GaussPDE: Graph-Based Partial Differential Equation-Driven Rendering for 3D Gaussian Splatting
Authors: Haoyuan Yue, Fengyuan Ye, Ziyin Li
Organizations: Department of Physics, Westlake University, Hangzhou, China · The Chinese University of Hong Kong, Shenzhen, China · Department of Accounting, Xi’an Jiaotong-Liverpool University, Suzhou, China
We present GaussPDE, a framework that injects physically structured partial differential equation (PDE) dynamics into pretrained 3D Gaussian scenes without mesh extraction, voxelization, or retraining. Our key observation is that PDE rendering requires not only accurate appearance, but also a reliable discrete computational domain. We therefore first introduce camera-aware regularization during 3DGS reconstruction to suppress camera-near floaters and oversized primitives that would create unstable graph topology. We then construct an active Gaussian graph using covariance-aware distances and opacity, appearance, and boundary-aware conductance, enabling mass-weighted graph Laplacian PDE evolution directly over Gaussian primitives. The evolving scalar PDE state is coupled back to rendering by modifying the direct-current spherical harmonic color coefficients while preserving geometry, opacity, and view-dependent rendering behavior. Experiments on real and synthetic scenes show that GaussPDE produces stable, controllable, and spatially coherent dynamic visualizations, with reduced cross-boundary leakage compared with baselines.
Figures & tables
Figure 1: GaussPDE pipeline. Camera-aware reconstruction produces Gaussian primitives, from which a sparse conductance graph is constructed. PDE states evolve on this graph and update Gaussian appearance for dynamic novel-view rendering. SAM denotes the Segment Anything Model [ 8 ] .
Figure 2: PDE-driven scalar-field visualization on NeRF-Synthetic, LLFF, and DTU. The evolving field modifies Gaussian appearance while the reconstructed geometry remains fixed.
Leakage (%) ↓ at g/h=
Mean leakage
Mean reference
Method
0.35
0.50
0.70
1.00
(%) ↓
error ↓
KNN
37.33
37.13
37.13
26.46
34.51
0.3451
RBF
38.00
37.78
36.76
25.85
34.60
0.3460
LBO [ 22 ]
47.73
<0.01
<0.01
<0.01
11.93
0.1197
GaussPDE
<0.01
<0.01
<0.01
<0.01
<0.01
0.0013
Table 1: Controlled diffusion on disconnected sheets with identical appearance. Leakage and grid-reference error are evaluated at matched in-sheet diffusion extent. Means average the four separation ratios.
Figure 3: Field visualization with GaussPDE, KNN, and RBF. The top row is ground truth, which contains static reference RGB images. The remaining rows illustrate how graph construction changes the rendered propagation pattern.
Figure 4: CamReg ablation on room and trex from LLFF. The upper row shows static reconstruction; the lower row shows PDE-rendered appearance. Each scene is displayed with and without CamReg.
We present BlitzGS, a distributed 3DGS framework that reduces active Gaussian workload for fast city-scale reconstruction. BlitzGS manages this workload at three coupled levels. At the system level, the framework shards Gaussians across GPUs by index parity rather than spatial blocks. This approach mitigates the cross-block visibility redundancy inherent in spatial partitioning. Furthermore, it distributes each rendering step through a single cross-GPU exchange that routes projected Gaussians to their tile owners. At the model level, scheduled importance-scoring passes shrink the global Gaussian population. During these passes, the framework generates a per-Gaussian visibility weight to bias density-control updates toward contributing primitives and a per-view importance mask for the view-level renderer. At the view level, BlitzGS trims each camera's active set with a distance-based LOD gate to exclude excessively fine primitives for the current frustum and the importance-based culling mask to skip Gaussians with negligible cross-view contribution. On large-scale benchmarks, BlitzGS matches the rendering quality of recent large-scale baselines while delivering an order-of-magnitude speedup, training city-scale scenes in tens of minutes. Our code is available at https: //github.com/AkierRaee/BlitzGS.
While 3D Gaussian Splatting (3DGS) has demonstrated impressive real-time rendering performance, its efficacy remains constrained by a reliance on heuristic density control. Despite numerous refinements to these handcrafted rules, such methods inherently lack the flexibility to adapt to diverse scenes with complex geometries. In this paper, we propose a paradigm shift for density control from rigid heuristics to fully learnable policies. Specifically, we introduce \textbf{LeGS}, a framework that reformulates density control as a parameterized policy network optimized via Reinforcement Learning (RL). Central to our approach is the tailored effective reward function grounded in sensitivity analysis, which precisely quantifies the marginal contribution of individual Gaussians to reconstruction quality. To maintain computational tractability, we derive a closed-form solution that reduces the complexity of reward calculation from O(N2) to O(N). Extensive experiments on the Mip-NeRF 360, Tanks & Temples, and Deep Blending datasets demonstrate that \textbf{LeGS} significantly outperforms state-of-the-art methods, striking a superior balance between reconstruction quality and efficiency. The code will be released at https://github.com/AaronNZH/LeGS
Zhenhua Ning, Xin Li, Jun Yu +3
Pengcheng Laboratory, Shenzhen · Harbin Institute of Technology, Shenzhen
3D Gaussian Splatting (3DGS) enables real-time novel view synthesis, but existing general-purpose acceleration methods suffer severe rendering quality degradation when extended to more complex, large-scale scenes. To address this issue, we propose EffGS, a more general acceleration framework that improves training and rendering efficiency while maintaining reconstruction quality comparable to or better than vanilla 3DGS across bounded and large-scale scenes. EffGS combines frequency-aware guidance, localized density control, and adaptive primitive scale modulation. First, an importance scoring mechanism combines pixel-wise reconstruction errors with a difference-of-Gaussians mask scheduled over training to provide stage-dependent spatial guidance. Second, localized densification and pruning restricts density modifications to Gaussians with valid projected footprints in the sampled views. Third, learnable per-Gaussian scale modulation adjusts effective primitive extent during optimization while retaining the Compact Box rasterization rule. Extensive experiments on bounded and large-scale scene datasets demonstrate a favorable balance between reconstruction quality, training time, and primitive count. Component ablations and matched-primitive-budget comparisons further support the effectiveness of the framework.
Changbai Li, Shuo Yang, Yichen Yang +2
Beihang University · Nanyang Technological University