Diffusion models for eye-gaze trajectory generation using position and velocity representations

Laxman Basnet; Alexander Szorkovszky; Pedro G. Lind; Anis Yazidi; Shailendra Bhandari

cs.CVSep 1, 2026

Diffusion models for eye-gaze trajectory generation using position and velocity representations

Authors: Laxman Basnet, Alexander Szorkovszky, Pedro G. Lind, Anis Yazidi, Shailendra Bhandari

Organizations: Department of Computer Science, Oslo Metropolitan University, Oslo, Norway · Department of Numerical Analysis and Scientific Computing, Simula Research Laboratory, Oslo, Norway · Department of Technology, Kristiania University of Applied Sciences, Oslo, Norway · Department of Informatics, University of Oslo, Oslo, Norway

Abstract

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.

Figures & tables

Figure 1: Example recording in both model representations. (a) Gaze path for the full 45 s trial. (b–e) One 8 s segment ( $L=2{,}000$ samples, $f_{s}=250$ Hz) from the same recording: (b) position $x(\tau)$ , $y(\tau)$ , where fixations appear as plateaus and saccades as steps (input to the position-space model). (c, d) Velocity components $v_{x}(\tau)$ , $v_{y}(\tau)$ (Eq. 3 ), where saccades become sparse high-amplitude spikes (input to the velocity-space model). (e) Scalar speed $\sqrt{v_{x}^{2}+v_{y}^{2}}$ .

Figure 2: Shared denoising architecture. Position or velocity windows $X_{0}\in\mathbb{R}^{2\times L}$ are noised to $X_{t}$ , and the 1D U-Net predicts $\varepsilon_{\theta}(X_{t},t)$ . Deterministic DDIM sampling ( $\eta=0$ ) produces $\hat{X}_{0}$ ; training and sampling settings differ between representations.

Feature	KS	JS
Mean speed	$0.149\pm 0.036$	$0.0249\pm 0.0096$
Max speed	$0.150\pm 0.034$	$0.0152\pm 0.0062$
Total path length	$0.149\pm 0.036$	$0.0249\pm 0.0096$
$x$ -range	$0.159\pm 0.020$	$0.0122\pm 0.0035$
$y$ -range	$0.115\pm 0.012$	$0.0067\pm 0.0018$
$x$ -std	$0.186\pm 0.016$	$0.0206\pm 0.0030$

Table 1: Position-space model. Feature-level agreement with real held-out trajectories, mean

\pm

SD over three training seeds, validation segments per seed, split held fixed. The two metrics are the KS statistic and the JS divergence (lower values indicate better agreement).

Figure 3: Representative gaze trajectories generated by the position-space DDPM (DDIM, 100 steps, $\eta=0$ ). Each panel shows the $xy$ path of one generated 8 s sequence in normalized coordinates.

Figure 4: Gaze-trajectory statistics for empirical data, the position-space DDPM, and the kinematic Markov baseline following Lencastre et al. [46] : (a) speed

|u|

, (b) autocorrelation of

|u|

, (c) movement direction

\theta

, and (d) turning angle

\phi

Figure 5: Real and generated gaze-velocity comparison for a representative seed. Pooled empirical distributions over all segments and time points for (a) $v_{x}$ , (b) $v_{y}$ , and (c) scalar speed $\sqrt{v_{x}^{2}+v_{y}^{2}}$ . All three seeds yield closely matching distributions; aggregate metrics are reported as mean $\pm$ SD over seeds in Table 2 .

Quantity	JS	$\Delta\rho_{1}$	$D_{\mathrm{PSD}}$
$v_{x}$	$(2.19\pm 0.50)\times 10^{-3}$	$0.0278\pm 0.0038$	$(1.31\pm 0.02)\times 10^{-4}$
$v_{y}$	$(7.31\pm 0.89)\times 10^{-3}$	$0.0568\pm 0.0092$	$(1.52\pm 0.04)\times 10^{-4}$
Speed	$(8.34\pm 1.36)\times 10^{-3}$	$0.0157\pm 0.0026$	$(1.82\pm 0.12)\times 10^{-4}$
Log-speed	$0.0146\pm 0.0049$	$0.0530\pm 0.0115$	$(1.72\pm 0.36)\times 10^{-4}$
Signed turning angle	$(3.0\pm 2.0)\times 10^{-4}$	–	–
Path length	$0.207\pm 0.020$	–	–

Table 2: Velocity-space model: agreement with real held-out data, reported as mean

\pm

SD over three training seeds (fixed 80/20 participant-level split).

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

Category	Quantity	Position-space	Velocity-space
Data	Split mode	Participant-stratified, 80/20, split	Participant-level, split
	Validation fraction	0.2	0.2
	Sampling rate	250 Hz
	Window length	2,000 samples (8 s)
	Window stride	250 samples	non-overlapping
	Participants / segments	28 / 4,401	–

Appendix

Table 3: Combined hyperparameter configuration. Rows with a single value are identical for both models; rows with two values differ. Architecture and diffusion settings are fully shared.

Figure 6: Marginal distributions of the nine kinematic features for real (blue) and generated (red) position-space trajectories (

n=1{,}136

each); numerical values in Table 1 .

Figure 7: Velocity-space temporal diagnostics for a representative seed. (a) Mean speed profile across segments. (b) Average speed autocorrelation. (c) Normalized speed power spectrum.

Feature	Real $\mu$	KS	JS
Mean speed	0.0058	0.731	0.347
Max speed	0.2095	0.460	0.355
$x$ -range	1.4699	0.589	0.225
$y$ -range	1.3502	0.348	0.108
$x$ -std	0.4405	0.339	0.112
$y$ -std	0.3815	0.157	0.049

Appendix

Table 4: Kinematic Markov baseline [ 46 ] : real-data feature means and per-feature agreement with real held-out trajectories. The baseline is deterministic given the training set, so no seed spread applies. Compared over the eight shared non-redundant features, the position-space DDPM reduces mean KS by

71.4\%

and mean JS by

93.0\%

. It also improves on the baseline for every individual feature.

Feature	W 1
Mean speed	$0.0006\pm 0.0002$
Max speed	$0.0379\pm 0.0075$
Total path length	$1.2195\pm 0.3671$
$x$ -range	$0.1355\pm 0.0254$
$y$ -range	$0.1071\pm 0.0056$
$x$ -std	$0.0631\pm 0.0065$

Appendix

Table 5: Position-space model: Wasserstein-1 distance per kinematic feature, mean

\pm

SD over three seeds (

n=1{,}136

per seed). W 1 is reported in each feature’s own units and is therefore not comparable across rows; total path length is

1{,}999\times

mean speed by construction, which is why its W 1 is correspondingly larger.

Setting	KS	JS
DDIM steps = 10	0.191	0.0565
DDIM steps = 25	0.211	0.0348
DDIM steps = 50	0.180	0.0243
DDIM steps = 100 (chosen)	0.158	0.0186
DDIM steps = 200	0.151	0.0140
$\eta=0.0$	0.135	0.0135

Appendix

Table 6: Position-space sampling ablations for the reference run. The DDIM-step and EMA rows report KS/JS for mean speed. The

\eta

rows report the mean over the eight non-redundant features. Lower is better.

Metric	$\mu_{r}$	$\mu_{g}$	KS	JS
Fixation duration (s)	0.344	0.351	0.053	0.0017
Fixation dispersion	0.0074	0.0108	0.162	0.0442
Fixation count / traj.	21.81	21.41	0.112	0.0155
Saccade amplitude	0.183	0.217	0.104	0.0027
Saccade peak speed	0.0624	0.0618	0.049	0.0012
Saccade duration (s)	0.0167	0.0195	0.111	0.0057

Appendix

Table 7: I-VT fixation and saccade statistics, real vs. generated (

n=1{,}136

each).

\mu_{r},\mu_{g}

: real/generated means.

Condition	$R^{2}$	MAE
TRTR (real $\to$ real, 5-fold)	$0.80\pm 0.05$	$1.9219$
TSTR (synthetic $\to$ real, 3 seeds)	$0.67\pm 0.02$	$2.74\pm 0.10$
AUG (real+synthetic $\to$ real)	$0.79\pm 0.02$	$2.04\pm 0.09$

Appendix

Table 8: Downstream TSTR protocol: MLP fixation-count regressor. TRTR uses real data only and is therefore identical across generative seeds; its reported spread is the five-fold cross-validation SD and serves as a real-data reference rather than a statistical upper bound.

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Open paper AskPDF arXiv

Diffusion models are increasingly used to generate synthetic training data, but precise label control remains difficult when the conditioning signal is low-dimensional and coarse. Text-conditioned images are judged by broad prompt consistency, whereas supervised training requires precise correspondence between each image and its numerical label. This is challenging in eye tracking, where a 4D binocular gaze is expressed through subtle, spatially localized pupil and iris geometry. We introduce GazeDiT, a diffusion model that generates images for a requested 4D gaze through an internally constructed spatial condition that grounds the global gaze label in this local geometry. During training, a frozen SegFormer extracts pupil/iris geometry from diverse real images, allowing the model to learn realistic appearance conditioned on that geometry. At inference, a physical eye renderer samples gaze-consistent geometries by varying anatomy and camera state, enabling diverse synthesis without a source image. GazeDiT achieves substantially lower tail gaze-label error than other diffusion baselines, approaching the error of the same frozen gaze estimator on real images. Its generated data also improves the downstream eye tracker, reducing gaze error on difficult cases from 3.05° to 2.80° in the smallest cohort.

Abstract

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