Expert-layman text style transfer technologies have the potential to improve communication between members of scientific communities and the general public. High-quality information produced by experts is often filled with difficult jargon laypeople struggle to understand. This is a particularly notable issue in the medical domain, where layman are often confused by medical text online. At present, two bottlenecks interfere with the goal of building high-quality medical expert-layman style transfer systems: a dearth of pretrained medical-domain language models spanning both expert and layman terminologies and a lack of parallel corpora for training the transfer task itself. To mitigate the first issue, we propose a novel language model (LM) pretraining task, Knowledge Base Assimilation, to synthesize pretraining data from the edges of a graph of expert- and layman-style medical terminology terms into an LM during self-supervised learning. To mitigate the second issue, we build a large-scale parallel corpus in the medical expert-layman domain using a margin-based criterion. Our experiments show that transformer-based models pretrained on knowledge base assimilation and other well-established pretraining tasks fine-tuning on our new parallel corpus leads to considerable improvement against expert-layman transfer benchmarks, gaining an average relative improvement of our human evaluation, the Overall Success Rate (OSR), by 106%.