We study the problem of human gaze modeling, which aims to generate the gaze patterns a viewer produces while observing a visual stimulus. Gaze is primarily captured through two modalities: continuous eye-tracking trajectories, which describe fine-grained motion dynamics, and discrete scanpaths, which describe high-level fixation structure. Because gaze varies substantially across viewers and trials, we treat this variability as a defining property rather than noise and model gaze as a stochastic generative process. Existing generative gaze models supervise on only one of these two representations in isolation. We hypothesize that trajectories and scanpaths describe gaze at complementary scales and are jointly informative during training, and test this hypothesis through ST-DiffEye, a joint trajectory-scanpath diffusion framework that couples both modalities by concatenating them as an additional raw input channel, requiring no architectural overhead beyond an input and output channel expansion. We further introduce a principled evaluation framework based on the Continuous Ranked Probability Score (CRPS), which generalizes any existing sequence similarity metric into a proper scoring rule that jointly assesses the accuracy and diversity of generated gaze. Experiments on task-driven visual search, covering both target-present and target-absent scenarios, and on free-viewing benchmarks demonstrate state-of-the-art performance. These results, along with detailed ablations, confirm the benefit of joint modeling and the value of distribution-aware evaluation in capturing the intrinsic variability of human gaze.