TILDE: TILt-based Distributional Erasure for Concept Unlearning

Concept unlearning in text-to-image diffusion models is critical for safe and practical deployment: with rising privacy concerns, copyright disputes, trademark constraints, and safety regulations, deployed systems must be able to suppress unwanted concepts after training. Existing methods often remove the target concept effectively, but practical unlearning also requires an equally fundamental property: the unlearned model should retain quality, diversity, and semantic coverage on benign generation. The gold standard is a retain-only model trained from scratch without the unwanted data. However, common erasure objectives do not specify which post-unlearning distribution should approximate this reference, leaving retention as an implicit consequence of the update rule. We propose TILDE, TILt-based Distributional Erasure, which formulates concept unlearning as a distributional alignment problem: the desired target is the minimum-deviation conditional distribution from the pretrained model under a forgetting constraint. This energy-tilted, anchor-free target suppresses concept-expressing images while preserving benign relative mass for each prompt. We instantiate this principle with residual $\nabla$-GFlowNet training, which learns the score correction induced by the forget energy relative to the pretrained diffusion model. Across objects, artistic styles, and characters, TILDE achieves strong forgetting while improving retention and distributional fidelity over prior baselines.