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

The success of text-to-image generation enabled by diffusion models has imposed an urgent need to erase 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 requires a precise removal of the target concept during generation (i.e., erasure efficacy), while a minimal impact on non-target content generation (i.e., prior preservation). Existing methods are either computationally costly or face challenges in maintaining an effective balance between erasure efficacy and prior preservation. To improve, we propose a precise, fast, and low-cost concept erasure method, called \textbf{Ada}ptive \textbf{V}aule \textbf{D}ecomposer (AdaVD), which is training-free. This method is grounded in a classical linear algebraic orthogonal complement operation, implemented in the value space of each cross-attention layer within the UNet of diffusion models. An effective shift factor is designed to adaptively navigate the erasure strength, enhancing prior preservation without sacrificing erasure efficacy. Extensive experimental results show that the proposed AdaVD is effective at both single and multiple concept erasure, showing a 2- to 10-fold improvement in prior preservation as compared to the second best, meanwhile achieving the best or near best erasure efficacy, when comparing with both training-based and training-free state of the arts. AdaVD supports a series of diffusion models and downstream image generation tasks, with code to be publicly available.