Large Vision-Language Foundation Models (VLFM), such as CLIP, ALIGN and Florence, are trained on large-scale datasets of image-caption pairs and achieve superior transferability and robustness on downstream tasks, but they are difficult to use in many practical applications due to their large size, high latency and fixed architectures. Unfortunately, recent work shows training a small custom VLFM for resource-limited applications is currently very difficult using public and smaller-scale data. In this paper, we introduce a new distillation mechanism (DIME-FM) that allows us to transfer the knowledge contained in large VLFMs to smaller, customized foundation models using a relatively small amount of inexpensive, unpaired images and sentences. We transfer the knowledge from the pre-trained CLIP-ViTL/14 model to a ViT-B/32 model, with only 40M public images and 28.4M unpaired public sentences. The resulting model "Distill-ViT-B/32" rivals the CLIP-ViT-B/32 model pre-trained on its private WiT dataset (400M image-text pairs): Distill-ViT-B/32 achieves similar results in terms of zero-shot and linear-probing performance on both ImageNet and the ELEVATER (20 image classification tasks) benchmarks. It also displays comparable robustness when evaluated on five datasets with natural distribution shifts from ImageNet.