Machine Unlearning (MU) aims to remove the influence of specific knowledge from a pretrained model. Existing methods often rely on retained training data to preserve utility; such dependence is impractical due to privacy and scalability constraints. A further complication arises when unlearning is applied to vision-language models (VLMs), where entangled multimodal representations make targeted forgetting especially challenging. We propose DIET, a principled retain-data-free unlearning method for VLMs that addresses these challenges by leveraging the geometry of hyperbolic space. The core idea is to push forget embeddings toward class-mismatched prototypes located at the boundary of the hyperbolic space. In hyperbolic geometry, points near the boundary become infinitely distant from interior points. As a result, moving forget embeddings to the boundary makes their influence on the model asymptotically negligible. To formalize this, we guide the forgetting process using the Busemann function, which quantifies directional distance to the boundary. We further develop an adaptive scheme based on optimal transport that selects mismatched prototypes for each forget embedding, enabling flexible unlearning dynamics. Extensive experiments on fine-grained datasets such as Flowers102, OxfordPets, and StanfordCars show that DIET achieves an average forget accuracy of 8.06%, while preserving 69.04% utility using only 16 samples per concept, significantly outperforming the best retain-free baselines with a 117.5% improvement in model utility, and showing competitive performance to retain-data baselines with only a 3.79% drop

We introduce a language-grounded visual prompting method to adapt the visual encoder of vision-language models for downstream tasks. By capitalizing on language integration, we devise a parameter-efficient strategy to adjust the input of the visual encoder, eliminating the need to modify or add to the model's parameters. Due to this design choice, our algorithm can operate even in black-box scenarios, showcasing adaptability in situations where access to the model's parameters is constrained. We will empirically demonstrate that, compared to prior art, grounding visual prompts with language enhances both the accuracy and speed of adaptation. Moreover, our algorithm excels in base-to-novel class generalization, overcoming limitations of visual prompting and exhibiting the capacity to generalize beyond seen classes. We thoroughly assess and evaluate our method across a variety of image recognition datasets, such as EuroSAT, UCF101, DTD, and CLEVR, spanning different learning situations, including few-shot adaptation, base-to-novel class generalization, and transfer learning.