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ChordEdit: One-Step Low-Energy Transport for Image Editing

Liangsi Lu, Xuhang Chen, Minzhe Guo, Shichu Li, Jingchao Wang, Yang Shi

arXiv:2602.19083v2cs.CV

TL;DR

One-step T2I models make real-time synthesis possible, but existing training-free editors become unstable in one-step image editing, causing distortion and background inconsistency. ChordEdit reframes editing as dynamic optimal transport and smooths observable drift differences into a low-energy Chord Control Field. It achieves real-time, high-fidelity editing with strong preservation and semantic alignment while remaining training-free, inversion-free, and model-agnostic.

  • Problem

    Training-free text-guided editors fail in one-step models because naive drift differences produce severe object distortion and loss of non-edited-region consistency.

  • Method

    ChordEdit uses dynamic optimal transport to construct a temporally smoothed, low-energy Chord Control Field from source and target observable drifts.

  • Results

    ChordEdit achieves state-of-the-art efficiency while maintaining high background preservation and semantic fidelity, with a reported runtime of 0.38s.

  • Takeaways & Limitations

    The framework enables true real-time, high-fidelity one-step editing without model-specific training, inversion, or protective masking.

  • Takeaways & Limitations

    The method models the observable field as the true editing field corrupted by a zero-mean noise term.

Abstract

from arXiv · show

The advent of one-step text-to-image (T2I) models offers unprecedented synthesis speed. However, their application to text-guided image editing remains severely hampered, as forcing existing training-free editors into a single inference step fails. This failure manifests as severe object distortion and a critical loss of consistency in non-edited regions, resulting from the high-energy, erratic trajectories produced by naive vector arithmetic on the models' structured fields. To address this problem, we introduce ChordEdit, a model agnostic, training-free, and inversion-free method that facilitates high-fidelity one-step editing. We recast editing as a transport problem between the source and target distributions defined by the source and target text prompts. Leveraging dynamic optimal transport theory, we derive a principled, low-energy control strategy. This strategy yields a smoothed, variance-reduced editing field that is inherently stable, facilitating the field to be traversed in a single, large integration step. A theoretically grounded and experimentally validated approach allows ChordEdit to deliver fast, lightweight and precise edits, finally achieving true real-time editing on these challenging models.

1. Introduction

One-step T2I models offer real-time synthesis, but training-free editing fails under single-step inference because naive drift differences distort edited objects and disrupt backgrounds. ChordEdit addresses this with a low-energy, smoothed control field for high-fidelity, efficient editing.

  • One-step T2I models provide unprecedented synthesis speed and motivate real-time text-guided image editing.
  • Training-free simple-drift editing fails in one-step models through severe object distortion and loss of non-edited-region consistency.
  • ChordEdit recasts editing as dynamic optimal transport and replaces erratic drift differences with a time-weighted Chord Control Field.
  • The resulting low-energy field supports a single large integration step and optional proximal refinement for stronger target semantics.
  • ChordEdit demonstrates state-of-the-art efficiency while maintaining high background preservation and semantic fidelity on PIE-bench.

2. Related Work

Existing fast image editors commonly rely on iterative inversion or few-step acceleration, limiting real-time interaction. One-step editing remains difficult because training-free differential fields collapse at single-step inference, while trained inversion networks sacrifice model-agnostic flexibility.

  • Prior diffusion and flow-based editors often require iterative multi-step inversion or few-step acceleration, making real-time interaction infeasible.
  • Training-free differential editors are stable when averaged over multiple steps but collapse in the single-step limit because of high energy and variance.
  • SwiftEdit achieves one-step performance with a dedicated inversion network but sacrifices model-agnostic flexibility.

3. Preliminaries

The paper models a pre-trained T2I system as a conditional probability flow and formulates editing as transport from a source-conditioned image state to a target-conditioned state. Because arbitrary intermediate states are inaccessible, observable fields are estimated from noisy proxies and prompt-conditioned residuals.

  • A pre-trained T2I model induces a conditional probability flow with drift v(x_t,t,c), where x_t is the image state and c is the text condition.
  • Editing transports a source image sampled under c_src to a target image sampled under c_tar by modifying the source flow with an instantaneous residual.
  • The ideal editing field aligns the source and target conditional dynamics in continuous time.
  • Because arbitrary-time states are unavailable, ChordEdit queries a synthetic noisy proxy and forms a target-minus-source observable residual through a time-only linear map.
  • The observable formulation applies to drift, noise-prediction, velocity, score-to-drift, x0, and consistency parameterizations through suitable time-only linear maps.

4. ChordEdit

ChordEdit treats one-step editing as low-energy transport estimation: it smooths noisy observable residuals into a stable Chord Control Field that can be integrated once. The resulting pipeline is lightweight, model-agnostic, and optionally refines target semantics after transport.

  • 4. ChordEdit: ChordEdit combines dynamic optimal transport with observable model fields to estimate a low-energy control field for stable one-step editing.
  • 4.1. OT View: Editing as an Estimation Problem: The ideal transport field is inaccessible, while directly using the noisy observable field is unstable for single-step integration.
  • 4.2. Chord Control: A Low-Energy Local Estimator: ChordEdit estimates a locally smoothed field by minimizing a strictly convex quadratic surrogate over a short temporal window.
  • 4.2. Chord Control: A Low-Energy Local Estimator: The practical Chord Control Field uses causal temporal averaging of observable fields at t and t−δ, producing a one-sided kernel smoothing of the naive field.
  • 4.2. Chord Control: A Low-Energy Local Estimator: Temporal averaging contracts field, time-derivative, and spatial-gradient norms, suppressing high-energy spikes and tightening explicit-Euler stability.
  • 4.2. Chord Control: A Low-Energy Local Estimator: The chord field satisfies C_cho ≤ C_nai, reducing local truncation error and improving the stability margin for a one-step integration.
  • 4.3. Proximal Refinement: An optional single forward-pass proximal refinement amplifies target semantics without reinversion and remains separate from transport energy measurements.
  • 4.4. Algorithm: The default single-noise implementation computes all intermediate variables in parallel, rendering transport 1-NFE.

5. Experiments

ChordEdit is evaluated on PIE-bench using background-fidelity and semantic-alignment metrics, with quantitative and qualitative comparisons against prior editors. The results emphasize fast, high-fidelity editing with preserved non-edited regions.

  • Experimental Setup: PIE-bench contains 700 512×512 editing examples across 10 categories, evaluated for background fidelity and semantic alignment.Background fidelity uses PSNR and MSE on non-edited regions.
  • Quantitative Results: ChordEdit achieves state-of-the-art efficiency while preserving competitive editing quality, including less than half SwiftEdit’s VRAM use.It is also reported as 19× faster than FlowEdit and over 208× faster than Direct Inversion.
  • One-Step Editing: At NFE=1, transport-only ChordEdit achieves high PSNR, while optional proximal refinement further improves semantic alignment.The full method balances transport stability with semantic enhancement without model-specific training, inversion, or protective masking.
  • Qualitative Results: Qualitative comparisons show prompt-faithful edits with strong background preservation and fewer artifacts or identity failures than competing methods.A user study reports preferences of 42.5% for editing semantics and 48.3% for background preservation.
  • Qualitative Results: Energy visualizations associate the naive field’s high energy with artifacts and background corruption, whereas ChordEdit produces a stable low-energy field.The comparisons use SwiftBrush-v2 and SD-Turbo results.

6. Ablation Study

Ablations show that ChordEdit’s temporal smoothing stabilizes one-step transport, single-noise operation is sufficient, and proximal refinement separates consistency from semantic amplification. The method also improves results across tested T2I models.

  • Chord Control Field: As integration steps approach one, the naive field’s energy spikes and PSNR collapses, while ChordEdit remains stable and Pareto-dominates the naive baseline.The comparison uses δ=0 for the naive baseline and δ=0.15 for ChordEdit.
  • Noise Samples: Increasing noise samples produces negligible marginal returns for ChordEdit, whose n=1 Pareto front remains nearly unchanged through n=4.Figure 10 qualitatively confirms the same pattern.
  • Noise Samples: ChordEdit’s single-noise configuration remains stable and Pareto-dominates the naive baseline even when the naive method uses four samples.The results attribute this behavior to geometric control and intrinsic variance reduction.
  • Transport and Refinement: The Chord field prioritizes consistency with 23.89 PSNR, while proximal refinement raises CLIP-Edited from 21.87 to 22.96.This ablation separates high-fidelity transport from semantic amplification.
  • Model Agnosticism: On SD-Turbo, ChordEdit improves PSNR from 21.38 to 22.20 and CLIP-Edited from 21.96 to 22.96 over the naive baseline.Table 3 reports consistent improvement across tested models.

7. Conclusion

ChordEdit addresses one-step editing instability with a low-energy Chord Control Field and achieves fast, high-fidelity, consistent editing. Its reported performance is model-agnostic and seed-insensitive, including with one noise sample.

  • Conclusion: ChordEdit replaces the naive high-energy drift difference with a temporally smoothed Chord Control Field that enables a single large integration step.The field preserves non-edited regions while maintaining semantic alignment.
  • Conclusion: ChordEdit achieves 0.38s runtime and low VRAM use while maintaining high fidelity and strong semantic alignment.The conclusion reports these results alongside comparisons with naive and other one-step methods.
  • Conclusion: The method remains robust across models and seeds, even with a single noise sample, supporting real-time high-fidelity editing.The stated scope is generative image editing for creative and assistive applications.

Supplementary Material

The supplementary material situates ChordEdit among editing methods, formalizes its optimal-transport formulation, and derives a model-agnostic observable-to-velocity mapping. The derivation uses local observability, short-window homogeneity, and a recursive energy prior.

  • Related Work: Prior editing methods trade off inversion, training, or multiple inference steps, while ChordEdit targets training-free, inversion-free, single-step editing.Fast one-step T2I backbones provide the foundation but have nonlinear dynamics that complicate control.
  • Our Method: ChordEdit constructs a control field in the observable residual domain to average and stabilize the high-energy signal.The field is paired with proximal refinement.
  • Optimal-Transport Formulation: The formulation treats ut as the complete vector field transporting the source density ρ1 to the target density ρ0.No reference flow or additive residual field is introduced.
  • Estimator Derivation: The causal estimator combines noisy local measurements, short-window homogeneity, and a recursive quadratic energy prior.Under these assumptions, the closed-form estimator is exact before first-order online approximations.
  • Estimator Derivation: The online approximation has O(δ) error under standard smoothness, while measurement noise enters through the observable surrogate.Density-weighted effective durations can replace scalar time weights without changing the closed form.
  • Model-Agnostic Mapping: A linear time-dependent map Bt converts model outputs into a unified velocity domain, with shared-noise residuals enforcing a fixed noisy state.The supplementary derivations cover noise-, velocity-, x0-, and v-prediction parameterizations.

C.5. Implementation and Numerical Stability

The implementation approximates continuous-time derivatives with first-order finite differences and avoids numerical instability near t ≈ 1 by querying times bounded away from that endpoint.

  • Implementation: Continuous-time derivatives ˙α(t) and ˙σ(t) are approximated using first-order finite differences.For example, ˙α(t) ≈ (α(t) − α(t − δ))/δ.
  • Numerical Stability: Maps containing α(t) in the denominator become numerically unstable as α(t) approaches zero near t ≈ 1.This instability affects maps such as A(ϵ)_t and threatens numerical conditioning near the endpoint.
  • Numerical Stability: ChordEdit queries the field at t and t − δ values bounded away from t = 1, keeping α(t) nonnegligible and B_t well-conditioned.An example uses t = 0.90 and δ = 0.15.

D. Energy Contraction Property of the Chord Control Field

The Chord Control Field is theoretically shown to reduce or preserve energy and consistency error through temporal smoothing. Experiments further report improved stability, risk, and performance trade-offs relative to the naive field.

  • Theoretical energy contraction: Temporal smoothing by convolution makes the Chord Control Field an L2-energy contraction of the observable proxy field.The contraction applies to the total Benamou–Brenier kinetic energy and can be strict for non-degenerate smoothing kernels.
  • Theoretical energy contraction: The chord field generates a dynamic flow with strictly lower or equal kinetic energy than the naive proxy field.This follows from convex averaging and Jensen’s inequality applied to the estimator.
  • Numerical error and stability: Ccho ≤ Cnai, so the chord-controlled path has a global error bound no larger than the naive path for the same step size.The result follows from contraction of field magnitude and consistency terms while preserving the same explicit-Euler stability condition.
  • Risk reduction: For an appropriately chosen non-degenerate kernel, the chord estimator achieves strictly lower risk than the naive estimator.The smoothing trades bias against variance, with the risk bound combining an O(δ2) bias contribution and an O(δ−1)σ2 variance contribution.
  • Empirical validation: ChordEdit’s smoothed field remains stable as the step count approaches one and strictly Pareto-dominates the naive baseline across reported trade-off spaces.The reported comparisons cover semantic alignment alongside structural or background preservation, while increasing Monte Carlo samples provides negligible marginal returns for ChordEdit.

F.3. Analysis of Temporal Parameters and Step Scale

The analysis shows predictable trade-offs among temporal parameters, smoothing, and step scale: stronger semantics generally reduce background preservation, while temporal smoothing improves preservation and can improve semantics at moderate values.

  • Analysis of Chord Time t: Increasing chord time t generally strengthens CLIP-Edited alignment but slightly reduces background fidelity.The reported comparison spans t values such as 0.80 to 1.00.
  • Analysis of Chord Time t: The t = 0.90 setting provides a robust balance between semantic strength and preservation.
  • Analysis of Refinement Time tc: Increasing proximal refinement time tc monotonically improves CLIP alignment while increasing LPIPS distortion.The reported sweep increases tc from 0.1 to 0.5.
  • Analysis of Refinement Time tc: The tc = 0.30 default strengthens the target semantic while limiting the refinement’s fidelity cost.The analysis describes higher tc as more prone to overediting non-target regions.
  • Joint Analysis of δ and λ: Across preservation metrics, the naive δ = 0 baseline is worst, while increasing δ monotonically improves LPIPS, MSE, SSIM, and PSNR.
  • Joint Analysis of δ and λ: Increasing λ directly strengthens semantic alignment at the expected cost of decreased background fidelity, producing a predictable control trade-off.

G. More Quantitative Results

Additional quantitative and qualitative analyses support ChordEdit’s stability, efficiency, and model-agnostic behavior, while also identifying practical societal and misuse boundaries.

  • Quantitative validation: ChordEdit consistently outperforms the naive field in structural and perceptual fidelity across three fast generative models.The comparison covers InstaFlow, SwiftBrush-v2, and SD-Turbo using structural and perceptual metrics.
  • Quantitative validation: The Chord Control Field preserves background consistency across pixel-space PSNR, structural SSIM, and deep-feature LPIPS measures.
  • Transport and refinement: NFE=1 transport prioritizes fidelity, whereas NFE=2 refinement provides stronger overall semantic alignment.The framework separates consistency-preserving transport from semantic-boosting proximal refinement.
  • User control: The step scale λ controls edit strength, with larger values producing progressively stronger target semantics.
  • Societal impacts: High-fidelity real-time editing can make deceptive content and misinformation more convincing.The authors identify misuse as a risk of realistic, structurally consistent edits.

J. User Study

The user study used randomized blind comparisons to evaluate semantic alignment and preservation quality, with ChordEdit receiving the strongest reported human preference in both criteria.

  • Study design: The study recruited 150 participants for randomized four-way blind comparisons of ChordEdit, InfEdit, FlowEdit, and SwiftEdit.Participants viewed the original image, prompt, and four edited results.
  • Study design: Participants judged semantic alignment and preservation quality, including naturalness, background preservation, and artifacts.
  • Results: The study collected 4,500 votes for each criterion and found a clear preference for ChordEdit.The total equals 150 participants × 30 prompts for each criterion.
  • Results: ChordEdit received 42.5% of semantic-alignment preferences, ahead of FlowEdit at 25.3%, InfEdit at 19.6%, and SwiftEdit at 12.6%.
  • Results: ChordEdit received 48.3% of preservation-quality preferences, exceeding InfEdit’s 35.4%, FlowEdit’s 7.1%, and SwiftEdit’s 9.2%.The study reports artifacts and distortion as reasons other methods were penalized.
  • Conclusion: ChordEdit was the only method to rank first in both semantic alignment and preservation quality.
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