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Cross-modal encoders for vision-language (VL) tasks are often pretrained with carefully curated vision-language datasets. While these datasets reach an order of 10 million samples, the labor cost is prohibitive to scale further. Conversely, unimodal encoders are pretrained with simpler annotations that are less cost-prohibitive, achieving scales of hundreds of millions to billions. As a result, unimodal encoders have achieved state-of-art (SOTA) on many downstream tasks. However, challenges remain when applying to VL tasks. The pretraining data is not optimal for cross-modal architectures and requires heavy computational resources. In addition, unimodal architectures lack cross-modal interactions that have demonstrated significant benefits for VL tasks. Therefore, how to best leverage pretrained unimodal encoders for VL tasks is still an area of active research. In this work, we propose a method to leverage unimodal vision and text encoders for VL tasks that augment existing VL approaches while conserving computational complexity. Specifically, we propose Multimodal Adaptive Distillation (MAD), which adaptively distills useful knowledge from pretrained encoders to cross-modal VL encoders. Second, to better capture nuanced impacts on VL task performance, we introduce an evaluation protocol that includes Visual Commonsense Reasoning (VCR), Visual Entailment (SNLI-VE), and Visual Question Answering (VQA), across a variety of data constraints and conditions of domain shift. Experiments demonstrate that MAD leads to consistent gains in the low-shot, domain-shifted, and fully-supervised conditions on VCR, SNLI-VE, and VQA, achieving SOTA performance on VCR compared to other single models pretrained with image-text data. Finally, MAD outperforms concurrent works utilizing pretrained vision encoder from CLIP. Code will be made available.