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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, Xiaobin Hu

arXiv:2610.29248v1cs.CV

TL;DR

One-step editing must introduce requested semantics while preserving the source, but temporal aggregation leaves spatial allocation insensitive to local reliability. ER-Chord redistributes a fixed control-energy budget according to endpoint consistency while preserving local directions. The paper reports improved source preservation alongside target alignment across the tested benchmarks and backbones.

  • Problem

    Temporal aggregation stabilizes editing fields but does not account for spatial differences in endpoint agreement, leaving spatial magnitude allocation unresolved.

    Source: §1 · pp. 1–3

  • Method

    ER-Chord uses endpoint consistency as a local reliability signal to redistribute a fixed control-energy budget while preserving the original editing directions.

    Source: §1 · p. 2, §3.2 · p. 5

  • Results

    Across PIE-Bench, TEdBench, and three generative backbones, ER-Chord improves source preservation while maintaining target alignment in the tested settings.

    Source: §1 · p. 3, §5 · p. 10

  • Takeaways & Limitations

    The results suggest that spatial allocation is a useful complement to temporal stabilization.

    Source: §1 · p. 3, §5 · p. 10

Abstract

from arXiv · show

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.

1 INTRODUCTION

One-step editing must make semantic changes while preserving the source, but temporal aggregation does not account for spatial differences in endpoint reliability. ER-Chord reallocates a fixed control-energy budget using endpoint consistency, and the reported results show improved source preservation across benchmarks and backbones.

1 INTRODUCTION

  • Temporal aggregation applies spatially uniform weights, so it can send large updates into unedited backgrounds despite local differences in endpoint agreement.The authors identify spatial magnitude allocation as an unresolved issue: temporal stability alone does not ensure spatial consistency.Source: §1 · pp. 1–3
  • Unlike localization methods, ER-Chord uses endpoint agreement to adjust the strength of existing editing directions, not to identify where an edit should occur.The paper distinguishes reliability-guided magnitude allocation from a spatial localization map.Source: §1 · p. 2
  • At identical total control energy, ER-Chord concentrates updates in semantically consistent regions, whereas ChordEdit disperses energy into irrelevant backgrounds.The overview depicts reliability-guided redistribution of the temporally aggregated field while retaining local directions and requiring no additional denoiser evaluations.Source: §1 · pp. 2–3, Figure 1 · p. 2, Figure 2 · p. 3
  • ER-Chord uses endpoint consistency as a reliability signal to reallocate control energy while preserving local directions and the total energy budget.The allocation is formulated as an equal-energy optimization with a unique global solution found through a one-dimensional scalar root.Source: §1 · pp. 2–3
  • Across PIE-Bench, TEdBench, and three generative backbones, ER-Chord improves source preservation while maintaining semantic edit fidelity.The method uses the same denoiser budget as the baselines and requires no additional denoiser calls.Source: §1 · pp. 2–3

2 RELATED WORK

Prior real-image and accelerated editors modify inversion paths, model features, attention, or spatial masks to support fidelity or localization. ER-Chord instead leaves the one-step temporal estimator intact and reallocates the field's spatial magnitudes; the paper illustrates this contrast under conserved energy.

2 RELATED WORK

  • Real-image editing methods commonly improve fidelity by modifying inversion paths, internal features, or spatial masks, whereas ER-Chord changes only local field magnitudes.The related-work discussion covers approaches such as attention control, feature reuse, and inversion methods.Source: §2 · p. 4
  • ER-Chord leaves ChordEdit's temporal estimator and cleanup unchanged, adding spatial magnitude redistribution without extra model evaluations.ChordEdit aggregates fields across nearby noise levels; other accelerated approaches include specialized inversion, learned inversion, and inversion-free transport.Source: §2 · p. 4
  • Localization methods identify where an edit should occur; ER-Chord instead rescales fixed local Chord directions under an unchanged per-image energy budget.The cited approaches use semantic or structural evidence to identify editable regions.Source: §2 · p. 4
  • Under identical conserved control energy, ChordEdit disperses energy into backgrounds while ER-Chord concentrates it on target regions.The figure caption associates background dispersion with artifacts and target concentration with clean edits.Source: Figure 3 · p. 4

3 METHOD

ER-Chord separates temporal stabilization from spatial magnitude allocation, using endpoint consistency to redistribute control energy while preserving Chord directions and total strength. A unique global solution reduces the coupled allocation to a shared scalar solve.

3.1 FROM TEMPORAL AGGREGATION TO SPATIAL ALLOCATION

  • ChordEdit’s global temporal mixing stabilizes each location’s editing vector but does not explicitly account for differences in endpoint agreement across locations.ER-Chord retains the temporally aggregated directions and treats their spatial magnitudes as the remaining degree of freedom.Source: §3.1 · p. 5

3 METHOD

  • ER-Chord uses local endpoint consistency to reallocate spatial magnitudes while preserving Chord directions and total pre-cleanup control energy.The fixed energy budget prevents improved source preservation from coming simply from globally weakening the edit.Source: §3.2 · p. 5, §3.1 · p. 5

3.2 RELIABILITY-GUIDED EQUAL-ENERGY REDISTRIBUTION

  • The redistribution penalizes control magnitude more at locations with lower endpoint consistency, while the equality constraint keeps total pre-cleanup energy unchanged.Any energy reduction in one subset of locations must be compensated elsewhere.Source: §3.2 · pp. 5–6

3.3 SCALAR-ROOT SOLUTION AND PROPERTIES

  • A unique global minimizer reduces the coupled allocation to a one-dimensional scalar solve that rescales each Chord vector without changing its direction.The local consistency scores determine spatial penalties, while a shared scalar enforces the energy budget; higher-consistency locations receive larger multipliers than lower-consistency locations.Source: §3.3 · p. 6
  • The scalar can be found by bisection using existing endpoint fields, with no additional denoiser evaluations.The additional computation consists of channel reductions and element-wise arithmetic.Source: §3.3 · pp. 6–7

4 EXPERIMENTS

The experiments compare ER-Chord with ChordEdit on PIE-Bench and TEdBench, then test ablations, backbone transfer, and computational cost. ER-Chord improves source-preservation and semantic-alignment metrics in the reported evaluations.

4.1 EVALUATION PROTOCOL

  • The evaluation uses PIE-Bench's 700 masked examples across ten categories and TEdBench's 100 real-image examples, with paired ChordEdit comparisons under identical inputs and settings.PIE-Bench reports background-preservation and semantic-alignment metrics; TEdBench reports source-preservation, text-image, and directional-similarity metrics.Source: §4.1 · p. 7

4.2 COMPARISON ON PIE-BENCH

  • On all 700 PIE-Bench examples, ER-Chord raises unedited-region PSNR from 22.20 to 22.77 dB and CLIP-Edited from 22.96 to 23.16.It also lowers MSE from 6.84 to 6.35 and LPIPS from 128.25 to 120.23 (103× scaling); both methods have equal total pre-cleanup control energy.Source: §4.2 · p. 8
  • In the PIE-Bench examples, ER-Chord produces cleaner target edits while retaining more background than ChordEdit and several multi-step and few-step editors.The qualitative comparison includes sofa and mountain-to-building transformations.Source: §4.2 · p. 8

4.3 ABLATIONS, CROSS-BACKBONE TRANSFER, AND EFFICIENCY

  • Without cleanup, ER-Chord improves PSNR from 23.89 to 24.31 dB and CLIP-Edited from 21.87 to 21.99 over the raw Chord field.With cleanup, PSNR is 22.77 versus 22.20 dB and CLIP-Edited is 23.16 versus 22.96; the passage describes cleanup as complementing transport.Source: §4.3 · p. 9
  • Spatially permuting ER-Chord's optimal multipliers drops PSNR to 21.05 dB, while Reweight-and-Normalize reaches 22.40 dB versus ER-Chord's 22.77 dB.The permutation result supports matching multipliers to their original spatial locations.Source: §4.3 · p. 9
  • For TEdBench, ER-Chord lowers LPIPS from 0.21 to 0.20 and raises CLIP-I from 0.91 to 0.92 versus ChordEdit.The evaluation uses 100 diverse real-image editing cases and reports improvements over listed multi-step and optimization-based baselines using one transport update.Source: §4.3 · p. 9
  • Across InstaFlow, SwiftBrush-v2, and SD-Turbo, ER-Chord improves PSNR over ChordEdit by +0.35 dB, +0.44 dB, and +0.57 dB, respectively.CLIP-Edited also improves on all three tested backbones, using fixed hyperparameters (µ, κ) = (0.25, 1.0).Source: §4.3 · p. 9
  • ER-Chord adds no network evaluations relative to ChordEdit; the full pipeline takes 0.37 s/image versus 0.38 s/image and uses the same 6988 MiB peak memory.The pipeline uses NFE = 2 with cleanup and NFE = 1 without cleanup; scalar bisection takes less than 0.01 s CPU time.Source: §4.3 · p. 9

5 CONCLUSION

The conclusion presents ER-Chord as a way to allocate editing strength spatially using endpoint agreement while preserving local directions and total pre-cleanup energy. The reported experiments show improved source preservation alongside target alignment in tested settings, while the approach depends on the underlying field's directions.

5 CONCLUSION

  • ER-Chord uses endpoint agreement to redistribute control energy under an exact pre-cleanup energy constraint, preserving local directions with a unique scalar-root solution and no additional denoiser evaluations.The conclusion reports improved source preservation alongside target alignment on PIE-Bench, TEdBench, and three tested backbones.Source: §5 · p. 10
  • Because ER-Chord rescales the Chord field without changing local directions, it cannot correct an erroneous direction supplied by that field.The conclusion identifies testing this dependence across additional editing tasks and backbones as future work.Source: §5 · p. 10

AI USE STATEMENT

  • The authors report using generative AI tools to improve manuscript clarity, grammar, and presentation, with the assisted content reviewed and verified by the authors.They state that the scientific ideas, methods, results, and conclusions were developed and validated by the authors.Source: AI USE STATEMENT · p. 10

A MATHEMATICAL DERIVATIONS AND PROOFS

The appendix derives the temporally aggregated Chord field from a quadratic objective over proxy fields. Its endpoint approximation produces a spatially uniform temporal combination of the two endpoint estimates.

A.1 DERIVATION OF THE TEMPORALLY AGGREGATED CHORD FIELD

  • The Chord estimator minimizes a quadratic objective over source-to-target proxy fields across the temporal interval.Source: §A.1 · p. 13
  • Strict convexity of the objective gives a unique minimizer characterized by its first-order condition.Source: §A.1 · p. 13
  • The endpoint approximation combines the estimates at t−δ and t with coefficients determined by time, independent of spatial location.Source: §A.1 · p. 13

A.2 PROOF OF THE UNIQUE GLOBAL SOLUTION

The proof establishes a unique global solution to the equal-energy redistribution problem by reducing it to a scalar dual root. The resulting multipliers preserve local directions and adjust relative spatial magnitudes according to endpoint consistency.

A.2 PROOF OF THE UNIQUE GLOBAL SOLUTION

  • A unique dual root in [−µ, 0] satisfies the equal-energy constraint, yielding the stated solution.Source: §A.2 · pp. 13–14
  • The constructed field is the unique global minimizer over all feasible fields with the prescribed control energy.Source: §A.2 · p. 14

A.3 PROPERTIES OF THE CLOSED-FORM REDISTRIBUTION

  • Positive local multipliers preserve every nonzero Chord vector’s direction, and their values lie between 1/(1+µ) and 1/(1−µ).Source: §A.3 · p. 14
  • For µ>0, a location with higher endpoint consistency receives a larger relative multiplier than one with lower consistency.Source: §A.3 · p. 14
  • When µ=0, or consistency is constant over the active support, redistribution leaves the Chord field unchanged; zero initial energy also yields a zero field.Source: §A.3 · p. 14

A.4 RELIABILITY-WEIGHTED ENERGY CERTIFICATE

This appendix gives a reliability-weighted energy certificate and bounds on the dual root, alongside implementation diagnostics. The certificate concerns control energy and does not establish decoded image quality or semantic correctness.

A.4 RELIABILITY-WEIGHTED ENERGY CERTIFICATE

  • The reliability-weighted energy certificate applies when µ>0 and EC>0, and concerns control energy rather than decoded image quality or semantic correctness.Source: §A.4 · p. 15
  • The dual-root bounds can tighten the bisection interval used to solve for the redistribution.Source: §A.4 · p. 15

B.1 ALGORITHMIC FLOW AND FINITE-PRECISION BISECTION

  • Across 700 PIE-Bench examples, solver residuals met stated tolerances, multipliers stayed within theoretical bounds, and no reliability-weighted energy inequality violations were observed.Source: §B.1 · p. 16, Table 5 · p. 16

B.2 EXPERIMENTAL SETUP AND REPRODUCIBILITY PROTOCOL

The experiments use fixed settings across all reported benchmark categories and backbones, with timing and memory measured under a shared protocol.

B.2 EXPERIMENTAL SETUP AND REPRODUCIBILITY PROTOCOL

  • ER-Chord uses fixed hyperparameters across PIE-Bench, TEdBench, and three backbones, averaging 0.37 s/img with peak VRAM identical to ChordEdit at 6988 MiB.Source: §B.2 · p. 16

C ADDITIONAL QUALITATIVE RESULTS

Additional PIE-Bench visual comparisons under matched random seeds show how editing methods affect target changes and non-target regions across representative categories.

C ADDITIONAL QUALITATIVE RESULTS

D EXTENDED QUANTITATIVE RESULTS AND NOTATION

Extended PIE-Bench results compare ER-Chord with ChordEdit across 700 examples and ten editing categories, alongside a notation reference.

D EXTENDED QUANTITATIVE RESULTS AND NOTATION

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