Towards Bounded Continuous Concepts Erasure in Text-to-image Diffusion Models

Text-to-image (T2I) diffusion models excel at generating high-fidelity images, yet they raise significant concerns regarding copyright infringement and unsafe content. Concept erasure mitigates these risks by removing specific semantics from a pretrained model. In real-world deployments, however, erasure requests often arrive sequentially rather than being known in advance. This continuous concept erasure setting requires a model to suppress each new target, retain all previous erasures, and preserve its generation ability on non-target concepts. Existing methods, primarily designed for isolated edits, struggle with the accumulated drift and historical erasure degradation caused by repeated updates. To address these challenges, we propose Lyapunov-constrained Continuous Concept Erasure (LCCE). LCCE formulates continuous erasure as an online control problem, using a dynamic virtual queue to accumulate preservation-budget violations and adaptively regulate subsequent edits. A historical retention loss further maintains the erased states established for previous targets. To provide the queue with a consistent preservation signal, LCCE identifies a semantic neighborhood for each target and incrementally consolidates these neighborhoods into a cumulative preservation bank. The resulting per-stage objective admits a closed-form solution, enabling efficient sequential editing without iterative fine-tuning. Comprehensive experiments demonstrate that LCCE outperforms state-of-the-art baselines. Even after sequentially erasing 100 artist concepts, LCCE reliably suppresses the target styles while maintaining high generative fidelity on non-target concepts. Our code will be released upon acceptance.