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

TL;DR

GeoEdit introduces a training-free, local manifold tangent space approach for efficient, fine-grained editing of diffusion models without full re-diffusion, enabling rapid and continuous semantic modifications.

Contribution

It proposes a novel Jacobian-free algorithm that estimates local tangent spaces from samples, allowing on-manifold edits in diffusion models without retraining or extensive computation.

Findings

Enables rapid, iterative edits with preserved fidelity.

Produces smooth, semantic traversals and effective CLIP-guided optimization.

Demonstrates practical interactive editing in diffusion models.

Abstract

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.