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

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

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 ·

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 ( $u_{\mathrm{ER}}(p)=m_{p}u_{\mathrm{C}}(p)$ ) under an exact conserved energy budget ( $\|u_{\mathrm{ER}}\|_{F}^{2}=\|u_{\mathrm{C}}\|_{F}^{2}$ ), concentrating updates onto semantically intended target regions without background artifacts.

Figure 3: Spatial energy redistribution under conserved total energy. Under identical conserved control energy ( $1.00\times$ ), ChordEdit disperses energy into backgrounds causing artifacts, while ER-Chord concentrates energy on target regions for clean edits.

		Background Preservation			Target Alignment		Properties		Efficiency
Type	Method	PSNR $\uparrow$	MSE $\downarrow$	LPIPS $\downarrow$	Whole $\uparrow$	Edit $\uparrow$	T-free	I-free	Steps $\downarrow$	NFE $\downarrow$	Time(s) $\downarrow$	VRAM(M) $\downarrow$
Multi-step	DDIM + MasaCtrl (2023)	21.25	8.58	106.59	24.13	21.13	✓	✗	50	100	55.20	12272
	Direct Inv. + MasaCtrl (2023)	21.78	7.99	87.38	24.42	21.38	✓	✗	50	100	79.10	12272
	DDIM + PnP (2023)	21.26	8.42	113.58	25.45	22.54	✓	✗	50	100	28.01	9262
	Direct Inv. + PnP (2023)	21.43	8.10	106.26	25.48	22.63	✓	✗	50	100	28.03	9262
	FlowEdit (SD3) (2025)	22.17	7.69	104.81	26.64	23.69	✓	✓	33	33	7.22	17140

Table 1: Editing results on PIE-Bench ( Ju et al., 2024 ) . MSE and LPIPS are scaled by

10^{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

Backbone	Method	PSNR $\uparrow$	CLIP-Edited $\uparrow$
InstaFlow	Naive	22.05	20.19
	ChordEdit	23.05	21.39
	ER-Chord (Ours)	23.40	21.54
SwiftBrush-v2	Naive	20.52	21.06
	ChordEdit	22.04	22.58
	ER-Chord (Ours)	22.48	22.74

Table 4: Cross-backbone generalization. Results across backbones. Bold: best per backbone.

Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

Certificate	Measured (required)
Active samples ( $E_{\mathrm{C}}>\varepsilon_{E}$ )	700 of 700
Dual root $\eta^{*}$ (mean; min; max)	$-0.012$ ; $-0.155$ ; $-0.001$ (within $[-0.25,0]$ )
Normalized dual residual $r_{\phi}$ (max)	$4.1\times 10^{-7}$ ( $\leq 10^{-6}$ )
Relative energy residual $r_{E}$ (max)	$5.3\times 10^{-7}$
Normalized KKT residual (max)	$2.8\times 10^{-8}$ ( $\leq 10^{-6}$ )
Multiplier range (min; max)	$0.801$ ; $1.183$ (within $[0.8,4/3]$ )

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 .

Metric	ChordEdit	ER-Chord
PSNR $\uparrow$ (dB)	22.20	22.77
MSE $\downarrow$ ( $\times 10^{-3}$ )	6.84	6.35
SSIM $\uparrow$ ( $\times 10^{-2}$ )	75.91	76.87
LPIPS $\downarrow$ ( $\times 10^{-3}$ )	128.25	120.23
Structure dist. $\downarrow$ ( $\times 10^{-3}$ )	16.58	15.44
CLIP-Whole $\uparrow$	25.58	25.74

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

10^{3}

, and SSIM is reported as a percentage, following the source table. Bold denotes the better result.

Image Editing

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

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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.

Abstract

Image Editing

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