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

arXiv: https://arxiv.org/abs/2609.34733 · HTML: https://mlsanity.com/paper/2609.34733/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 34 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [4D Gaussian Splatting for Real-Time Dynamic Scene Rendering](https://mlsanity.com/paper/2310.08528/) (2023)
- [Deformable 3D Gaussians for High-Fidelity Monocular Dynamic Scene Reconstruction](https://mlsanity.com/paper/2309.13101/) (2023)
- [Genie: Generative Interactive Environments](https://mlsanity.com/paper/2402.15391/) (2024)
- [Dynamic 3D Gaussians: Tracking by Persistent Dynamic View Synthesis](https://mlsanity.com/paper/2308.09713/) (2023)
- [Revisiting Feature Prediction for Learning Visual Representations from Video](https://mlsanity.com/paper/2404.08471/) (2024)
- [Real-time Photorealistic Dynamic Scene Representation and Rendering with 4D Gaussian Splatting](https://mlsanity.com/paper/2310.10642/) (2023)
- [Spacetime Gaussian Feature Splatting for Real-Time Dynamic View Synthesis](https://mlsanity.com/paper/2312.16812/) (2023)
- [Neural Rendering for Stereo 3D Reconstruction of Deformable Tissues in Robotic Surgery](https://mlsanity.com/paper/2206.15255/) (2022)
- [V-JEPA 2.1: Unlocking Dense Features in Video Self-Supervised Learning](https://mlsanity.com/paper/2603.14482/) (2026)
- [TKAN: Temporal Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.07344/) (2024)
- [EndoSurf: Neural Surface Reconstruction of Deformable Tissues with Stereo Endoscope Videos](https://mlsanity.com/paper/2307.11307/) (2023)
- [GaussianWorld: Gaussian World Model for Streaming 3D Occupancy Prediction](https://mlsanity.com/paper/2412.10373/) (2024)
- [Learning How To Robustly Estimate Camera Pose in Endoscopic Videos](https://mlsanity.com/paper/2304.08023/) (2023)
- [Endo-4DGS: Endoscopic Monocular Scene Reconstruction with 4D Gaussian Splatting](https://mlsanity.com/paper/2401.16416/) (2024)
- [Dynamic 3D Gaussian Tracking for Graph-Based Neural Dynamics Modeling](https://mlsanity.com/paper/2410.18912/) (2024)
- [Deform3DGS: Flexible Deformation for Fast Surgical Scene Reconstruction with Gaussian Splatting](https://mlsanity.com/paper/2405.17835/) (2024)
- [GaussianAD: Gaussian-Centric End-to-End Autonomous Driving](https://mlsanity.com/paper/2412.10371/) (2024)
- [GaussianPrediction: Dynamic 3D Gaussian Prediction for Motion Extrapolation and Free View Synthesis](https://mlsanity.com/paper/2405.19745/) (2024)
- [Efficient Deformable Tissue Reconstruction via Orthogonal Neural Plane](https://mlsanity.com/paper/2312.15253/) (2023)
- [SurgicalGS: Dynamic 3D Gaussian Splatting for Accurate Robotic-Assisted Surgical Scene Reconstruction](https://mlsanity.com/paper/2410.09292/) (2024)
- [SurgicalGaussian: Deformable 3D Gaussians for High-Fidelity Surgical Scene Reconstruction](https://mlsanity.com/paper/2407.05023/) (2024)
- [ODE-GS: Latent ODEs for Dynamic Scene Extrapolation with 3D Gaussian Splatting](https://mlsanity.com/paper/2506.05480/) (2025)
- [Online 3D reconstruction and dense tracking in endoscopic videos](https://mlsanity.com/paper/2409.06037/) (2024)
- [ParticleGS: Learning Neural Gaussian Particle Dynamics from Videos for Prior-free Physical Motion Extrapolation](https://mlsanity.com/paper/2505.20270/) (2025)
- [Video Generation Models as World Models: Efficient Paradigms, Architectures and Algorithms](https://mlsanity.com/paper/2603.28489/) (2026)

## Abstract (arXiv)

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.