Text-to-image (T2I) diffusion models have achieved impressive image generation quality and are increasingly fine-tuned for personalized applications. However, these models often inherit unsafe behaviors from toxic pretraining data, raising growing safety concerns. While recent safety-driven unlearning methods have made promising progress in suppressing model toxicity, they are found to be fragile to downstream fine-tuning, as we reveal that state-of-the-art methods largely fail to retain their effectiveness even when fine-tuned on entirely benign datasets. To mitigate this problem, in this paper, we propose ResAlign, a safety-driven unlearning framework with enhanced resilience against downstream fine-tuning. By modeling downstream fine-tuning as an implicit optimization problem with a Moreau envelope-based reformulation, ResAlign enables efficient gradient estimation to minimize the recovery of harmful behaviors. Additionally, a meta-learning strategy is proposed to simulate a diverse distribution of fine-tuning scenarios to improve generalization. Extensive experiments across a wide range of datasets, fine-tuning methods, and configurations demonstrate that ResAlign consistently outperforms prior unlearning approaches in retaining safety, while effectively preserving benign generation capability. Our code and pretrained models are publicly available here. . Disclaimer: This paper includes AI-generated images containing partially nude human figures and other sensitive content, shown only for research purposes.

The optimal policy in various real-world strategic decision-making problems depends both on the environmental configuration and exogenous events.

In this work, we propose Natural Hypergradient Descent (NHGD), a new method for solving bilevel optimization problems. To address the computational bottleneck in hypergradient estimation--namely, the need to compute or approximate Hessian inverse--we exploit the statistical structure of the inner optimization problem and use the empirical Fisher information matrix as an asymptotically consistent surrogate for the Hessian. This design enables a parallel optimize-and-approximate framework in which the Hessian-inverse approximation is updated synchronously with the stochastic inner optimization, reusing gradient information at negligible additional cost. Our main theoretical contribution establishes high-probability error bounds and sample complexity guarantees for NHGD that match those of state-of-the-art optimize-then-approximate methods, while significantly reducing computational time overhead. Empirical evaluations on representative bilevel learning tasks further demonstrate the practical advantages of NHGD, highlighting its scalability and effectiveness in large-scale machine learning settings.

Toaddress theabovechallenges, wepropose anovelhyperparameter mutation (HPM) scheduling algorithm in this study, which adopts a population based training framework to explicitly learn a trade-off (i.e., a mutation schedule) between using the hypergradient-guided local search and the mutation-driven global search.

Now we return to the second part of (9). This illustrates how tight the upper bound is. We use a GeForce RTX 2080 Ti GPU for all experiments. Instead, we always carve out a validation set from our training set. Figure 1 The batch size is set to 128, and 1000 fixed images are used for the validation data. Here we provide the raw hypergradients corresponding to the outer optimization shown in Appendices: Figure 1.