Unlearning in Diffusion Models: A Unified Framework with KL Divergence and Likelihood Constraints

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.

Concept unlearning aims to erase a target concept from a pretrained text-to-image diffusion model without retraining. Closed-form methods are attractive in this setting because they apply a single deterministic edit to the cross-attention weights and add no inference-time cost. Existing closed-form methods, however, represent the target concept through the text encoder's response to a few short anchor prompts that name it, and paraphrased prompts that evoke the concept without naming it consistently bypass the edit. We argue that the target should instead be represented in the cross-attention activation space. Text embeddings describe the user's prompt, while cross-attention activations describe what the model is about to render, and the latter generalize to paraphrase the anchor templates do not cover. Building on this observation, we propose PURE (Projection in U-Net Rendering for Erasure), a closed-form method that builds the forget and retain bases from per-layer cross-attention activations captured along a short denoising trajectory and applies a single linear projector to the cross-attention key and value weights. On a recent holistic concept-unlearning benchmark covering ten concepts across artistic style, intellectual property, celebrity, and NSFW categories, PURE significantly reduces target leakage under paraphrased and adversarial prompts while preserving retain concepts close to the unedited model, yielding the best overall forget-retain trade-off among evaluated methods.

Machine unlearning aims to remove the influence of specific forget training data due to privacy, copyright or bias concerns while maintaining the model performance on the remaining retain data. Existing unlearning algorithms, such as optimizing a weighted combination of losses, have tried to achieve these objectives of improving forget quality and maintaining retain utility. However, they do not guarantee that these objectives can be improved by a specified extent for all forget and retain data. In this work, we address this limitation with a novel and theoretically-grounded approach from a constrained optimization perspective. Firstly, we identify that the hardness of reconciling both objectives can be quantified by the similarity between the forget data and the retain data. Next, we derive an unlearning algorithm (HAMU) with the overall goal of guaranteeing a specified improvement in forget quality while minimizing the retain utility cost/degradation by updating the model weights based on our hardness measure. Our hardness measure also informs users when retain utility degradation is unavoidable, i.e., both objectives cannot be improved simultaneously, and stopping should be considered. Our algorithm is applicable to non-convex models and is easily parallelizable, making it readily deployable in real-world scenarios. We empirically demonstrate HAMU's superior performance over baselines on both image and text datasets using large models. Our code is available at https://github.com/aoi3142/HAMU.