Hyperbolic embeddings have demonstrated their effectiveness in capturing measures of uncertainty and hierarchical relationships across various deep-learning tasks, including image segmentation and active learning. However, their application in modern vision-language models (VLMs) has been limited. A notable exception is MERU, which leverages the hierarchical properties of hyperbolic space in the CLIP ViT-large model, consisting of hundreds of millions of parameters. In our work, we address the challenges of scaling multi-modal hyperbolic models by orders of magnitude in terms of parameters (billions) and training complexity using the BLIP-2 architecture. Although hyperbolic embeddings offer potential insights into uncertainty not present in Euclidean embeddings, our analysis reveals that scaling these models is particularly difficult. We propose a novel training strategy for a hyperbolic version of BLIP-2, which allows to achieve comparable performance to its Euclidean counterpart, while maintaining stability throughout the training process and showing a meaningful indication of uncertainty with each embedding.