Eye-tracking data are expensive to collect, requiring specialized hardware and controlled laboratory conditions, and difficult to share due to privacy regulations, which together limit the quantity and diversity of gaze data available for research. We investigate unconditional gaze generation using diffusion models in position and component-wise velocity representations. The models are trained and evaluated on eight-second visual-search trajectories from 28 participants, using a split of 23 training participants and five held-out validation participants, with three training seeds. Evaluation includes kinematic distributions, trajectory geometry, event statistics, and a temporal Wasserstein GAN with gradient penalty as a learned comparator. Across eight position-derived features, mean Jensen-Shannon divergence is $0.016 \pm 0.004$ for the position model and $0.037 \pm 0.002$ for the velocity model, with standard deviations calculated across training seeds. These scores do not establish that representation choice caused the difference. A separate comparison using the same evaluation method shows that the ordering of the models varies across training seeds. The position model also produces smaller feature discrepancies than a kinematic Markov baseline. Differences in saccade counts between real and generated data depend strongly on the velocity threshold used to detect events. The results provide quantitative reference measurements for unconditional gaze generation on this visual-search task and show how evaluation choices affect conclusions about generated gaze.

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