# Precise, Fast, and Low-cost Concept Erasure in Value Space: Orthogonal Complement Matters

arXiv: https://arxiv.org/abs/2412.06143 · HTML: https://mlsanity.com/paper/2412.06143/

## Key facts

- Cited by 40 papers in the map (data through 14 Oct 2026).
- Placed in Robustness, privacy and adversarial aspects, one of 14 directions in Diffusion models.
- Builds on 39 of its 48 references that are in the map.
- First posted on arXiv 9 Dec 2024.

## Placed in

- Diffusion models / [Robustness, privacy and adversarial aspects](https://mlsanity.com/diffusion/robustness-privacy-and-adversarial-aspects/)

## Builds on (most cited first, 30 of 39)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [LAION-5B: An open large-scale dataset for training next generation image-text models](https://mlsanity.com/paper/2210.08402/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Prompt-to-Prompt Image Editing with Cross Attention Control](https://mlsanity.com/paper/2208.01626/) (2022)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [LAION-400M: Open Dataset of CLIP-Filtered 400 Million Image-Text Pairs](https://mlsanity.com/paper/2111.02114/) (2021)
- [IP-Adapter: Text Compatible Image Prompt Adapter for Text-to-Image Diffusion Models](https://mlsanity.com/paper/2308.06721/) (2023)
- [Extracting Training Data from Diffusion Models](https://mlsanity.com/paper/2301.13188/) (2023)
- [Erasing Concepts from Diffusion Models](https://mlsanity.com/paper/2303.07345/) (2023)
- [Safe Latent Diffusion: Mitigating Inappropriate Degeneration in Diffusion Models](https://mlsanity.com/paper/2211.05105/) (2022)
- [Diffusion Art or Digital Forgery? Investigating Data Replication in Diffusion Models](https://mlsanity.com/paper/2212.03860/) (2022)
- [Unified Concept Editing in Diffusion Models](https://mlsanity.com/paper/2308.14761/) (2023)
- [Multimodal datasets: misogyny, pornography, and malignant stereotypes](https://mlsanity.com/paper/2110.01963/) (2021)
- [Ablating Concepts in Text-to-Image Diffusion Models](https://mlsanity.com/paper/2303.13516/) (2023)
- [MACE: Mass Concept Erasure in Diffusion Models](https://mlsanity.com/paper/2403.06135/) (2024)
- [Red-Teaming the Stable Diffusion Safety Filter](https://mlsanity.com/paper/2210.04610/) (2022)
- [Ring-A-Bell! How Reliable are Concept Removal Methods for Diffusion Models?](https://mlsanity.com/paper/2310.10012/) (2023)
- [Controlling Text-to-Image Diffusion by Orthogonal Finetuning](https://mlsanity.com/paper/2306.07280/) (2023)
- [Glaze: Protecting Artists from Style Mimicry by Text-to-Image Models](https://mlsanity.com/paper/2302.04222/) (2023)
- [Key-Locked Rank One Editing for Text-to-Image Personalization](https://mlsanity.com/paper/2305.01644/) (2023)

## Built on by (most cited first, 30 of 40)

- [SPEED: Scalable, Precise, and Efficient Concept Erasure for Diffusion Models](https://mlsanity.com/paper/2503.07392/) (2025)
- [Easier Painting Than Thinking: Can Text-to-Image Models Set the Stage, but Not Direct the Play?](https://mlsanity.com/paper/2509.03516/) (2025)
- [Mass Concept Erasure in Diffusion Models with Concept Hierarchy](https://mlsanity.com/paper/2601.03305/) (2026)
- [Erasing Concepts, Steering Generations: A Comprehensive Survey of Concept Suppression](https://mlsanity.com/paper/2505.19398/) (2025)
- [SAEmnesia: Erasing Concepts in Diffusion Models with Supervised Sparse Autoencoders](https://mlsanity.com/paper/2509.21379/) (2025)
- [EraseFlow: Learning Concept Erasure Policies via GFlowNet-Driven Alignment](https://mlsanity.com/paper/2511.00804/) (2025)
- [CE-SDWV: Effective and Efficient Concept Erasure for Text-to-Image Diffusion Models via a Semantic-Driven Word Vocabulary](https://mlsanity.com/paper/2501.15562/) (2025)
- [Semantic Surgery: Zero-Shot Concept Erasure in Diffusion Models](https://mlsanity.com/paper/2510.22851/) (2025)
- [Safe and Reliable Diffusion Models via Subspace Projection](https://mlsanity.com/paper/2503.16835/) (2025)
- [Multimodal Unlearning Across Vision, Language, Video, and Audio: Survey of Methods, Datasets, and Benchmarks](https://mlsanity.com/paper/2607.07907/) (2026)
- [Concept Unlearning by Modeling Key Steps of Diffusion Process](https://mlsanity.com/paper/2507.06526/) (2025)
- [Generative Model Unlearning: A Survey through Target Events, Unlearning Operators, and Evaluation Protocols](https://mlsanity.com/paper/2507.19894/) (2025)
- [Reminiscence Attack on Residuals: Exploiting Approximate Machine Unlearning for Privacy](https://mlsanity.com/paper/2507.20573/) (2025)
- [Now You See It, Now You Don't - Instant Concept Erasure for Safe Text-to-Image and Video Generation](https://mlsanity.com/paper/2511.18684/) (2025)
- [ActErase: A Training-Free Paradigm for Precise Concept Erasure via Activation Redirection](https://mlsanity.com/paper/2601.00267/) (2026)
- [Neighbor-Aware Localized Concept Erasure in Text-to-Image Diffusion Models](https://mlsanity.com/paper/2603.25994/) (2026)
- [Thinking with Frames: Generative Video Distortion Evaluation via Frame Reward Model](https://mlsanity.com/paper/2601.04033/) (2026)
- [To Erase, or Not to Erase: Robust Training-Free Concept Erasure with Preservation aware Adaptive Ranked Subspace Expansion](https://mlsanity.com/paper/2607.23492/) (2026)
- [VCE: Safe Autoregressive Image Generation via Visual Contrast Exploitation](https://mlsanity.com/paper/2509.16986/) (2025)
- [GrOCE:Graph-Guided Online Concept Erasure for Text-to-Image Diffusion Models](https://mlsanity.com/paper/2511.12968/) (2025)
- [M-ErasureBench: A Comprehensive Multimodal Evaluation Benchmark for Concept Erasure in Diffusion Models](https://mlsanity.com/paper/2512.22877/) (2025)
- [FlowErase-RL: Rethinking Concept Erasure as Reward Optimization in Flow Matching Models](https://mlsanity.com/paper/2605.19739/) (2026)
- [Orthogonal Concept Erasure for Diffusion Models](https://mlsanity.com/paper/2605.28902/) (2026)
- [Prototype-Guided Concept Erasure in Diffusion Models](https://mlsanity.com/paper/2603.08271/) (2026)
- [MoKus: Leveraging Cross-Modal Knowledge Transfer for Knowledge-Aware Concept Customization](https://mlsanity.com/paper/2603.12743/) (2026)
- [PEAK: Precise and Persistent Concept Erasure via k-Sparse Autoencoders](https://mlsanity.com/paper/2608.10985/) (2026)
- [Your Unlearning Gives You Away: Identifying Erased Concepts in Diffusion Models](https://mlsanity.com/paper/2610.05601/) (2026)
- [Zero-Residual Concept Erasure via Progressive Alignment in Text-to-Image Model](https://mlsanity.com/paper/2508.04472/) (2025)
- [DICE: Disentangling Artist Style from Content via Contrastive Subspace Decomposition in Diffusion Models](https://mlsanity.com/paper/2602.08059/) (2026)
- [ADAPT: Attention Driven Adaptive Prompt Scheduling and InTerpolating Orthogonal Complements for Rare Concepts Generation](https://mlsanity.com/paper/2603.19157/) (2026)

## Abstract (arXiv)

Recent success of text-to-image (T2I) generation and its increasing practical applications, enabled by diffusion models, require urgent consideration of erasing unwanted concepts, e.g., copyrighted, offensive, and unsafe ones, from the pre-trained models in a precise, timely, and low-cost manner. The twofold demand of concept erasure includes not only a precise removal of the target concept (i.e., erasure efficacy) but also a minimal change on non-target content (i.e., prior preservation), during generation. Existing methods face challenges in maintaining an effective balance between erasure efficacy and prior preservation, and they can be computationally costly. To improve, we propose a precise, fast, and low-cost concept erasure method, called Adaptive Value Decomposer (AdaVD), which is training-free. Our method is grounded in a classical linear algebraic operation of computing the orthogonal complement, implemented in the value space of each cross-attention layer within the UNet of diffusion models. We design a shift factor to adaptively navigate the erasure strength, enhancing effective prior preservation without sacrificing erasure efficacy. Extensive comparative experiments with both training-based and training-free state-of-the-art methods demonstrate that the proposed AdaVD excels in both single and multiple concept erasure, showing 2 to 10 times improvement in prior preservation than the second best, meanwhile achieving the best or near best erasure efficacy. AdaVD supports a series of diffusion models and downstream image generation tasks, with code available on: https://github.com/WYuan1001/AdaVD.