Assured safe-separation is essential for achieving seamless high-density operation of airborne vehicles in a shared airspace. To equip resource-constrained aerial systems with this safety-critical capability, we present ViSafe, a high-speed vision-only airborne collision avoidance system. ViSafe offers a full-stack solution to the Detect and Avoid (DAA) problem by tightly integrating a learning-based edge-AI framework with a custom multi-camera hardware prototype designed under SWaP-C constraints. By leveraging perceptual input-focused control barrier functions (CBF) to design, encode, and enforce safety thresholds, ViSafe can provide provably safe runtime guarantees for self-separation in high-speed aerial operations. We evaluate ViSafe's performance through an extensive test campaign involving both simulated digital twins and real-world flight scenarios. By independently varying agent types, closure rates, interaction geometries, and environmental conditions (e.g., weather and lighting), we demonstrate that ViSafe consistently ensures self-separation across diverse scenarios. In first-of-its-kind real-world high-speed collision avoidance tests with closure rates reaching 144 km/h, ViSafe sets a new benchmark for vision-only autonomous collision avoidance, establishing a new standard for safety in high-speed aerial navigation.