SurgGMF: Fully Causal Gaussian Motion Forecasting for Anticipatory Surgical Scene Rendering

Dynamic surgical scene modeling is essential for robotic perception, simulation, and decision support. Although existing neural rendering methods enable efficient reconstruction and rendering of deformable surgical scenes, they remain primarily focused on observed-frame reconstruction rather than forecasting future scene states. To this end, we present SurgGMF, a fully causal Gaussian motion forecasting framework for anticipatory surgical scene rendering. Rather than predicting future RGB images directly, SurgGMF forecasts future Gaussian motion states represented by position, scale, and rotation residuals (X/S/R) from historical Gaussian motion fields. To prevent target leakage, we introduce a full-causal-last rendering protocol, where future Gaussian states are rendered without accessing target-frame Gaussian attributes while preserving causal appearance propagation. We evaluate SurgGMF on 12 EndoNeRF and StereoMIS video slices using neural temporal learners and classical dynamics baselines under a unified forecasting protocol. Learned Gaussian motion forecasting consistently outperforms classical dynamics baselines in render space, demonstrating gains beyond hand-crafted state extrapolation. Latency analysis further reveals an accuracy--efficiency trade-off: under the current implementations, TKAN achieves the highest accuracy, whereas GRU and LSTM provide more favorable module-level latency profiles. These results establish SurgGMF as a reproducible framework for causal Gaussian motion forecasting and advance surgical Gaussian representations from retrospective reconstruction toward predictive scene modeling.