A Unified Framework for Diffusion Model Unlearning with f-Divergence

Most existing methods for concept unlearning in text-to-image diffusion models minimize a mean squared error (MSE) loss between the denoiser outputs conditioned on a target and an anchor concept, which is implicitly the KL divergence between two Gaussians. We generalize this objective to any f-divergence, recovering MSE as the KL instance, and identify a family of α-divergences whose Gaussian closed-form yields cheap, MSE-like training objectives. For the remaining f-divergences, we provide a min-max objective based on the variational formulation of the f-divergence. We theoretically analyze and numerically validate how different f-divergences impact the gradient magnitude and the convergence properties of the algorithm, affecting the quality of unlearning. For instance, we observe that the Hellinger closed-form instance consistently dominates MSE across multiple scenarios. More generally, the proposed unified framework offers a flexible paradigm for selecting the optimal divergence based on the application and user goal, allowing for finer control over the trade-off between unlearning efficacy and generative fidelity.