mlsanityData to 7 Oct 2026

Exploring Low-Dimensional Subspaces in Diffusion Models for Controllable Image Editing

arXiv 2409.02374 ↗First posted 4 Sep 2024cs.CV cs.LGcited by 15

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

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.

Key facts. Cited by 15 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 64 of its 87 references that are in the map. First posted on arXiv 4 Sep 2024.

Builds on

64 of 87 references.

Closest ancestors · 20

Same direction, newest first

  1. 2024Enabling Local Editing in Diffusion Models by Joint and Individual Component Analysis29 Aug
  2. 2024Diffusion Models and Representation Learning: A Survey30 Jun
  3. 2024Scaling Rectified Flow Transformers for High-Resolution Image Synthesis5 Mar
  4. 2023NoiseCLR: A Contrastive Learning Approach for Unsupervised Discovery of Interpretable Directions in Diffusion Models8 Dec
  5. 2023The Hidden Linear Structure in Score-Based Models and its Application17 Nov
  6. 2023Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference6 Oct
  7. 2023On the Posterior Distribution in Denoising: Application to Uncertainty Quantification24 Sep
  8. 2023Understanding the Latent Space of Diffusion Models through the Lens of Riemannian Geometry24 Jul
  9. 2023Discovering Interpretable Directions in the Semantic Latent Space of Diffusion Models20 Mar
  10. 2022Diffusion Models already have a Semantic Latent Space20 Oct
  11. 2022All are Worth Words: A ViT Backbone for Diffusion Models25 Sep
  12. 2022Understanding Diffusion Models: A Unified Perspective25 Aug
8 more
  1. 2022Classifier-Free Diffusion Guidance26 Jul
  2. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps2 Jun
  3. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  4. 2022Perception Prioritized Training of Diffusion Models1 Apr
  5. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  6. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  7. 2020Denoising Diffusion Implicit Models6 Oct
  8. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 44

  1. 2021Learning Transferable Visual Models From Natural Language Supervisioncited by 33,456
  2. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  3. 2021LoRA: Low-Rank Adaptation of Large Language Modelscited by 14,084
  4. 2018The Unreasonable Effectiveness of Deep Features as a Perceptual Metriccited by 11,029
  5. 2023Segment Anythingcited by 8,158
  6. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,539
  7. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,322
  8. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 5,986
  9. 2023Adding Conditional Control to Text-to-Image Diffusion Modelscited by 5,466
  10. 2022LAION-5B: An open large-scale dataset for training next generation image-text modelscited by 4,131
  11. 2014Deep Learning Face Attributes in the Wildcited by 3,679
  12. 2022DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generationcited by 3,286
32 more
  1. 2022InstructPix2Pix: Learning to Follow Image Editing Instructionscited by 2,591
  2. 2023Stable Video Diffusion: Scaling Latent Video Diffusion Models to Large Datasetscited by 2,526
  3. 2022Prompt-to-Prompt Image Editing with Cross Attention Controlcited by 2,409
  4. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,375
  5. 2015LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loopcited by 1,350
  6. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,339
  7. 2020Training Generative Adversarial Networks with Limited Datacited by 1,184
  8. 2022Null-text Inversion for Editing Real Images using Guided Diffusion Modelscited by 1,168
  9. 2019StarGAN v2: Diverse Image Synthesis for Multiple Domainscited by 1,095
  10. 2021Blended Diffusion for Text-driven Editing of Natural Imagescited by 924
  11. 2024Eyes Wide Shut? Exploring the Visual Shortcomings of Multimodal LLMscited by 719
  12. 2023Text2Video-Zero: Text-to-Image Diffusion Models are Zero-Shot Video Generatorscited by 666
  13. 2022DiffEdit: Diffusion-based semantic image editing with mask guidancecited by 643
  14. 2021DiffusionCLIP: Text-Guided Diffusion Models for Robust Image Manipulationcited by 640
  15. 2020WaveGrad: Estimating Gradients for Waveform Generationcited by 620
  16. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraintscited by 501
  17. 2023Instruct-NeRF2NeRF: Editing 3D Scenes with Instructionscited by 482
  18. 2021The Intrinsic Dimension of Images and Its Impact on Learningcited by 307
  19. 2023Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistencycited by 180
  20. 2023Video Probabilistic Diffusion Models in Projected Latent Spacecited by 171
  21. 2022Uncovering the Disentanglement Capability in Text-to-Image Diffusion Modelscited by 116
  22. 2023InstructEdit: Improving Automatic Masks for Diffusion-based Image Editing With User Instructionscited by 64
  23. 2023ZONE: Zero-Shot Instruction-Guided Local Editingcited by 61
  24. 2024Zero-Shot Unsupervised and Text-Based Audio Editing Using DDPM Inversioncited by 58
  25. 2021Low-Rank Subspaces in GANscited by 52
  26. 2022Understanding 3D Object Articulation in Internet Videoscited by 36
  27. 2023Understanding Deep Representation Learning via Layerwise Feature Compression and Discriminationcited by 31
  28. 2024Compressible Dynamics in Deep Overparameterized Low-Rank Learning & Adaptationcited by 26
  29. 2023Boundary Guided Learning-Free Semantic Control with Diffusion Modelscited by 23
  30. 2024PaCE: Parsimonious Concept Engineering for Large Language Modelscited by 19
  31. 2024A Global Geometric Analysis of Maximal Coding Rate Reductioncited by 13
  32. 2023Robust Physics-based Deep MRI Reconstruction Via Diffusion Purificationcited by 4

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 8; 2025: 6; 2026: 1.

15 papers.

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  1. 2024O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptionscited by 48
  2. 2024Denoising diffusion probabilistic models are optimally adaptive to unknown low dimensionalitycited by 44
  3. 2024Understanding Generalizability of Diffusion Models Requires Rethinking the Hidden Gaussian Structurecited by 38
  4. 2024Manifolds, Random Matrices and Spectral Gaps: The geometric phases of generative diffusioncited by 31
  5. 2024SITCOM: Step-wise Triple-Consistent Diffusion Sampling for Inverse Problemscited by 23
  6. 2025Emergence and Evolution of Interpretable Concepts in Diffusion Modelscited by 20
  7. 2025A Closer Look at Model Collapse: From a Generalization-to-Memorization Perspectivecited by 18
  8. 2025Point Prompting: Counterfactual Tracking with Video Diffusion Modelscited by 5
  9. 2025Concept Lancet: Image Editing with Compositional Representation Transplantcited by 4
  10. 2026Personalized Image Generation via Human-in-the-loop Bayesian Optimizationcited by 2
  11. 2024Shallow Diffuse: Robust and Invisible Watermarking through Low-Dimensional Subspaces in Diffusion Modelscited by 1
  12. 2025Instructing Text-to-Image Diffusion Models via Classifier-Guided Semantic Optimizationcited by 1
3 more
  1. 2024Unsupervised Panoptic Interpretation of Latent Spaces in GANs Using Space-Filling Vector Quantizationcited by 0
  2. 2024Subspace Langevin Monte Carlocited by 0
  3. 2025Generative human motion mimicking through feature extraction in denoising diffusion settingscited by 0

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  2. 2025Self-Attention Decomposition For Training Free Diffusion Editing
  3. 2025Exploring the latent space of diffusion models directly through singular value decomposition
  4. 2026Guidance for Low-Level Perceptual Editing in Unconditional Diffusion Models
  5. 2023High-Fidelity Diffusion-based Image Editing
  6. 2023Unsupervised Discovery of Semantic Latent Directions in Diffusion Models
  7. 2022Image Embedding for Denoising Generative Models
  8. 2024Latent Space Disentanglement in Diffusion Transformers Enables Precise Zero-shot Semantic Editing