This paper considers contrastive training for cross-modal 0-shot transfer wherein a pre-trained model in one modality is used for representation learning in another domain using pairwise data. The learnt models in the latter domain can then be used for a diverse set of tasks in a 0-shot way, similar to Contrastive Language-Image Pre-training (CLIP) and Locked-image Tuning (LiT) that have recently gained considerable attention. Classical contrastive training employs sets of positive and negative examples to align similar and repel dissimilar training data samples. However, similarity amongst training examples has a more continuous nature, thus calling for a more `non-binary' treatment. To address this, we propose a new contrastive loss function called Continuously Weighted Contrastive Loss (CWCL) that employs a continuous measure of similarity. With CWCL, we seek to transfer the structure of the embedding space from one modality to another. Owing to the continuous nature of similarity in the proposed loss function, these models outperform existing methods for 0-shot transfer across multiple models, datasets and modalities. By using publicly available datasets, we achieve 5-8% (absolute) improvement over previous state-of-the-art methods in 0-shot image classification and 20-30% (absolute) improvement in 0-shot speech-to-intent classification and keyword classification.