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

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.