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

arXiv: https://arxiv.org/abs/2609.32841 · HTML: https://mlsanity.com/paper/2609.32841/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Image generation, text-to-image and editing, one of 14 directions in Diffusion models.
- Builds on 29 of its 34 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Placed in

- Diffusion models / [Image generation, text-to-image and editing](https://mlsanity.com/diffusion/image-generation-text-to-image-and-editing/)

## Builds on (most cited first, 29 of 29)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [InstructPix2Pix: Learning to Follow Image Editing Instructions](https://mlsanity.com/paper/2211.09800/) (2022)
- [Prompt-to-Prompt Image Editing with Cross Attention Control](https://mlsanity.com/paper/2208.01626/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Null-text Inversion for Editing Real Images using Guided Diffusion Models](https://mlsanity.com/paper/2211.09794/) (2022)
- [MUSIQ: Multi-scale Image Quality Transformer](https://mlsanity.com/paper/2108.05997/) (2021)
- [Plug-and-Play Diffusion Features for Text-Driven Image-to-Image Translation](https://mlsanity.com/paper/2211.12572/) (2022)
- [Adversarial Diffusion Distillation](https://mlsanity.com/paper/2311.17042/) (2023)
- [Attend-and-Excite: Attention-Based Semantic Guidance for Text-to-Image Diffusion Models](https://mlsanity.com/paper/2301.13826/) (2023)
- [InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generation](https://mlsanity.com/paper/2309.06380/) (2023)
- [FlowEdit: Inversion-Free Text-Based Editing Using Pre-Trained Flow Models](https://mlsanity.com/paper/2412.08629/) (2024)
- [StyleGAN-NADA: CLIP-Guided Domain Adaptation of Image Generators](https://mlsanity.com/paper/2108.00946/) (2021)
- [SwiftBrush: One-Step Text-to-Image Diffusion Model with Variational Score Distillation](https://mlsanity.com/paper/2312.05239/) (2023)
- [TurboEdit: Text-Based Image Editing Using Few-Step Diffusion Models](https://mlsanity.com/paper/2408.00735/) (2024)
- [KV-Edit: Training-Free Image Editing for Precise Background Preservation](https://mlsanity.com/paper/2502.17363/) (2025)
- [SwiftBrush v2: Make Your One-step Diffusion Model Better Than Its Teacher](https://mlsanity.com/paper/2408.14176/) (2024)
- [SwiftEdit: Lightning Fast Text-Guided Image Editing via One-Step Diffusion](https://mlsanity.com/paper/2412.04301/) (2024)
- [ChordEdit: One-Step Low-Energy Transport for Image Editing](https://mlsanity.com/paper/2602.19083/) (2026)
- [SpotEdit: Selective Region Editing in Diffusion Transformers](https://mlsanity.com/paper/2512.22323/) (2025)
- [InstantEdit: Text-Guided Few-Step Image Editing with Piecewise Rectified Flow](https://mlsanity.com/paper/2508.06033/) (2025)
- [FlowDC: Flow-Based Decoupling-Decay for Complex Image Editing](https://mlsanity.com/paper/2512.11395/) (2025)
- [WhereEdit: Mask-aware Local Latent Editing for One-Step Image Editing](https://mlsanity.com/paper/2607.20883/) (2026)
- [Rethinking One-Step Image Editing through ChordEdit: Reproduction, Simplification, and New Insights](https://mlsanity.com/paper/2606.14042/) (2026)
- [Bridging the Manifold Gap: Riemannian Residual Line Search for One-Step Image Editing](https://mlsanity.com/paper/2606.24844/) (2026)

## Abstract (arXiv)

One-step text-guided diffusion editing is efficient but prone to spatially misallocated updates that distort the edited object and alter the background. Existing methods often improve stability by averaging the editing field across timesteps. We instead identify spatial energy misallocation as a distinct and measurable failure mode: across two independent noise draws, the residual field is essentially unrepeatable, making the background field unreliable for direct transport, while its total energy still sets a usable magnitude for the draw at hand. BudEdit turns that magnitude into an explicit budget and reallocates it to edit-relevant regions selected jointly by residual energy and cross-attention, controlling where editing energy is spent rather than averaging over timesteps. The resulting training-free, inversion-free editor spends the budget on transport and reuses it to scale a correction in a lower-noise gated refinement. The budgeted injection field matches its prescribed budget exactly and vanishes on the identified background support, by construction. On PIE-Bench with SD-Turbo, BudEdit outperforms ChordEdit under each method's reported default settings on all 11 evaluated metrics, including a 2.1,dB gain in background PSNR, 31% lower DINO, and 36% lower LPIPS, while improving all five editing-quality metrics and reporting the lowest runtime in the comparison.