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 — manifesting as severe object distortion and critical loss of consistency in non-edited regions, resulting from high-energy, erratic trajectories produced by naive vector arithmetic on the models' structured fields.

We introduce ChordEdit, a model-agnostic, training-free, and inversion-free method for high-fidelity one-step editing. We recast editing as a transport problem between source and target distributions defined by prompts. Leveraging dynamic optimal transport, we derive a low-energy control strategy yielding a smoothed, variance-reduced Chord Control Field that can be traversed in a single, large integration step.

One-step T2I models such as SD-Turbo, SwiftBrush-v2 and InstaFlow distill large diffusion models into a compact, single-step pathway, promising truly interactive applications. This progress raises the expectation that real-time capability can be leveraged for text-guided image editing.

However, this promise remains unmet. Existing one-step method SwiftEdit achieves speed by training dedicated networks, sacrificing model-agnostic flexibility. The training-free alternative computes an editing field by differencing drifts conditioned on source and target prompts — effective in multi-step generators but fails in one-step models: severe object distortion and background disintegration (Figure 3).

The root cause: naive editing field is the arithmetic difference of two large-magnitude, divergent trajectories — an erratic, high-energy control field. A single large integration step accumulates significant error.

We introduce ChordEdit, recasting editing from dynamic OT perspective, seeking a low-energy chord to transport source to target. Our Chord Control Field is a time-weighted average of source and target drifts, acting as temporal smoothing. Optional proximal refinement enhances semantics. Results on PIE-bench demonstrate state-of-the-art efficiency with high background preservation.

A pre-trained T2I model induces conditional probability flow $\frac{dx_t}{dt}=v(x_t,t,c)$. Given prompts $c_{\rm src}, c_{\rm tar}$ and source image $x_{\rm src}:=x_1$, editing transports toward target $x_{\rm tar}$ via instantaneous residual:

$$\Delta v(x_t,t)=v(x_t,t,c_{\rm tar})-v(x_t,t,c_{\rm src}) \quad\text{(Eq. 3.2)}$$

In practice we anchor at clean source $x_\tau:=x_1$ and query the model at synthetic noisy proxy $z\sim K_t(\cdot\mid x_\tau)$. The observable proxy field is:

$$\mathbf{R}(x_\tau,t)=\mathbb{E}_{z\sim K_t(\cdot\mid x_\tau)}\!\big[\,\mathcal{B}_t\,\Delta Q(z,t)\,\big] \quad\text{(Eq. 3.3)}$$

where $\Delta Q=Q(\cdot,c_{\rm tar})-Q(\cdot,c_{\rm src})$ and $\mathcal{B}_t$ is a time-only linear map (e.g. for SD-Turbo: $Q=\hat\epsilon_\theta$, $\mathcal{B}_t=A_t^{(\epsilon)}$).

Dynamic OT view: ideal editing field $u_t$ minimizes Benamou–Brenier kinetic energy subject to continuity equation. We only observe $\mathbf{R}(x_\tau,t)=u_t+\varepsilon_t$ (measurement model). Naive control $u_{\rm nai}=\mathbf{R}$ is high-energy and unstable for single-step integration.

To obtain low-energy estimator $\hat u_t$, minimize quadratic surrogate over window $[t-\delta,t]$:

$$\Phi_t(u;x_\tau)=t\,\|u-\hat u_{t-\delta}(x_\tau)\|^2+\int_{t-\delta}^{t}\!\|u-\mathbf{R}(x_\tau,\xi)\|^2\,d\xi \quad\text{(Eq. 4.3)}$$

Setting $\nabla_u\Phi_t=0$ and using first-order causal approximations yields the Chord Control Field:

$$\hat u_t(x_\tau)=\frac{t\,\mathbf{R}(x_\tau,t-\delta)+\delta\,\mathbf{R}(x_\tau,t)}{t+\delta} \quad\text{(Eq. 4.5)}$$

By Jensen's inequality, $\int\!\|\hat u\|^2\leq\int\!\|\mathbf{R}\|^2$ — an $L^2$ contraction suppressing high-energy spikes; consistency proxy $\mathcal{C}(\hat u)\leq\mathcal{C}(\mathbf{R})$ tightens Euler error for $h=1$ step.

Proximal refinement (optional):

$$\operatorname{prox}(x^{\rm pred},t_c,c_{\rm tar})=\mathcal{B}_{t_c}\,Q(x^{\rm pred},t_c,c_{\rm tar}) \quad\text{(Eq. 4.7)}$$

Algorithm 1 (simplified):

1. $x_{\rm in}\leftarrow x_{\rm src}$
2. $\hat u\leftarrow\frac{t\,\mathbf{R}(x_{\rm in},t-\delta)+\delta\,\mathbf{R}(x_{\rm in},t)}{t+\delta}$
3. $x^{\rm pred}\leftarrow x_{\rm in}+\lambda\,\hat u$
4. $x_{\rm tar}\leftarrow\operatorname{prox}(x^{\rm pred},t_c,c_{\rm tar})$ (optional)
Default: $n=1$, $t=0.90$, $\delta=0.15$, $\lambda=1.00$, $t_c=0.30$ — transport-only is 1-NFE; full pipeline is 2-NFE.

We evaluate on PIE-bench (700 samples, 512×512, 10 editing categories). Metrics: PSNR/MSE on non-edited regions; CLIP-Whole and CLIP-Edited for semantic alignment. Single NVIDIA Titan 24GB GPU.

Table 1 compares multi-step, few-step, and one-step editors. ChordEdit achieves state-of-the-art efficiency — less than half VRAM of SwiftEdit on same model, 19× faster than FlowEdit, 3.4× faster than fastest few-step alternative.

Ablation — Chord Control Field ($\delta$): Setting $\delta=0$ degenerates to naive baseline. As step count $S\to 1$, naive field energy spikes and PSNR collapses; CCF ($\delta=0.15$) remains stable and strictly Pareto-dominates naive on perceptual-semantic trade-off (Figure 9).

Noise samples: ChordEdit with $n=1$ is seed-robust (CLIP CoV 0.20%, PSNR CoV 0.07%); increasing $n$ yields negligible marginal returns — intrinsic variance reduction from smoothing.

We introduced ChordEdit, a training-free, inversion-free framework solving one-step editing instability. Our Chord Control Field replaces naive high-energy drift difference with temporal smoothing, enabling a single large integration step while preserving non-edited regions.

ChordEdit achieves state-of-the-art efficiency — runtime 0.38s, low VRAM — without sacrificing quality: high fidelity and strong semantic alignment, robustly model-agnostic and seed-insensitive with a single noise sample. True real-time, high-fidelity generative image editing.