Beyond Temporal Smoothing:
Spatial Energy Budgets Stabilize One-Step Diffusion Editing

BudEdit separates how much editing energy is administered from where and how it is spent. A residual-energy support and a cross-attention localization signal, both read off the same transport forward pass at no additional UNet evaluation, determine where the budget is allocated, while a constrained allocation problem determines how it is distributed.

On PIE-Bench with SD-Turbo (700 images, 10 editing categories, all $512{\times}512$, seed fixed at 42 for all methods), BudEdit is compared against multi-step, few-step, and one-step editors under each method's own reported default configuration. Like ChordEdit, BudEdit uses one sampling step and two UNet evaluations, with $t_s{=}0.78$, $t_e{=}0.38$, $\alpha{=}0.7$ and $\beta{=}4.0$; runtimes are measured on an RTX 4090. Among one-step methods, BudEdit achieves the highest PSNR, CLIP-D, MUSIQ and MUSIQ-E while using two UNet evaluations and reporting the lowest runtime of 0.21 s per image. Among training-free one-step editors it leads all six background-fidelity metrics and exceeds ChordEdit on all five editing-quality metrics — a 2.1 dB background PSNR gain, 31% lower DINO, and 36% lower LPIPS — while SwiftEdit reaches its background numbers only with task-specific training. The few-step and multi-step methods provide a broader quality–compute reference rather than a same-budget ablation: they use $4$–$100$ evaluations and report $0.84$–$15.03$ s per image, compared with BudEdit's two evaluations and $0.21$ s.

Comparison with chord transport. Disabling ChordEdit's chord window ($\delta{=}0$) raises CLIP-E from $22.15$ to $22.54$, but lowers MUSIQ-E from $60.19$ to $55.97$ and background PSNR from $22.63$ to $20.13$ dB, and the window-off outputs show visible background and structural distortion. CLIP-E alone therefore does not fully reflect edit quality, which is why MUSIQ-E is reported as a complementary measure of edited-region perceptual quality. Without relying on temporal smoothing, BudEdit improves all five metrics over ChordEdit's smoothed default; against the window-off row it gives up only $0.02$ CLIP-E while improving background PSNR by $4.58$ dB and MUSIQ-E by $4.34$ points.

Matched effective timestep. ChordEdit's default window assigns six sevenths of its weight to $t_s-\delta$, so with $t_s{=}0.9$ and $\delta{=}0.15$ its weighted-average time is $t_s-6\delta/7=0.771$, close to BudEdit's direct timestep $t_s{=}0.78$. This is consistent with temporal smoothing shifting ChordEdit toward a lower effective timestep, while the mechanisms remain different: ChordEdit averages fields globally over time, whereas BudEdit evaluates directly at $t_s{=}0.78$ and controls the trade-off through spatial energy budgeting.

Component ablations. Setting $\beta{=}0$ drops the budgeted injection field $f^{\star}$ from the composed field, leaving only the attenuated residual term; disabling cleanup drops the second UNet evaluation, halving NFE. Each factor helps alone: energy reallocation alone raises CLIP-E/CLIP-D by $0.31$/$1.57$ without cleanup, while cleanup gives the larger editing-quality gain, $+1.30$/$+5.87$ and $+1.08$ CLIP-W. They also interact — with cleanup on, the reallocation gains grow to $0.71$/$2.93$ — and the full configuration attains the best CLIP-W, CLIP-E and CLIP-D. Transporting less energy changes the background less, so the no-energy, no-cleanup setting holds the highest PSNR and SSIM. In the office chair $\to$ straw chair edit, budgeted energy reallocation alone overlays straw texture on the cushion, cleanup alone yields only a slight change to the armrests, and only the full configuration converts the chair coherently.

BudEdit addresses spatially misallocated updates in one-step diffusion editing by converting single-draw background residual energy into an image-dependent budget and re-injecting it into the regions selected jointly by residual energy and cross-attention, with exact injection-budget matching and zero injection on the operational background support. On PIE-Bench, it outperforms the temporal-smoothing approach of ChordEdit on all 11 reported metrics, including a 2.1 dB PSNR gain, at the lowest runtime in the comparison. Together, these results establish explicit spatial energy budgeting as an alternative to temporal smoothing for stable, efficient, controllable one-step editing.