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

Conference: CVPR 2026
arXiv: 2602.19083
Code: Available (Project Page: https://chordedit.github.io)
Area: Image Generation
Keywords: Image Editing, Optimal Transport, One-step Inference, Diffusion Distillation Models, Training-free Editing

TL;DR

Based on dynamic optimal transport theory, a low-energy Chord control field is derived to smooth unstable naive editing fields, achieving the first training-free, inversion-free, and high-fidelity real-time image editing for distilled one-step T2I models.

Background & Motivation

1. State of the Field

One-step text-to-image (T2I) models, such as SD-Turbo, SwiftBrush-v2, and InstaFlow, have achieved unprecedented generation speeds through distillation of large-scale diffusion models, generating high-quality images in a single forward pass. This real-time generation capability naturally raises expectations for its application in text-guided image editing—if generation takes only one step, can editing also be real-time?

2. Limitations of Prior Work

Existing image editing methods face a dilemma between two camps:

  • Multi-step methods (DDIM+PnP, FlowEdit, etc.): Require 30-50 inference steps, with runtimes ranging from 7-80 seconds, making real-time interaction impossible.
  • One-step trained methods (SwiftEdit): Require training specialized inversion networks, sacrificing model-agnosticism and relying on precise inversion.
  • Training-free differential methods (InfEdit, FlowEdit): Work well on multi-step models but fail completely on one-step models—resulting in severe object distortion and collapse of non-edited regions.

3. Root Cause

The distillation process of one-step models makes the mapping from text conditions to vector fields highly non-linear and sensitive. A naive editing field (target drift - source drift) is essentially the arithmetic difference between two large-magnitude, diverging trajectories, producing an unstable high-energy control field. In multi-step models, this instability is gradually absorbed through iterative small-step integration; however, in one-step models, the entire path must be covered in a single step, where the massive integration step size sharply magnifies errors, leading to total editing failure.

4. Paper Goals

The goal is to enable high-fidelity text-guided image editing for one-step T2I models under the premise of being training-free and inversion-free, while maintaining real-time speeds.

5. Starting Point

The authors move beyond the approach of "simple arithmetic on drifts" and redefine the editing problem as a dynamic optimal transport (OT) problem—finding a low-energy transport path between the source and target distributions. Starting from the Benamou-Brenier framework, they derive a theoretically guaranteed control field estimator.

6. Core Idea

Use time-weighted averaging instead of naive differentiation to construct a low-energy, low-variance Chord control field, allowing one-step large-step integration to complete the editing transport stably.

Method

Overall Architecture

The workflow of ChordEdit is extremely concise (Algorithm 1):

  1. Input: Source image \(x_{\rm src}\), source/target text \(c_{\rm src}, c_{\rm tar}\), hyperparameters \(t, \delta, \lambda, t_c\).
  2. Compute Chord Control Field: Query the model at two time points \(t\) and \(t-\delta\), and perform time-weighted averaging.
  3. One-step Transport: \(x^{\rm pred} = x_{\rm in} + \lambda \hat{u}\).
  4. Optional Proximal Refinement: One additional forward pass to enhance target semantics.

The entire editing process requires only 1-2 network forward evaluations (NFE), with a runtime of 0.20-0.38 seconds.

Key Designs

Module 1: Observable Model

Function: Defines a unified interface to query one-step models with different parameterizations.

Mechanism: The editing anchor is fixed as the clean source image \(x_\tau = x_1\). A noisy proxy \(z\) is synthesized via the forward noising kernel \(K_t(\cdot|x_\tau)\), and the model is queried to obtain an observable output \(Q(z, t, c)\). An observable proxy field is defined:

\[\mathbf{R}(x_\tau, t) = \mathbb{E}_{z \sim K_t}[\mathcal{B}_t \Delta Q(z, t)]\]

where \(\mathcal{B}_t\) is a time-dependent linear mapping that unifies different parameterizations (noise prediction, velocity prediction, etc.) into the drift/velocity space.

Design Motivation: Different one-step models (e.g., SD-Turbo using noise prediction, InstaFlow using velocity prediction) need to be handled uniformly. By introducing the linear mapping \(\mathcal{B}_t\), the method becomes model-agnostic.

Module 2: Chord Control Field (CCF)

Function: Smooths the unstable naive editing field \(\mathbf{R}\) into a low-energy control field \(\hat{u}\).

Mechanism: From the perspective of dynamic OT, editing is viewed as an estimation problem. The observable field \(\mathbf{R}\) is an observation of the true field \(u_t\) plus zero-mean noise \(\varepsilon_t\). Within a short time window \([t-\delta, t]\), the optimal estimate is obtained by minimizing a strictly convex quadratic proxy objective (balancing the recursive energy prior with the consistency of new observations):

\[\hat{u}_t(x_\tau) = \frac{t \cdot \mathbf{R}(x_\tau, t-\delta) + \delta \cdot \mathbf{R}(x_\tau, t)}{t + \delta}\]

This is essentially a causal one-sided kernel smoothing operator that performs time-weighted averaging on the naive field.

Design Motivation: - The naive field \(\mathbf{R}\) experiences energy explosion in the one-step limit (experimentally verified: energy surges as steps \(S \to 1\)). - Via Jensen's inequality, time averaging guarantees \(L^2\) contractivity: \(\int\|\hat{u}\|^2 \leq \int\|\mathbf{R}\|^2\). - The \(L^\infty\) norm, time derivative, and spatial gradient of the field are simultaneously contracted, reducing the consistency constant \(\mathcal{C}(u)\) for explicit Euler. - This directly tightens the global \(O(h)\) error bound for \(h=1\) step, ensuring the stability of one-step integration.

Module 3: Proximal Refinement

Function: Optionally enhances target semantics after the transport is completed.

Mechanism: Performs a forward pass on the transport result \(x^{\rm pred}\) using only the target prompt \(c_{\rm tar}\):

\[\operatorname{prox}(x^{\rm pred}, t_c, c_{\rm tar}) = \mathcal{B}_{t_c} Q(x^{\rm pred}, t_c, c_{\rm tar})\]

Design Motivation: Chord transport tends to be conservative (high PSNR, lower CLIP). By decoupling structural preservation (handled by transport) and semantic enhancement (handled by refinement) into a modular design, users can balance them as needed.

Loss & Training

ChordEdit is a completely training-free method. Its core formula (Eq. 4.5) is derived analytically from optimal transport theory, requiring no learning process. The only requirements are hyperparameters during the inference stage:

  • \(t=0.90\): Stepping time point.
  • \(\delta=0.15\): Smoothing window width (trade-off between stability and semantic strength).
  • \(\lambda=1.00\): Step size scaling.
  • \(t_c=0.30\): Noise level for proximal refinement.

Key Experimental Results

Main Results

Comprehensive comparison with multi-step/few-step/one-step methods on PIE-bench (700 samples, 10 editing categories, 512×512):

Type Method PSNR↑ MSE↓(×10³) LPIPS↓(×10³) CLIP-Whole↑ CLIP-Edited↑ Training-free Inversion-free Steps NFE Runtime(s) Memory(MiB)
Multi-step DirectInv+PnP 21.43 8.10 106.26 25.48 22.63 ✓ ✗ 50 150 28.03 9262
Multi-step FlowEdit (SD3) 22.17 7.69 104.81 26.64 23.69 ✓ ✓ 33 33 7.22 17140
Few-step InfEdit (SD1.4) 24.14 6.82 55.69 24.89 21.88 ✓ ✓ 4 4 1.41 6502
One-step SwiftEdit 21.71 8.22 91.22 24.93 21.85 ✗ ✗ 1 2 0.54 15060
One-step Ours (SD-Turbo) 22.20 6.84 128.25 25.58 22.96 ✓ ✓ 1 2 0.38 6988
One-step Ours (w/o prox) 23.89 5.05 88.36 24.97 21.87 ✓ ✓ 1 1 0.20 6988

Ablation of transport and refinement:

Method Naive Field PSNR↑ Naive Field CLIP-Ed↑ Chord Field PSNR↑ Chord Field CLIP-Ed↑ NFE
w/o prox 21.89 20.83 23.89 21.87 1
w/ prox 21.38 21.96 22.20 22.96 2

Ablation Study

Model-agnosticism Verification: Tested on three different one-step T2I models, ChordEdit consistently outperforms the naive baseline:

T2I Model Naive PSNR ChordEdit PSNR Naive CLIP-Ed ChordEdit CLIP-Ed
InstaFlow 22.05 23.05 20.19 21.39
SwiftBrush-v2 20.52 22.04 21.06 22.58
SD-Turbo 21.38 22.20 21.96 22.96

Noise Sample Analysis: With \(n=1\), the Pareto front of ChordEdit nearly overlaps with \(n=2, 3, 4\), and strictly Pareto-dominates the naive method at \(n=4\). The CLIP CoV across 20 seeds is only 0.20%, and PSNR CoV is only 0.07%.

Key Findings

  1. Energy and Stability Relationship: When steps \(S \to 1\), the energy of the naive field surges and PSNR collapses; the Chord field maintains low energy and stable PSNR.
  2. Pareto Dominance: On the LPIPS-CLIP trade-off curve, ChordEdit (\(\delta \neq 0\)) strictly Pareto-dominates the naive baseline (\(\delta = 0\)).
  3. Significant Speed Advantage: 19× faster than FlowEdit, 208× faster than Direct Inversion, with VRAM usage around 46% of SwiftEdit.
  4. User Study: Participants overwhelmingly preferred ChordEdit for both editing semantics (42.5%) and background preservation (48.3%).

Highlights & Insights

  1. Theoretical Elegance: Derives the editing control field from dynamic optimal transport (Benamou-Brenier) rather than heuristic design. Jensen's inequality directly guarantees energy contraction, and the tightening of the consistency constant provides an error bound guarantee for one-step integration.
  2. Minimalist Implementation: The core formula is just a one-line weighted average (Eq. 4.5), requiring no additional networks, no inversion, and no masks—true plug-and-play.
  3. Modular Decoupling: Splits the problem into "structure-preserving low-energy transport" + "optional semantic-enhancing refinement." The functions are orthogonal, allowing flexible selection by the user.
  4. Single Noise Sufficiency: Proves that the intrinsic low-variance property of the Chord field makes Monte Carlo averaging unnecessary, yielding seed-robust results with \(n=1\).
  5. Parameterization Unification: Through the design of the linear mapping \(\mathcal{B}_t\), different parameterizations (noise prediction, velocity prediction, etc.) are unified under the same framework.

Limitations & Future Work

  1. Higher LPIPS Scores: Full ChordEdit (w/ prox) has an LPIPS of 128.25, higher than InfEdit's 55.69, indicating that proximal refinement sacrifices perceptual similarity while enhancing semantics.
  2. Limited Editing Intensity: As a training-free method, it may struggle with complex structural edits (e.g., large-scale pose changes).
  3. Hyperparameter Sensitivity: \(\delta\) controls the stability vs. semantics trade-off, and \(t_c\) controls refinement intensity; different editing scenarios may require different hyperparameter combinations.
  4. Text-guided Only: Currently supports only source/target prompt pair editing, without extension to other control modalities (e.g., image references, regional masks).
  5. Future Directions: Exploring adaptive \(\delta\) selection strategies, integration with attention control methods, or extending the OT framework to video editing.
  • FlowEdit: Also a training-free and inversion-free method, but relies on multi-step integration to average out instability; ChordEdit resolves the one-step problem from a theoretical level.
  • SwiftEdit: The only one-step editing competitor, but requires training an inversion network and has high VRAM overhead (15GB vs 7GB).
  • InfEdit: Best background preservation among few-step methods (PSNR 24.14), but still requires 4 inference steps.
  • Dynamic OT Inspiration: Applying the Benamou-Brenier framework to generative model editing is a novel perspective that might inspire more OT-guided generative control methods.

Rating

⭐⭐⭐⭐ — The theoretical derivation is solid and elegant, the method is minimalist and efficient, and it demonstrates strong model-agnosticism. While high LPIPS and limited editing intensity are minor drawbacks, the core contributions (theoretical guarantees for low-energy transport fields + real-time performance) are highly valuable.

Rating

  • Novelty: TBD
  • Experimental Thoroughness: TBD
  • Writing Quality: TBD
  • Value: TBD