Gaze stabilization reflexes reduce motion blur and simplify the processing of visual information by keeping the eyes level. These reflexes typically depend on estimates of the rotational motion of the body, head, and eyes, acquired by visual or mechanosensory systems. During rapid movements, there can be insufficient time for sensory feedback systems to estimate rotational motion, and additional mechanisms are required. The solutions to this common problem likely reflect an animal's behavioral repertoire. Here, we examine gaze stabilization in three families of dipteran flies, each with distinctly different flight behaviors. Through frequency response analysis based on tethered-flight experiments, we demonstrate that fast roll oscillations of the body lead to a stable gaze in hoverflies, whereas the reflex breaks down at the same speeds in blowflies and horseflies. Surprisingly, the high-speed gaze stabilization of hoverflies does not require sensory input from the halteres, their low-latency balance organs. Instead, we show how the behavior is explained by a hybrid control system that combines a sensory-driven, active stabilization component mediated by neck muscles, and a passive component which exploits physical properties of the animal's anatomy---the mass and inertia of the head. This solution requires hoverflies to have specializations of the head-neck joint that can be employed during flight. Our comparative study highlights how species-specific control strategies have evolved to support different visually-guided flight behaviors.