# Exploring Low-Dimensional Subspaces in Diffusion Models for Controllable Image Editing Source: [Exploring Low-Dimensional Subspaces in Diffusion Models for Controllable Image Editing]() Collection index: [llms.txt]() Data updated: 2026-03-18T05:00:04.466Z Authors: Siyi Chen, Huijie Zhang, Minzhe Guo, Yifu Lu, Peng Wang, Qing Qu Published: 2024-09-04T01:47:01.000Z ## Abstract Recently, diffusion models have emerged as a powerful class of generative models. Despite their success, there is still limited understanding of their semantic spaces. This makes it challenging to achieve precise and disentangled image generation without additional training, especially in an unsupervised way. In this work, we improve the understanding of their semantic spaces from intriguing observations: among a certain range of noise levels, (1) the learned posterior mean predictor (PMP) in the diffusion model is locally linear, and (2) the singular vectors of its Jacobian lie in low-dimensional semantic subspaces. We provide a solid theoretical basis to justify the linearity and low-rankness in the PMP. These insights allow us to propose an unsupervised, single-step, training-free LOw-rank COntrollable image editing (LOCO Edit) method for precise local editing in diffusion models. LOCO Edit identified editing directions with nice properties: homogeneity, transferability, composability, and linearity. These properties of LOCO Edit benefit greatly from the low-dimensional semantic subspace. Our method can further be extended to unsupervised or text-supervised editing in various text-to-image diffusion models (T-LOCO Edit). Finally, extensive empirical experiments demonstrate the effectiveness and efficiency of LOCO Edit. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Image Editing on CelebA-HQ](): Image Editing; CelebA-HQ; LPIPS: 0.08. - [Semantic Image Editing on CelebA-HQ (test)](): Semantic Image Editing; CelebA-HQ (test); Editing Time (s): 79. - [Image Editing on CelebA-HQ (test)](): Image Editing; CelebA-HQ (test); SSIM: 0.87. ## Original sources and implementation [Original paper]() [PDF]()