Implicit 4D Gaussian Splatting for Fast Motion with Large Inter-Frame Displacements
Authors: Seung-gyeom Kim, Areum Kim, Yongjae Yoo, Sukmin Yun
Organizations: Department of Applied Artificial Intelligence, Hanyang University · Hanyang University ERICA
Abstract
Recent 4D Gaussian Splatting (4DGS) methods often fail under fast motion with large inter-frame displacements, where Gaussian attributes are poorly learned during training, and fast-moving objects are often lost from the reconstruction. In this work, we introduce Spatiotemporal Position Implicit Network for 4DGS, coined SPIN-4DGS, which learns Gaussian attributes from explicitly collected spatiotemporal positions rather than modeling temporal displacements, thereby enabling more faithful splatting under fast motions with large inter-frame displacements. To avoid the heavy memory overhead of explicitly optimizing attributes across all spatiotemporal positions, we instead predict them with a lightweight feed-forward network trained under a rasterization-based reconstruction loss. Consequently, SPIN-4DGS learns shared representations across Gaussians, effectively capturing spatiotemporal consistency and enabling stable high-quality Gaussian splatting even under challenging motions. Across extensive experiments, SPIN-4DGS consistently achieves higher fidelity under large displacements, with clear improvements in PSNR and SSIM on challenging sports scenes from the CMU Panoptic dataset. For example, SPIN-4DGS notably outperforms the strongest baseline, D3DGS, by achieving +1.83 higher PSNR on the Basketball scene.
Recent progress in 4D Gaussian Splatting (4DGS) has achieved impressive dynamic scene reconstruction results. While these methods demonstrate remarkable performance, the specific factors behind their gains remain underexplored, making a systematic understanding of the underlying principles challenging. In this paper, we perform a comprehensive analysis of these hidden factors to provide a clearer perspective on the 4DGS framework. We first establish a controlled baseline, FreeTimeGS_ours, by formalizing and reproducing the heuristics of the state-of-the-art FreeTimeGS. Using this framework, we examine 4DGS along its fundamental axes and identify practical secrets, including the emergent temporal partitioning driven by Gaussian durations and the decoupling between photometric fidelity and motion behavior. Based on these insights, we propose FreeTimeGS++, a principled method that employs gated marginalization, UFM-guided initialization, and color correction to improve stability and reproducibility. Our approach yields reproducible results with reduced run-to-run variance.
We present GP-4DGS, a novel framework that integrates Gaussian Processes (GPs) into 4D Gaussian Splatting (4DGS) for principled probabilistic modeling of dynamic scenes. While existing 4DGS methods focus on deterministic reconstruction, they are inherently limited in capturing motion ambiguity and lack mechanisms to assess prediction reliability. By leveraging the kernel-based probabilistic nature of GPs, our approach introduces three key capabilities: (i) uncertainty quantification for motion predictions, (ii) motion estimation for unobserved or sparsely sampled regions, and (iii) temporal extrapolation beyond observed training frames. To scale GPs to the large number of Gaussian primitives in 4DGS, we design spatio-temporal kernels that capture the correlation structure of deformation fields and adopt variational Gaussian Processes with inducing points for tractable inference. Our experiments show that GP-4DGS enhances reconstruction quality while providing reliable uncertainty estimates that effectively identify regions of high motion ambiguity. By addressing these challenges, our work takes a meaningful step toward bridging probabilistic modeling and neural graphics.
4D Gaussian Splatting (4DGS) excels in dynamic 3D reconstruction and real-time novel view synthesis via efficient 4D Gaussian representations and parallelizable rendering. However, existing 4DGS approaches rely on a single polynomial to model motion, which limits performance in complex dynamic scenes where high-frequency motion components are prevalent, and fails to ensure long-term stability due to cumulative trajectory drift. To address these issues, we propose a Fourier Motion Modeling module: this paradigm decomposes motion into frequency-based sinusoidal components, capturing both low-frequency global trajectories and high-frequency local details to model complex motion patterns accurately. It retains the real-time rendering capability of 4DGS while improving complex motion fitting and long-term coherence. Additionally, we integrate a motion-aware regularization strategy into the loss function: it uses frequency-dependent weights to suppress high-frequency jitter while preserving low-frequency motion coherence. Extensive experiments on N3V and Google Immersive datasets from multiple scenarios demonstrate the effectiveness of our method.