Several upper-limb exoskeleton robots have been developed for stroke rehabilitation, but their rather low level of individualized assistance typically limits their effectiveness and practicability. Individualized assistance involves an upper-limb exoskeleton robot continuously assessing feedback from a stroke patient and then meticulously adjusting interaction forces to suit specific conditions and online changes. This paper describes the development of a new upper-limb exoskeleton robot with a novel online generative capability that allows it to provide individualized assistance to support the rehabilitation training of stroke patients. Specifically, the upper-limb exoskeleton robot exploits generative models to customize the fine and fit trajectory for the patient, as medical conditions, responses, and comfort feedback during training generally differ between patients. This generative capability is integrated into the two working modes of the upper-limb exoskeleton robot: an active mirroring mode for patients who retain motor abilities on one side of the body and a passive following mode for patients who lack motor ability on both sides of the body. The performance of the upper-limb exoskeleton robot was illustrated in experiments involving healthy subjects and stroke patients.