无需训练即可快速编辑扩散模型，保持图像质量并支持连续微调。
GeoEdit: Local Frames for Fast, Training-Free On-Manifold Editing in Diffusion Models
- 通过扰动样本估计数据流形的局部切空间，实现高效局部更新。
- 在切空间内移动可避免重复去噪，编辑速度提升数倍且保真度高。
- 适合需要实时交互式编辑的生成模型应用，如图像设计与内容创作。
扩散模型是主流的数据生成范式，但无训练编辑通常需为每种编辑强度重新运行完整去噪过程，导致迭代优化成本高昂。为此，我们转而在数据流形附近进行编辑，利用小规模局部更新替代重复重合成。通过从扰动样本中直接估计局部流形切空间，并证明该基于样本的估计器能紧密逼近真实切空间，我们提出一种无雅可比矩阵的算法：通过初始噪声的小扰动构建切空间框架，交替执行小步切向移动与基于扩散的投影。在该框架内的更新遵循流形上的合理方向，有效抑制偏离流形的漂移，实现无需全量重扩散或额外训练的细粒度编辑。编辑强度由迭代步数控制，支持快速、连续调整，同时保持图像保真度，兼容现有采样器。实验表明，所得切向方向可产生平滑、语义连贯的无监督遍历，以及高效的CLIP引导优化，验证了其在实际交互式连续编辑中的有效性。
原文摘要 · Abstract (English)
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.
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