Wavelet-Guided Semantic Signal Compensation for Inversion-Free Image Editing¶

Conference: ECCV 2026
Paper: ECCV Official
Code: https://zoey-tang-33.github.io/wavelet-edit-project
Area: Image Generation
Keywords: Inversion-Free Image Editing / Rectified Flow / Wavelet Transform / Semantic Signal Compensation / Diffusion Models

TL;DR¶

To tackle the semantic indistinguishability problem in rectified flow models where early manifold-seeking transport suppresses global attribute modifications, this paper introduces a training-free wavelet-guided semantic compensation framework that extracts co-located low-frequency prompt directions via Haar wavelets and injects them under a quadratic time schedule, markedly boosting global editing capability while preserving background fidelity.

Background & Motivation¶

Text-guided image editing built upon diffusion models and rectified flows (RFs) has demonstrated remarkable generative priors by mapping noise to complex data distributions. Traditional pipelines typically rely on explicit inversion schemes (e.g., DDIM Inversion or RF-Inversion) to trace source images back into latent noise and reconstruct them conditioned on modified prompts. However, the numerical approximation inherent in inversion inevitably introduces reconstruction drift, layout distortion, and heavy computational overhead. To circumvent explicit inversion bottlenecks, inversion-free frameworks such as FlowEdit emerged, modifying images directly by estimating the velocity difference between source and target trajectories while integrating this differential velocity field along ODE paths to inherit source structural priors.

Despite their impressive efficiency and local layout preservation, inversion-free methods exhibit a fundamental failure mode when tasked with global semantic modifications, such as shifting overall color palettes, object materials, or broad environmental attributes. In the early high-noise regime, the latent state is overwhelmingly dominated by unstructured Gaussian noise. Under this condition, the predicted velocity field is governed by the primary generative objective—transporting the noise distribution toward the natural data manifold. This dominant manifold-seeking flow substantially outweighs the subtle semantic signal introduced by prompt conditioning, causing what the authors term "semantic indistinguishability in the high-noise regime." As coarse structures and low-frequency components are determined in these early steps, the target trajectory fails to accumulate sufficient directional momentum away from the source distribution. By the time noise diminishes and text guidance strengthens, the global spatial layout and color composition have already solidified, causing the edit to fail or yield incomplete attribute shifts.

The fundamental tension stems from spatial-frequency conflict: attempting to amplify raw text-conditioned velocity differences between spatially separated source and target latents introduces severe geometric confounding and high-frequency noise perturbations, which rapidly disintegrate unedited background structures. Core idea: probe the co-located text-induced editing direction at identical source latent states to eliminate geometric confounding, isolate its spatially coherent low-frequency component using 2D discrete Haar wavelet decomposition, and inject it into the flow update via a quadratic time-decaying schedule to empower early global attribute divergence without harming background integrity.

Method¶

Overall Architecture¶

The proposed framework is constructed as a training-free plug-and-play augmentation to FlowEdit within the rectified flow formulation. Instead of relying solely on the coupled differential velocity field $\Delta v_t$, which intertwines spatial trajectory separation with prompt conditioning differences, the method incorporates an auxiliary prompt-guided direction. At each active sampling timestep, the network is evaluated at the source noisy latent under the target prompt to probe a co-located semantic editing direction. This raw direction is then decomposed via a multi-level 2D discrete Haar wavelet transform (DWT), where high-frequency detail sub-bands are eliminated to isolate smooth, low-frequency structural components. Finally, the low-frequency compensation signal is modulated by a quadratic time-decaying schedule and added to the standard geometric update, driving immediate trajectory deviation in the early generation steps.

%%{init: {'flowchart': {'rankSpacing': 24, 'nodeSpacing': 28, 'padding': 6, 'wrappingWidth': 400}}}%%
flowchart TD
    A["Input Source Latent & Target Prompt"] --> B["Same-Point Semantic Probing<br/>Evaluate on source latent to remove spatial confound"]
    B --> C["Multi-Level Wavelet Low-Frequency Extraction<br/>Haar DWT isolates low-frequency components"]
    C --> D["Quadratic Time-Modulated Injection<br/>Quadratic decay prioritizes early global guidance"]
    D --> E["Rectified Flow Trajectory Integration<br/>Synthesize edited image"]

Key Designs¶

1. Same-Point Semantic Probing: Eliminating Spatial-Geometric Confounding In standard FlowEdit, the geometric velocity update $\Delta v_{t_i} = v_\theta(x^{\mathrm{tar}}_{t_i}, t_i; e_{\mathrm{tar}}) - v_\theta(x^{\mathrm{src}}_{t_i}, t_i; e_{\mathrm{src}})$ evaluates the neural network at two spatially separated latent points $x^{\mathrm{tar}}_{t_i}$ and $x^{\mathrm{src}}_{t_i}$. In the high-noise regime, the resulting vector reflects both the text-conditioning difference and the arbitrary spatial separation between the coupled states, confounding the true semantic direction. To capture an uncorrupted prompt guidance direction, the authors introduce same-point semantic probing. By evaluating the network at the exact source noisy latent $x^{\mathrm{src}}_{t_i}$ under the target prompt embedding $e_{\mathrm{tar}}$, the co-located semantic editing signal is obtained: $$v_{\mathrm{sem}}(x^{\mathrm{src}}_{t_i}, t_i) = v_\theta(x^{\mathrm{src}}_{t_i}, t_i; e_{\mathrm{tar}}) - v_\theta(x^{\mathrm{src}}_{t_i}, t_i; e_{\mathrm{src}})$$ Because both velocity evaluations share the identical spatial latent coordinate, the baseline manifold-seeking flow is completely canceled out, isolating the pure directional vector induced solely by the textual change. Since $v_\theta(x^{\mathrm{src}}_{t_i}, t_i; e_{\mathrm{src}})$ is already computed in the source trajectory, this probing requires only one single extra forward pass per active timestep. Unlike FlowAlign or CVC which apply corrections at the target latent $x^{\mathrm{tar}}$, anchoring the probe at the source latent $x^{\mathrm{src}}$ provides a stable reference trajectory that prevents compounding drift.

2. Multi-Level Wavelet Low-Frequency Extraction: Decoupling Global Semantics from Noise Perturbations Although $v_{\mathrm{sem}}$ provides an accurate prompt-induced direction, the noisy latent $x^{\mathrm{src}}_{t_i}$ contains high variance forward Gaussian noise $\epsilon_i$ during early timesteps. Directly injecting raw $v_{\mathrm{sem}}$ introduces spatially incoherent, high-frequency perturbations into the velocity field, degrading fine background textures. To resolve this frequency conflict, an $L$-level 2D discrete Haar wavelet transform (DWT) is applied as a low-frequency extraction operator $\mathcal{F}_{\mathrm{low}}$. The decomposition recursively splits the approximation sub-band into coarse approximation coefficients $cA$ and horizontal $cH$, vertical $cV$, and diagonal $cD$ detail sub-bands: $$(cA^{(l)}, cH^{(l)}, cV^{(l)}, cD^{(l)}) = \mathrm{DWT}(cA^{(l-1)})$$ All high-frequency detail sub-bands across levels $1 \le l \le L$ are zeroed out, retaining solely the $L$-th level approximation sub-band $cA^{(L)}$. The purified low-frequency component is reconstructed back to spatial dimension via multi-level inverse DWT: $$v_{\mathrm{low}} = \mathcal{F}_{\mathrm{low}}(v_{\mathrm{sem}}(x^{\mathrm{src}}_{t_i}, t_i)) = \mathrm{IDWT}^{(1:L)}\left(cA^{(L)}, \{\mathbf{0}, \mathbf{0}, \mathbf{0}\}_{l=1}^L\right)$$ This operator strips away random noise spikes, isolating smooth velocity shifts that correspond to global color distributions, large-scale material properties, and coarse spatial composition. Concurrently, high-frequency textural details and boundaries continue to be governed by the standard geometric signal $\Delta v_{t_i}$, achieving clean frequency-domain orthogonality.

3. Quadratic Time-Modulated Injection: Early Deviation and Late-Stage Fidelity Generative dynamics follow distinct temporal schedules: global semantic layout is established at early timesteps ($t_i \approx 1$), whereas fine-grained textural synthesis and background fidelity solidify near convergence ($t_i \to 0$). Continuous static compensation throughout the trajectory would over-smooth high-frequency textures in later stages. To address this, the authors design a smooth time-dependent weighting function $w(t_i) = \lambda t_i^2$, yielding the modified Euler integration rule: $$x_{t_{i+1}} = x_{t_i} + (t_{i+1} - t_i) \left( \Delta v_{t_i} + \lambda t_i^2 \cdot v_{\mathrm{low}} \right)$$ where $\lambda \ge 0$ denotes the global semantic strength. This quadratic formulation provides four desirable properties: at $t_i \approx 1$, the injection weight reaches its peak $\lambda$, supplying maximum corrective momentum exactly when $\Delta v_t$ is overwhelmed by noise; as $t_i \to 0$, the weight quadratically vanishes to zero, smoothly reverting the ODE update back to the exact FlowEdit rule to preserve pristine background textures; the injection schedule remains continuous and monotonically decreasing without requiring heuristic threshold switching; and setting $\lambda = 0$ perfectly recovers the original FlowEdit trajectory. For spatially localized edits, an optional binary mask $M$ can be applied via element-wise multiplication $M \odot (\Delta v_{t_i} + \lambda t_i^2 v_{\mathrm{low}})$.

A Worked Example¶

Consider editing an image of a "green lizard" to a "brown lizard": 1. Early Stage ($t=1.0 \to 0.8$): In vanilla FlowEdit, the Tweedie one-step projection $\hat{x}_0$ reveals that the trajectory remains trapped in the green lizard mode due to dominant manifold transport. Under the proposed method, same-point probing measures $v_{\mathrm{sem}}$, extracts its $L=3$ low-frequency brown attribute direction $v_{\mathrm{low}}$, and injects it with maximum strength $\lambda t_i^2 \approx 3.0 \times 1.0 = 3.0$. The target latent rapidly accumulates directional momentum toward the brown distribution within the first 20% of steps. 2. Intermediate Stage ($t=0.8 \to 0.3$): The macro color tone is now established as brown. The quadratic weight drops steeply from $0.64$ to $0.09$, gradually attenuating the low-frequency bias. The primary geometric difference $\Delta v_{t_i}$ takes over to refine 3D body contours, light reflectance, and limb poses. 3. Refinement Stage ($t=0.3 \to 0.0$): The compensation factor vanishes ($3.0 \times 0.01 \to 0$). Denoising transitions entirely into standard FlowEdit transport, allowing fine background rock textures, soil grains, and lizard scales to resolve cleanly without any color bleeding or blurring.

Key Experimental Results¶

Main Results¶

Quantitative evaluations are conducted on PIE-Bench across 700 test images over ten editing categories using FLUX as the primary generative backbone. Baselines include diffusion-based methods (PnP, MasaCtrl, FreeDiff), rectified flow inversion methods (RF-Inv, StableFlow, RF-Edit, FireFlow, DNA-Edit), and the inversion-free baseline FlowEdit. Metrics assess structural consistency (DINO feature distance Struct), background preservation (PSNR, LPIPS, MSE, SSIM outside editing masks), and text-image alignment (CLIP similarity on whole image and edited region).

Method	Backbone	Struct. $\times 10^3$ $\downarrow$	PSNR $\uparrow$	LPIPS $\times 10^3$ $\downarrow$	MSE $\times 10^4$ $\downarrow$	SSIM $\times 10^2$ $\uparrow$	CLIP-Whole $\uparrow$	CLIP-Edited $\uparrow$
PnP [36]	Diffusion	23.47	22.48	105.70	79.83	80.22	25.44	22.60
MasaCtrl [4]	Diffusion	23.68	22.66	87.54	80.66	81.89	24.37	21.36
FreeDiff [40]	Diffusion	17.98	24.78	89.02	54.81	81.92	25.16	22.15
RF-Inv [32]	FLUX	64.61	17.97	242.00	221.24	64.92	25.29	22.91
StableFlow [1]	FLUX	19.25	23.04	77.09	84.78	87.22	24.06	21.18
RF-Edit [38]	FLUX	24.45	24.41	113.44	56.46	83.84	25.03	22.28
FireFlow [7]	FLUX	27.27	23.08	128.65	71.11	81.25	25.34	22.92
FlowEdit [19]	FLUX	27.61	22.23	111.32	90.98	83.64	25.39	22.62
DNA-Edit [41]	FLUX	16.83	25.21	86.48	48.11	87.23	24.82	22.12
Ours	FLUX	30.95	26.17	54.02	39.24	90.60	25.52	23.05

Ablation Study¶

1. Frequency-Band Selection Ablation Evaluates the effect of injecting different frequency components of $v_{\mathrm{sem}}$ into the FLUX pipeline on PIE-Bench:

Frequency Band Setting	Struct. $\times 10^3$ $\downarrow$	PSNR $\uparrow$	LPIPS $\times 10^3$ $\downarrow$	MSE $\times 10^4$ $\downarrow$	SSIM $\times 10^2$ $\uparrow$	CLIP-Whole $\uparrow$	CLIP-Edited $\uparrow$	Note
Zero (no comp.)	27.61	22.23	111.32	90.98	83.64	25.39	22.62	Original FlowEdit baseline
Identity (full-spectrum)	41.53	23.61	69.77	63.31	88.05	25.03	22.24	High-frequency noise destroys layout, Struct degrades
Highpass only	33.20	24.81	59.69	50.37	89.25	24.97	22.34	Lacks global semantic drive, lowest CLIP scores
Haar wavelet (Ours)	30.95	26.17	54.02	39.24	90.60	25.52	23.05	Optimal trade-off between fidelity and editability

2. Wavelet Decomposition Level $L$ and Semantic Strength $\lambda$ Sensitivity

Setting	$L$	$\lambda$	Struct. $\times 10^3$ $\downarrow$	PSNR $\uparrow$	LPIPS $\times 10^3$ $\downarrow$	MSE $\times 10^4$ $\downarrow$	SSIM $\times 10^2$ $\uparrow$	CLIP-Whole $\uparrow$	CLIP-Edited $\uparrow$
$L$ sweep ($\lambda=3.0$)	1	3.0	35.31	25.26	58.48	46.12	89.95	25.56	23.01
$L$ sweep ($\lambda=3.0$)	2	3.0	34.21	25.51	57.36	44.14	90.16	25.59	23.01
Default setup	3	3.0	30.95	26.17	54.02	39.24	90.60	25.52	23.05
$L$ sweep ($\lambda=3.0$)	4	3.0	26.06	27.05	49.12	33.36	91.17	25.39	22.90
$\lambda$ sweep ($L=3$)	3	2.0	25.72	26.88	49.64	34.09	91.16	25.48	22.98
$\lambda$ sweep ($L=3$)	3	2.5	28.30	26.52	51.83	36.59	90.88	25.54	23.05
$\lambda$ sweep ($L=3$)	3	3.5	33.67	25.80	56.24	41.99	90.33	25.55	23.09
$\lambda$ sweep ($L=3$)	3	4.0	36.65	25.44	58.68	45.00	90.04	25.44	22.94

Key Findings¶

Low-Frequency Wavelet Filtering Is Crucial: Injecting the raw full-spectrum signal without wavelet low-pass filtering (Identity) degrades structural distance to $41.53 \times 10^3$ and suppresses CLIP alignment, confirming that uncurated high-frequency noise destabilizes the trajectory. Highpass-only injection fails to produce sufficient global shift. Isolating the low-frequency approximation coefficients via Haar wavelets provides the necessary global push while safeguarding structural consistency.
Superior Background Preservation Across All Metrics: The proposed method establishes state-of-the-art background preservation among all evaluated FLUX baselines, delivering 26.17 dB PSNR (nearly 4 dB higher than FlowEdit's 22.23 dB), cutting LPIPS by more than 50% ($54.02 \times 10^3$ vs. $111.32 \times 10^3$), and achieving an SSIM of 90.60.
Robust Hyperparameter Frontiers: Increasing decomposition levels $L$ preserves background structures more conservatively, while increasing $\lambda$ boosts target prompt responsiveness. The configuration $L=3, \lambda=3.0$ resides at the optimal Pareto frontier balancing prompt adherence and scene fidelity.
Strong Human Preference in User Studies: Across 100 randomized paired comparisons judged by ten participants, our method achieved decisive win rates against baselines: 66% vs. FlowEdit (34%), 71% vs. FireFlow (29%), and 68% vs. StableFlow (32%), with users highlighting precise global color/texture modification without blurring or background warping.

Highlights & Insights¶

Diagnosing the Manifold-Seeking Masking Effect: Clearly explains why inversion-free methods fail at global attribute editing—not because text differences are absent, but because the powerful manifold-seeking generative flow completely dwarfs subtle semantic gradients during early high-noise steps.
Co-Located Probing Decouples Geometry from Semantics: Evaluating the prompt shift at identical source latent coordinates isolates pure prompt responsiveness without the geometric confounding caused by distinct trajectory points, requiring only one single extra forward inference.
Orthogonal Frequency-Time Modulation: Leverages 2D Haar wavelets to separate low-frequency semantic compensation from high-frequency structural maintenance, combined with a smooth quadratic time-decay schedule that guarantees early global guidance and asymptotic exactness to standard FlowEdit at late steps.
Broad Applicability to Continuous Generative Flows: Operates directly in velocity space without modifying transformer attention maps or training task-specific adapters, providing a foundational frequency-aware guidance paradigm that extends naturally to video flow matching and 3D Gaussian generation.

Limitations & Future Work¶

Additional Forward Pass Overhead: Performing same-point probing requires one additional network evaluation per active editing step, increasing per-step computational latency by roughly 50% relative to vanilla FlowEdit. Future optimizations could explore timestep-sparse probing in the high-noise interval.
Severe Topological Reconfiguration: While highly effective for global color, texture, and style transitions, radical structural morphing (e.g., completely replacing an animal's posture and morphology) remains constrained by the shared geometric transport of the source trajectory.
Fixed Wavelet Basis Functions: The framework relies on standard Haar wavelets with fixed level decomposition rather than adaptive or learnable frequency filters tailored to specific semantic granularities.

vs FlowEdit [19]: FlowEdit establishes the foundational inversion-free paradigm via coupled ODE transport, but suffers from severe semantic indistinguishability in global attribute shifts; our method directly repairs this deficiency by introducing co-located wavelet low-frequency compensation.
vs FreeDiff [40]: FreeDiff operates via FFT in the latent noise space of diffusion models to impose structural constraints for preventing collapse; in contrast, our method operates in the velocity space of rectified flow models to actively inject low-frequency semantic guidance vectors.
vs FlowAlign [18] & CVC [21]: FlowAlign and CVC inject velocity corrections evaluated at the target latent $x^{\mathrm{tar}}$, which can exacerbate drift; our method anchors probing at the source latent $x^{\mathrm{src}}$, functioning as a clean auxiliary reference prior.

Rating¶

Novelty: ⭐⭐⭐⭐☆ [Insightful diagnosis of early manifold dominance in rectified flows paired with elegant same-point wavelet frequency decomposition]
Experimental Thoroughness: ⭐⭐⭐⭐⭐ [Exhaustive comparisons against 9 baselines on PIE-Bench, comprehensive frequency ablations, power spectral density curves, and blind user studies]
Writing Quality: ⭐⭐⭐⭐⭐ [Clear mathematical formulations, clean intuition, and excellent exposition bridging frequency domain analysis with flow dynamics]
Value: ⭐⭐⭐⭐☆ [Training-free, architecture-agnostic, and remarkably effective for practical text-guided editing with modern flow matching models]

Setting	\(L\)	\(\lambda\)	Struct. \(\times 10^3\) \(\downarrow\)	PSNR \(\uparrow\)	LPIPS \(\times 10^3\) \(\downarrow\)	MSE \(\times 10^4\) \(\downarrow\)	SSIM \(\times 10^2\) \(\uparrow\)	CLIP-Whole \(\uparrow\)	CLIP-Edited \(\uparrow\)
\(L\) sweep (\(\lambda=3.0\))	1	3.0	35.31	25.26	58.48	46.12	89.95	25.56	23.01
\(L\) sweep (\(\lambda=3.0\))	2	3.0	34.21	25.51	57.36	44.14	90.16	25.59	23.01
Default setup	3	3.0	30.95	26.17	54.02	39.24	90.60	25.52	23.05
\(L\) sweep (\(\lambda=3.0\))	4	3.0	26.06	27.05	49.12	33.36	91.17	25.39	22.90
\(\lambda\) sweep (\(L=3\))	3	2.0	25.72	26.88	49.64	34.09	91.16	25.48	22.98
\(\lambda\) sweep (\(L=3\))	3	2.5	28.30	26.52	51.83	36.59	90.88	25.54	23.05
\(\lambda\) sweep (\(L=3\))	3	3.5	33.67	25.80	56.24	41.99	90.33	25.55	23.09
\(\lambda\) sweep (\(L=3\))	3	4.0	36.65	25.44	58.68	45.00	90.04	25.44	22.94