cs.CVOct 21, 2026

ER-Chord: Spatially Consistent One-Step Image Editing via Equal-Energy Reliability Redistribution

Authors: Peize Li, Hanzhen Zhao, Xingguo Xu, Yilong Fan, Zhen Tao, Bo Yin, Zhifei Liu, Qingdong He, 

Organizations: National University of Singapore · Kuaishou Technology · Dalian University of Technology · Tianjin University · 

Read PDF
Ask AI
Cite

Copy citation

DOINot available for this paper

Abstract

One-step generative models enable fast text-guided image editing, yet they often introduce unintended changes to regions that should remain unchanged. Temporal aggregation stabilizes editing fields across noise levels, but leaves their spatial allocation insensitive to local variations in reliability. Consequently, temporal stability alone does not ensure spatially consistent editing. To address this lim- itation, we propose ER-Chord, a training-free and inversion-free framework for reliability-guided spatial redistribution. Our key insight is that agreement between editing fields at neighboring noise levels provides a local reliability signal for allocating editing strength. We formulate this allocation as an equal-energy op- timization that redistributes control energy according to local reliability while preserving the original editing directions and total control energy. This formu- lation admits a unique global solution that can be efficiently computed using existing field evaluations, requiring no additional denoiser calls. Experiments on two benchmarks, PIE-Bench and TEdBench, demonstrate improvements over state-of-the-art one-step editing baselines, achieving superior source preservation alongside consistent gains across multiple generative backbones.The project page is at https://github.com/Peizeli1/ER-Chord.

Figures & tables

Figure 1: Method overview. Starting from a temporally aggregated control field, ER-Chord measures local endpoint consistency and redistributes a fixed control energy budget while preserving local directions. The framework requires no auxiliary guidance, training, inversion, additional denoiser evaluations, or backpropagation.
Figure 2: Temporal vs. spatial control in one-step editing. (a) ChordEdit temporally aggregates endpoint fields with uniform weights across space, which fails to reflect local differences in prediction consistency and disperses edit energy into irrelevant backgrounds. (b) ER-Chord measures local endpoint consistency as a reliability signal and redistributes control energy ( uER(p)=mpuC(p)u_{\mathrm{ER}}(p)=m_{p}u_{\mathrm{C}}(p) ) under an exact conserved energy budget ( ∥uER∥F2=∥uC∥F2\|u_{\mathrm{ER}}\|_{F}^{2}=\|u_{\mathrm{C}}\|_{F}^{2} ), concentrating updates onto semantically intended target regions without background artifacts.
Figure 3: Spatial energy redistribution under conserved total energy. Under identical conserved control energy ( 1.00×1.00\times ), ChordEdit disperses energy into backgrounds causing artifacts, while ER-Chord concentrates energy on target regions for clean edits.
  Background PreservationTarget AlignmentPropertiesEfficiency
TypeMethodPSNR ↑\uparrowMSE ↓\downarrowLPIPS ↓\downarrowWhole ↑\uparrowEdit ↑\uparrowT-freeI-freeSteps ↓\downarrowNFE ↓\downarrowTime(s) ↓\downarrowVRAM(M) ↓\downarrow
Multi-stepDDIM + MasaCtrl (2023)21.258.58106.5924.1321.13✓✗5010055.2012272
Direct Inv. + MasaCtrl (2023)21.787.9987.3824.4221.38✓✗5010079.1012272
DDIM + PnP (2023)21.268.42113.5825.4522.54✓✗5010028.019262
Direct Inv. + PnP (2023)21.438.10106.2625.4822.63✓✗5010028.039262
FlowEdit (SD3) (2025)22.177.69104.8126.6423.69✓✓33337.2217140
Table 1: Editing results on PIE-Bench ( Ju et al., 2024 ) . MSE and LPIPS are scaled by 10310^{3} . Best, second-best, and third-best results are highlighted with green , yellow , and purple backgrounds, respectively. T-/I-free: training-/inversion-free. Extended metrics appear in Appendix D .
Figure 4: Qualitative comparison on PIE-Bench. Real images are in the first column. Multi-step, few-step, and one-step methods are arranged horizontally. Prompts are noted under each row. ChordEdit and ER-Chord use the identical SD-Turbo backbone.
Table 6
BackboneMethodPSNR ↑\uparrowCLIP-Edited ↑\uparrow
InstaFlowNaive22.0520.19
ChordEdit23.0521.39
ER-Chord (Ours)23.4021.54
SwiftBrush-v2Naive20.5221.06
ChordEdit22.0422.58
ER-Chord (Ours)22.4822.74
Table 4: Cross-backbone generalization. Results across backbones. Bold: best per backbone.
Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

CertificateMeasured (required)
Active samples ( EC>εEE_{\mathrm{C}}>\varepsilon_{E} )700 of 700
Dual root η∗\eta^{*} (mean; min; max)−0.012-0.012 ; −0.155-0.155 ; −0.001-0.001 (within [−0.25,0][-0.25,0] )
Normalized dual residual rϕr_{\phi} (max)4.1×10−74.1\times 10^{-7} ( ≤10−6\leq 10^{-6} )
Relative energy residual rEr_{E} (max)5.3×10−75.3\times 10^{-7}
Normalized KKT residual (max)2.8×10−82.8\times 10^{-8} ( ≤10−6\leq 10^{-6} )
Multiplier range (min; max)0.8010.801 ; 1.1831.183 (within [0.8,4/3][0.8,4/3] )
Appendix
Table 5: Solver checks on PIE-Bench (700 examples, seed 42). Residuals, multiplier bounds, direction preservation, and the mismatch inequality are computed on the realized ER-Chord field after dtype conversion.
Figure 5: Additional qualitative comparison on PIE-Bench (Part 1). Extended visual comparisons across representative categories under matched random seeds, supplementing Figure 4 .
Figure 6: Additional qualitative comparison on PIE-Bench (Part 2). Extended visual comparisons across representative categories under matched random seeds, supplementing Figure 4 .
MetricChordEditER-Chord
PSNR ↑\uparrow (dB)22.2022.77
MSE ↓\downarrow ( ×10−3\times 10^{-3} )6.846.35
SSIM ↑\uparrow ( ×10−2\times 10^{-2} )75.9176.87
LPIPS ↓\downarrow ( ×10−3\times 10^{-3} )128.25120.23
Structure dist. ↓\downarrow ( ×10−3\times 10^{-3} )16.5815.44
CLIP-Whole ↑\uparrow25.5825.74
Appendix
Table 6: Additional PIE-Bench metrics (700 examples, seed 42). ChordEdit values reproduce the extended metrics in Lu et al. (2026) . MSE, LPIPS, and structure distance are scaled by 10310^{3} , and SSIM is reported as a percentage, following the source table. Bold denotes the better result.
More in this topic

Image Editing

Image editing changes selected visual content while preserving the parts of an image that should remain unchanged.

See all 313 papers

Explore similar work

CardsList
Feb 22, 2026

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

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.

Liangsi Lu, Xuhang Chen, Minzhe Guo +3

Guangdong University of Technology · Huizhou University · Shenzhen University +1

Text-Guided Image EditingDiffusion-Based Image EditingT2I Diffusion ModelsOne-Step Generative Modeling
AskPDF
Jun 12, 2026

Rethinking One-Step Image Editing through ChordEdit: Reproduction, Simplification, and New Insights

One-step image editing is important for making text-guided editing fast, practical, and easy to deploy, but its underlying mechanism is still not fully understood. We revisit ChordEdit through reproduction, ablation, and simplification. Our analysis shows that a) the chord window δδ largely acts as an effective timestep shift from tt to t−δt - δ; b) chord transport acts on high-noise images and mainly performs low-frequency semantic editing; and c) proximal alignment acts on low-noise images and complements it by adding high-frequency target details. In this view, ChordEdit naturally decomposes editing into a coarse low-frequency transport stage and a fine high-frequency alignment stage. These findings suggest a path toward prompt-conditioned dynamic timestep selection for adaptive image editing. All code and results can be found at link.

Minghan Li, Jeremy Moebel, Mengyu Wang

Harvard AI and Robotics Lab

Text-Guided Image EditingOne-Step Generative ModelingDiffusion-Based Image EditingImage Editing
AskPDF
Aug 1, 2026

ChordVideo: One-Step, Training-Free, Temporally Consistent Video Editing via Low-Energy Transport

One-step text-to-image models enable training-free, inversion-free editing with only 1--2 network function evaluations (NFE), while ChordEdit stabilizes such edits through low-energy smoothing along sampling time. Applied independently to video frames, however, it produces temporal flicker and edit-strength drift. We introduce ChordVideo, which extends the same low-energy principle to video time through shared noise, motion-aligned causal aggregation of per-frame Chord fields, and an optional temporally smoothed proximal correction. We derive a warping-error bound that separates motion bias from stochastic flicker and predicts diminishing returns with larger temporal windows. On TGVE/DAVIS with two one-step backbones, ChordVideo reduces warping error by 78% and flicker by 49%, improves CLIP frame consistency by 9--10 points, and increases background PSNR by about 1.5,dB, while retaining 2 NFE/frame. Compared with seven multi-step editors, it achieves competitive temporal consistency and source preservation using \textbf{10--60×\times fewer model steps per clip

Zhiqiang Lao

Independent Researcher

Video EditingDiffusion ModelsDiffusion-Based Video Editing
AskPDF