Spatial understanding from vision is crucial for robots operating in unstructured environments. In the real world, spatial understanding is often an ill-posed problem. There are a number of powerful classical methods that accurately regress relative pose, however, these approaches often lack the ability to leverage data-derived priors to resolve ambiguities. In multi-robot systems, these challenges are exacerbated by the need for accurate and frequent position estimates of cooperating agents. To this end, we propose CoViS-Net, a cooperative, multi-robot, visual spatial foundation model that learns spatial priors from data. Unlike prior work evaluated primarily on offline datasets, we design our model specifically for online evaluation and real-world deployment on cooperative robots. Our model is completely decentralized, platform agnostic, executable in real-time using onboard compute, and does not require existing network infrastructure. In this work, we focus on relative pose estimation and local Bird's Eye View (BEV) prediction tasks. Unlike classical approaches, we show that our model can accurately predict relative poses without requiring camera overlap, and predict BEVs of regions not visible to the ego-agent. We demonstrate our model on a multi-robot formation control task outside the confines of the laboratory.