eq. (19) penalizes ||x0 - xsrc||^2, and the reported source-preservation metrics (PSNR, DINO, LPIPS, MSE against the source) quantify essentially the same deviation. Adding this terminal loss therefore forces the measured source-consistency improvement; it is an optimization objective, not an emergent or predicted property. The derivation from the cost to the Tweedie-gradient update is mathematically valid, so this is a mild by-construction element rather than a false equivalence of the whole method.

full rationale

The core of FlowAlign is an explicit optimal-control problem: minimize running cost (18) plus terminal cost m(x0)=η/2||x0-xsrc||^2. Proposition 1 solves this variational problem; solving a stated optimization problem is not circular, and the Hamiltonian/Lemma derivation is independent of the empirical claims. The only by-construction element is that the terminal loss literally measures distance to xsrc, so the later source-consistency gains (Table 1) are partly the objective being optimized, not an emergent discovery. The semantic-alignment, human-preference, and backward-editing results are not forced by this term and provide independent content. The approximation in Eq. (41)-(42) and the sign/coefficient mismatch between Eq. (21)/(24) and Algorithm 1 are correctness concerns, not circularity. No load-bearing self-citation chain exists: [1,6] are external textbooks, [28,29] are external groups, and the authors' self-citations [10,11,14,24] concern video/motion/score-distillation and do not carry the main argument. Overall, the paper would not reduce to its inputs by definition, so the score is low.

Assumptions & free parameters 4 free parameters · 3 assumptions · 0 invented entities

The method introduces no new physical entities. It relies on a pre-trained flow model and two scalar hyperparameters (ω, ζ). The main axiom is the constant-velocity approximation used to derive the correction term.

free parameters (4)
  • CFG scale ω = 10.0 (swept 5.0, 7.5, 10.0, 13.5)
    Controls guidance strength toward the target text in Eq. (23). Chosen empirically by balancing CLIP and background PSNR.
  • Source consistency scale ζ = 0.01
    Weights the term ζ(E[q0|qt]−E[p0|pt]) in Algorithm 1. Set after the ablation study where ζ=0.01 gave balanced performance.
  • Terminal regularization weight η = Not directly reported; absorbed into ζ via ζ=−γdt
    Appears in Proposition 1; the paper does not state a value for η, instead using ζ in the algorithm.
  • NFE (number of function evaluations) = 33
    Follows FlowEdit's setting; not tuned but affects run-time and quality.
assumptions (3)
  • ad hoc to paper First-order approximation: ∫_t^0 (vt(pt)−vt(qt))dt ≃ −t vt(pt)+t vt(qt)
    Used in the proof of Proposition 1 (Eq. 41-42). Assumes the velocity field is constant over the remaining interval, which is not justified and is load-bearing for the final source-consistency term.
  • domain assumption The pre-trained Stable Diffusion 3 flow model provides reliable Tweedie estimates E[q0|qt] = qt − t vt(qt) along the edited trajectories.
    The method relies on the validity of the flow-matching velocity as a denoiser at all timesteps.
  • domain assumption The optimal-control solution for an ideal deterministic ODE applies to the discrete-time algorithm with freshly sampled noise ϵ at each step.
    The derivation assumes a deterministic trajectory, but Algorithm 1 samples new ϵ per timestep; this gap is not addressed.

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Cite this review

Pith. "Pith review of FlowAlign: Trajectory-Regularized, Inversion-Free Flow-based Image Editing." pith.science (2026). https://pith.science/paper/Q6F5PTGB

@misc{pith2026250523145,
  author       = {Pith},
  title        = {Pith review of: FlowAlign: Trajectory-Regularized, Inversion-Free Flow-based Image Editing},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Q6F5PTGB}},
  note         = {Machine review of arXiv:2505.23145}
}
read the original 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 optimal control-based trajectory control. Specifically, FlowAlign 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 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.

Figures

Figures reproduced from arXiv: 2505.23145 by the authors.

Figure 1
Figure 1. Representative editing results produced by FlowAlign, where the red portion of the prompt [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Overview. (a) Starting from the inverted latent, the ODE from source to target images can be obtained. (b) In contrast, existing inversion-free approaches suffer from nonsmooth trajectories, as qt is sampled with random noise at each step, often resulting in editing artifacts. (c) FlowAlign uses the regularized velocity v x t from the similarity regularization at the terminal point, producing smoother and more consi… view at source ↗
Figure 3
Figure 3. Quantitative and human preference evaluation. (a) Trade-off between CLIP similarity versus background PSNR. (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 0 to emphasize directional preference. Across all comparisons, our method is preferred. 4 Experimental Results Dataset, Baselin… view at source ↗
Figures from the paper (13 more)
Figure 4
Figure 4. Figure 4: Qualitative comparison of text-based image editing methods. Insets provide zoomed-in [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Qualitative comparison of editing (odd columns) and backward editing (even columns) [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: Ablation study for ω and ζ. Top-left points represent to balanced performance. Ablation Study. The proposed method introduces two hyperparameters, ω and ζ, which control the relative strength of each regularization term in Eq. (22). These parameters govern the trade-of…
Figure 7
Figure 7. Figure 7: Editing results for (a) 3D Gaussian splatting rendered from four different viewpoints, and [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: User interface for AB-test. 1. Randomly select one sample from the 100-image pool. 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 instruct…
Figure 9
Figure 9. Figure 9: Additional qualitative comparison results. [PITH_FULL_IMAGE:figures/full_fig_p019_9.png]
Figure 10
Figure 10. Figure 10: Additional qualitative comparison results. [PITH_FULL_IMAGE:figures/full_fig_p020_10.png]
Figure 11
Figure 11. Figure 11: Ablation results for ζ. 21 [PITH_FULL_IMAGE:figures/full_fig_p021_11.png]
Figure 12
Figure 12. Figure 12: Additional results for video editing: texture change. [PITH_FULL_IMAGE:figures/full_fig_p022_12.png]
Figure 13
Figure 13. Figure 13: Additional results for video editing: object change. [PITH_FULL_IMAGE:figures/full_fig_p022_13.png]
Figure 14
Figure 14. Figure 14: Additional results for 3D editing [PITH_FULL_IMAGE:figures/full_fig_p023_14.png]
Figure 15
Figure 15. Figure 15: Video results of 3D editing. Click each image to play the video in Acrobat Reader. 23 [PITH_FULL_IMAGE:figures/full_fig_p023_15.png]
Figure 16
Figure 16. Figure 16: Qualitative image editing results using FLUX. [PITH_FULL_IMAGE:figures/full_fig_p024_16.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 5 Pith papers

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    h-Flow extends Doob's h-transform to deterministic rectified flows via an equivalent SDE, yielding closed-form reconstruction guidance plus orthogonal velocity editing for controllable text-based image editing.

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  3. Bridging the Manifold Gap: Riemannian Residual Line Search for One-Step Image Editing

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    Second-order curvature-corrected residual line search over energy-field transport candidates yields SOTA one-step text-guided image editing on PIE-Bench++.

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  5. FlowSteer: Conditioning Flow Field for Consistent Image Restoration

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    A sparse mid-to-late schedule of null-space fidelity updates lets a frozen text-to-image flow model restore images with high measurement consistency.

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    For inversion, we adopt the backward flow ODE

    DDIB [32] : 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...

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    timestep), and its performance can vary significantly depending on this choice

    SDEdit [21] : SDEdit requires specifying the initial SNR (i.e. timestep), and its 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 ...

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    We follow the official implementation, setting γ = 0.5, η = 0.9, the starting time s = 0, and the stopping time τ = 0.25

    RF-inversion [28] : RF-Inversion introduces an optimal-control-based guidance mechanism that ensures the inverted representation aligns with a target terminal state, resuling in a sampling process that is more likely under a predefined terminal distribution. We follow the offi...

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    Additionally, we solve the flow ODE starting from the 18th timestep out of 50, resulting in 33 ODE timesteps

    FlowEdit [16] : We follow the official implementation of FlowEdit, setting the CFG scale to 3.0 for the source direction and 13.5 for the target direction. Additionally, we solve the flow ODE starting from the 18th timestep out of 50, resulting in 33 ODE timesteps. Evaluation ...

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    Accordingly, we compute the PSNR by excluding the masked region, resulting in the background PSNR

    Background PSNR : PIEbench [ 13] provides masks that cover the object to be edited. Accordingly, we compute the PSNR by excluding the masked region, resulting in the background PSNR

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    Background LPIPS : We measure the LPIPS [ 2], which is defined as distance between feature maps of pre-trained VGG network, by excluding the masked region

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    Background SSIM : We compute the structural similarity [ 35] by excluding the masked region

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    Background MSE : we compute pixel-wise mean-squared-error by excluding the masked region

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    For the CLIP score within the edited region, we apply it only to the masked area

    CLIP-score : We report the similarity between features embedded by pre-trained CLIP [27]3 image encoder and text encoder. For the CLIP score within the edited region, we apply it only to the masked area. C Human preference test protocol To evaluate the quality of image editing...

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    Randomly select one sample from the 100-image pool

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    Randomly choose one baseline method from the four

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    Randomly assign the baseline and the proposed method to gruops A and B

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    Display AB-test user instruction with editing instruction, source image, and edited results from both methods

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    A is better

    The participant selects one of the following options: "A is better", "B is better", or "Not sure"

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    The participant clicks "Submit", and the response is recorded

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    Step 1-6 are repeated until 20 cases are completed

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    Not sure

    If more than half of the responses are "Not sure", an additional 5 comparisons is presented following the same protocol. Although the editing methods utilize source–target text pairs, we present the editing instructions from PIEBench to participants instead, aiming to improve ...

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.