# GeoEdit: Local Frames for Fast, Training-Free On-Manifold Editing in Diffusion Models

arXiv: https://arxiv.org/abs/2604.24238 · HTML: https://mlsanity.com/paper/2604.24238/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 29 of its 37 references that are in the map.
- First posted on arXiv 27 Apr 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

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

- [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)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Sigmoid Loss for Language Image Pre-Training](https://mlsanity.com/paper/2303.15343/) (2023)
- [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)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Null-text Inversion for Editing Real Images using Guided Diffusion Models](https://mlsanity.com/paper/2211.09794/) (2022)
- [Plug-and-Play Diffusion Features for Text-Driven Image-to-Image Translation](https://mlsanity.com/paper/2211.12572/) (2022)
- [MasaCtrl: Tuning-Free Mutual Self-Attention Control for Consistent Image Synthesis and Editing](https://mlsanity.com/paper/2304.08465/) (2023)
- [DiffEdit: Diffusion-based semantic image editing with mask guidance](https://mlsanity.com/paper/2210.11427/) (2022)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Zero-shot Image-to-Image Translation](https://mlsanity.com/paper/2302.03027/) (2023)
- [SDXL-Lightning: Progressive Adversarial Diffusion Distillation](https://mlsanity.com/paper/2402.13929/) (2024)
- [Manifold Preserving Guided Diffusion](https://mlsanity.com/paper/2311.16424/) (2023)
- [CFG++: Manifold-constrained Classifier Free Guidance for Diffusion Models](https://mlsanity.com/paper/2406.08070/) (2024)
- [Understanding the Latent Space of Diffusion Models through the Lens of Riemannian Geometry](https://mlsanity.com/paper/2307.12868/) (2023)
- [DiffMorpher: Unleashing the Capability of Diffusion Models for Image Morphing](https://mlsanity.com/paper/2312.07409/) (2023)
- [A Geometric View of Data Complexity: Efficient Local Intrinsic Dimension Estimation with Diffusion Models](https://mlsanity.com/paper/2406.03537/) (2024)
- [Pathways on the Image Manifold: Image Editing via Video Generation](https://mlsanity.com/paper/2411.16819/) (2024)
- [IMPUS: Image Morphing with Perceptually-Uniform Sampling Using Diffusion Models](https://mlsanity.com/paper/2311.06792/) (2023)
- [Boomerang: Local sampling on image manifolds using diffusion models](https://mlsanity.com/paper/2210.12100/) (2022)
- [TCFG: Tangential Damping Classifier-free Guidance](https://mlsanity.com/paper/2503.18137/) (2025)
- [SDDM: Score-Decomposed Diffusion Models on Manifolds for Unpaired Image-to-Image Translation](https://mlsanity.com/paper/2308.02154/) (2023)
- [Exploring the Representation Manifolds of Stable Diffusion Through the Lens of Intrinsic Dimension](https://mlsanity.com/paper/2302.09301/) (2023)

## Abstract (arXiv)

Diffusion models are a leading paradigm for data generation, but training-free editing typically re-runs the full denoising trajectory for every edit strength, making iterative refinement expensive. To address this issue, we instead edit near the data manifold, where small local updates can replace repeated re-synthesis. To enable this, we estimate a local manifold tangent space directly from perturbed samples and prove that this sample-based estimator closely approximates the true tangent. Building on this guarantee, we devise a Jacobian-free algorithm that constructs a tangent frame via small perturbations to the initial noise and alternates small tangent moves with diffusion-based projections. Updates within this frame follow principled on-manifold directions while suppressing off-manifold drift, enabling fine-grained edits without full re-diffusion or additional training. Edit strength is controlled by the number of steps for rapid, continuous adjustments that preserve fidelity and plug into existing samplers. Empirically, the resulting tangent directions yield smooth, semantic unsupervised traversals and effective CLIP-guided optimization, demonstrating practical interactive continuous editing.