Eye-tracking data are expensive to collect, requiring specialized hardware and controlled laboratory conditions, and difficult to share because of privacy constraints. We address this using two complementary denoising diffusion probabilistic models (DDPMs) for unconditional generation of eye-gaze dynamics from visual-search data. Both use an identical FiLM-conditioned one-dimensional U-Net with self-attention (19.35,M parameters), trained on 8,s sliding-window sequences from 28 participants. One model generates raw two-dimensional gaze-position sequences, while the other generates two-component velocity sequences; each uses representation-specific preprocessing, training settings, data partitions, and evaluation protocols. Both are evaluated across three independent training seeds, with aggregated metrics reported as mean,$\pm$,SD. The position-space model achieves a mean Jensen-Shannon (JS) divergence of $0.016\pm0.004$ across nine kinematic features, with the highest feature-wise mean below $0.030$, fixation duration within 2% of real data, and a Fr'echet Gaze Distance more than an order of magnitude below statistical and Markovian baselines. Under a Train-on-Synthetic-Test-on-Real protocol, synthetic-only training achieves $R^2=0.66\pm0.02$, or 82.7% of the real-data $R^2$ point estimate. The velocity-space model achieves a mean JS divergence of $0.0065$ across velocity components, speed, log-speed, and turning angle, with a maximum of $0.015\pm0.005$. Reconstructed path length is less accurate ($0.21\pm0.02$ versus $0.03\pm0.01$ in position space), although the protocols differ. Overall, unconditional diffusion captures local gaze kinematics and short-range temporal and directional structure, while long-range properties such as saccade counts and cumulative path geometry remain targets for future conditioned models.

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