Diffusion data-point unlearning is typically evaluated immediately after each deletion, even though subsequent requests may repeatedly update the same model. We identify sequential reappearance, a failure mode in which an instance that is initially judged to be forgotten later returns to the memorized regime without reuse of the deleted data or adversarial fine-tuning. To capture this behavior, we introduce a target-level evaluation protocol that tracks whether each target is forgotten immediately, remains forgotten at the end of the sequence, or reappears during subsequent deletions. We further find that targets that later reappear exhibit sharper local denoising-loss geometry after deletion than targets that remain forgotten.
Data unlearning aims to remove the influence of specific training samples from a trained model. In fine-tuning methods, data unlearning relies primarily on loss maximization over forget samples, which often leads to quality degradation or incomplete forgetting. Existing methods perform unlearning uniformly across diffusion stages, ignoring diffusion dynamics from noise to data. Our systematic study of diffusion phases shows that forgetting in diffusion models is uneven across time and frequency, with theoretical justification of distributive distortion and forgetting-utility trade-off. By selectively forgetting time and frequency in diffusion models, we achieve both higher unlearning success rates and improved generation quality across diverse settings, including both conditional and unconditional scenarios. We also introduce an improved SSCD metric that measures dissimilarity using a normalized perturbation distance. Together, we provide practical insights for understanding and improving data unlearning in diffusion models.
Unlearning in diffusion models aims to remove undesirable data or concepts while preserving the utility of pretrained models -- two fundamentally conflicting objectives. We propose a principled constrained optimization framework that formulates unlearning as minimizing the deviation from a pretrained model, subject to explicit separation constraints from the unlearning distributions. Specifically, we formulate three constrained optimization problems based on reverse and forward KL divergences, and likelihood constraints. The first two generalize existing approaches for concept and data unlearning, while the third offers a novel and natural formulation for unlearning. Despite the nonconvexity of the KL constraints, we establish strong duality for all three problems, enabling us to explicitly characterize their optimal solutions as unlearning targets and develop primal-dual algorithms for each formulation. Experimental results demonstrate that our KL-constrained approach achieves superior retention-unlearning tradeoffs compared to weight-based baselines for concept and data unlearning, and that our likelihood-based approach matches unlearning effectiveness while better preserving retained concepts compared to baselines.
Real-world deployment of text-to-image diffusion models requires continual concept removal as new privacy, copyright, or safety obligations arise over time. Existing unlearning methods, however, are designed for single-step deletion and collapse after only 3-5 sequential applications. We trace this instability to two compounding factors: (i) coarse mapping targets that cause degradation to accumulate unnecessarily across steps, and (ii) the absence of local protection for semantically neighboring concepts, whose shared internal representations make them the first to suffer collateral damage. Because this damage is strongest in the local semantic neighborhood of the forget concept, global replay alone cannot prevent it. Building on this analysis, we propose Locality-Aware Continual Unlearning (LACU), a framework with two complementary mechanisms. Locality-Aware Target Selection chooses, for each forget prompt, the context-preserving mapping prompt that the diffusion model itself treats as most similar to the original prompt, measured by score-prediction distance (how differently the model denoises the same noisy image under two text conditions), ensuring each update is as small and targeted as possible. Locality-Aware Replay uses the same metric to identify the retain concepts closest to the forget concept in the model's own representation and replays them as a local functional regularizer, directly shielding the most vulnerable neighborhood. Combined with teacher-student distillation and lightweight ℓ2 parameter regularization, LACU maintains stable unlearning over 10 sequential steps, preserving significantly higher related retention (RRacc) and general retention (GRacc) than recent baselines.