One Evaluation Is Enough: Inversion-Free Image Editing with Trajectory Correction
ECT asks whether inversion-free image editing can be done with just one noise-level evaluation instead of averaging fields at multiple times. It proposes Endpoint-Calibrated Transport (ECT), a training-free method that extracts both an angular semantic tangent and a clean endpoint displacement from a single shared noisy state, then calibrates the update via a closed-form projection. The result is a one-step editor that halves the temporal support of recent one-step baselines and claims competitive quality with lower latency.
The paper delivers a theoretically motivated single-evaluation editor that is simpler and measurably more efficient than comparable one-step methods. Its key derivation—collapsing angular transport and endpoint shrinkage into a scalar-rescaled displacement along the clean endpoint difference—is elegant, though the practical gains come with modest alignment trade-offs that the authors disclose honestly. The efficiency accounting is careful and reproducible in principle, but the restriction to epsilon-prediction VP backbones narrows its immediate applicability.
The paper’s strongest feature is its disciplined cost accounting: by isolating temporal supports from batching, the authors make a crisp case that ECT halves condition-time branches relative to ChordEdit while improving background preservation metrics. The ablation studies are unusually thorough, including seed-stability tests across eleven seeds, explicit transport-stage ablations, and parameter sweeps for $t$, $\zeta$, and $\lambda$ that expose trade-offs rather than hiding them. The closed-form specification in Section 3.4 makes the pipeline easy to implement once a backbone is available.
Despite its geometric framing, the method collapses to a scalar rescaling of the naive endpoint displacement because Equation 21 shows $g_t = -d_t / \sigma_t$, making the transport-and-correction narrative operationally much simpler than it appears. Proposition 1 only provides a standard Lipschitz quadrature bound that does not characterize actual prediction error, and Appendix C’s shrinkage-risk analysis assumes unbiased noise rather than realistic model mistakes. More importantly, the derivation is tightly bound to epsilon-prediction VP schedules, so modern velocity-prediction and rectified-flow backbones like FLUX or SD3 are explicitly excluded with no migration path.
The user-study analysis is purely descriptive, and the authors correctly note that the reported win rates "do not establish statistical significance." The hyperparameters $t=0.75$, $\zeta=0.7$, and $\lambda=1$ are tuned empirically without an automatic selection criterion, and while sensitivity plots are provided, the method remains sensitive to their interaction.
The evidence supports efficiency and preservation claims more strongly than absolute quality dominance. Matched comparisons against ChordEdit on identical SD-Turbo and SwiftBrush-v2 backbones are fair and show consistent improvements in PSNR and judge scores, but CLIP alignment drops slightly on SNR-Bench for both backbones and on PIE-Bench for SwiftBrush-v2. Comparisons to multi-step methods on different architectures (FLUX, SD3.5) are grouped separately in the tables, yet latencies and capacities differ so widely that readers should treat them as contextual baselines rather than direct competitors. The user study’s first-place shares favor ECT, but the authors transparently state that these are descriptive statistics without significance testing.
The method is fully specified in closed form with explicit hyperparameters ($t=0.75$, $\zeta=0.7$, $\lambda=1$), which aids reproduction, but the paper does not provide a public code repository or data release link in the main text. The authors state that the supplementary material will include configuration files and commands, yet absent an accessible archive, independent reproduction currently depends on re-implementing Equation 22 and the benchmark preprocessing from the appendices. Resource accounting is admirably detailed in Appendix E, but peak VRAM savings are minimal—only 0.24%—indicating that the main bottleneck shifts to VAE encoding/decoding and framework overhead rather than denoiser evaluation.
Real-image editing commonly relies on inversion and iterative sampling, while efficient one-step editors often stabilize a large update by estimating and averaging editing fields at multiple noise levels. We ask a stricter question: is a single temporal field evaluation sufficient for reliable inversion-free editing? Our answer rests on a previously underused duality in a variance-preserving (VP) one-step model: one source-target query at a shared noisy state simultaneously determines a local angular semantic tangent and a clean endpoint displacement. We integrate the tangent over the analytically known remaining VP angle to obtain a nominal one-step transport, and use the endpoint displacement to correct its long-horizon extrapolation through a constrained projection. This transport-first, correction-second construction yields Endpoint-Calibrated Transport (ECT), a closed-form, training-free editor requiring only one noise level, two text conditions packed into one denoiser batch, and one latent update. ECT requires no image inversion, trajectory integration, second temporal observation, or iterative optimization, and can be directly applied to pretrained epsilon-prediction VP one-step generators. Across the reported benchmark settings, ECT delivers stable gains in editing quality within an extremely short editing time.
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