Closed-Form Concept Erasure via Double Projections

Concept erasure is extensively utilized in image generation to prevent text-to-image models from generating undesired content. Existing methods can effectively erase narrow concepts that are specific and concrete, such as distinct intellectual properties (e.g. Pikachu) or recognizable characters (e.g. Elon Musk). However, their performance degrades on broad concepts such as sexual'' or violent'', whose wide scope and multi-faceted nature make them difficult to erase reliably. To overcome this limitation, we exploit the model's intrinsic embedding geometry to identify latent embeddings that encode a given concept. By clustering these embeddings, we derive a set of concept prototypes that summarize the model's internal representations of the concept, and employ them as negative conditioning signals during inference to achieve precise and reliable erasure. Extensive experiments across multiple benchmarks show that our approach achieves substantially more reliable removal of broad concepts while preserving overall image quality, marking a step towards safer and more controllable image generation.

Concept erasure has emerged as a promising approach to mitigate undesired or unsafe content in diffusion models, yet existing methods still face significant limitations. While training-based methods are effective, their high computational cost limits scalability. Editing-based methods are more efficient and deployment-friendly, yet they struggle to simultaneously achieve precise concept erasure and preserve overall generative capacity. We identify this core limitation of the editing-based methods as reliance on additive parameter updates. Our empirical analysis reveals that concept semantics primarily depend on neuron direction rather than neuron magnitude, while overall generative capacity relies on the angular geometry of neurons. As additive updates inherently entangle direction, magnitude, and angular geometry, they inevitably introduce unintended interference between concept erasure and overall generation performance. To address this, we propose Orthogonal Concept Erasure (OCE), which reformulates editing-based erasure as multiplicative parameter updates from a geometric perspective. Specifically, OCE applies layer-wise orthogonal transformations derived from a closed-form solution to the parameters, enabling precise concept erasure while preserving the neuron magnitude and angular geometry. Furthermore, to address conflicting constraints in multi-concept erasure, OCE introduces a subspace-level objective with structured subspace manipulation, yielding a more effective and scalable erasure. Extensive experiments on single- and multi-concept erasure demonstrate that OCE outperforms existing methods in concept erasure and non-target preservation, erasing up to 100 concepts in 4.3 s. Code: https://github.com/HansSunY/OCE.

As text-to-image diffusion models grow increasingly prevalent, the ability to remove specific concepts-mostly explicit content and many copyrighted characters or styles-has become essential for safety and compliance. Existing unlearning approaches often require costly re-training, modify parameters at the cost of degradation of unrelated concept fidelity, or depend on indirect inference-time adjustment that compromise the effectiveness of concept erasure. Inspired by the success of energy-guided sampling for preservation of the condition of diffusion models, we introduce Energy-Guided Latent Optimization for Concept Erasure (EGLOCE), a training-free approach that removes unwanted concepts by re-directing noisy latent during inference. Our method employs a dual-objective framework: a repulsion energy that steers generation away from target concepts via gradient descent in latent space, and a retention energy that preserves semantic alignment to the original prompt. Combined with previous approaches that either require erroneous modified model weights or provide weak inference-time guidance, EGLOCE operates entirely at inference and enhances erasure performance, enabling plug-and-play integration. Extensive experiments demonstrate that EGLOCE improves concept removal while maintaining image quality and prompt alignment across baselines, even with adversarial attacks. To the best of our knowledge, our work is the first to establish a new paradigm for safe and controllable image generation through dual energy-based guidance during sampling.