# Bridging the Manifold Gap: Riemannian Residual Line Search for One-Step Image Editing

arXiv: https://arxiv.org/abs/2606.24844 · HTML: https://mlsanity.com/paper/2606.24844/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 39 references that are in the map.
- First posted on arXiv 23 Jun 2026.

## Builds on (most cited first, 30 of 33)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (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)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (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)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [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)
- [Imagic: Text-Based Real Image Editing with Diffusion Models](https://mlsanity.com/paper/2210.09276/) (2022)
- [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)
- [MasaCtrl: Tuning-Free Mutual Self-Attention Control for Consistent Image Synthesis and Editing](https://mlsanity.com/paper/2304.08465/) (2023)
- [An Edit Friendly DDPM Noise Space: Inversion and Manipulations](https://mlsanity.com/paper/2304.06140/) (2023)
- [FlowEdit: Inversion-Free Text-Based Editing Using Pre-Trained Flow Models](https://mlsanity.com/paper/2412.08629/) (2024)
- [Stable Flow: Vital Layers for Training-Free Image Editing](https://mlsanity.com/paper/2411.14430/) (2024)
- [DiT4Edit: Diffusion Transformer for Image Editing](https://mlsanity.com/paper/2411.03286/) (2024)
- [TurboEdit: Text-Based Image Editing Using Few-Step Diffusion Models](https://mlsanity.com/paper/2408.00735/) (2024)
- [EEdit: Rethinking the Spatial and Temporal Redundancy for Efficient Image Editing](https://mlsanity.com/paper/2503.10270/) (2025)
- [Lightning-Fast Image Inversion and Editing for Text-to-Image Diffusion Models](https://mlsanity.com/paper/2312.12540/) (2023)
- [FlowAlign: Trajectory-Regularized, Inversion-Free Flow-based Image Editing](https://mlsanity.com/paper/2505.23145/) (2025)
- [SwiftEdit: Lightning Fast Text-Guided Image Editing via One-Step Diffusion](https://mlsanity.com/paper/2412.04301/) (2024)

## Built on by (most cited first, 1 of 1)

- [Beyond Temporal Smoothing: Spatial Energy Budgets Stabilize One-Step Diffusion Editing](https://mlsanity.com/paper/2609.32841/) (2026)

## Abstract (arXiv)

One-step diffusion editors are fast because they avoid inversion and iterative optimization, but a single transport update must be aggressive enough to realize the target prompt and conservative enough to preserve the source image--and no fixed update strength satisfies both demands across edit types. We treat this tension as a post-hoc candidate-selection problem on top of energy-field transport rather than as a new editing model. Our proposed method, Riemannian Residual Line Search, first builds a stronger edit by estimating the local time curvature of the prompt-delta field and projecting the corrected direction back onto the update norm of the original first-order energy-field transport estimation. It then forms a small residual path from the source image to this strong edit, retains the original first-order output as one candidate, and picks the final image by maximizing target-prompt CLIP alignment. On a 700-sample PIE-Bench++ evaluation across 10 edit type IDs, our method achieves state-of-the-art (SOTA) performance among current one-step update algorithms.