# Laplacian Frequency Hierarchies for Efficient 3D Gaussian Splatting Training

arXiv: https://arxiv.org/abs/2609.03334 · HTML: https://mlsanity.com/paper/2609.03334/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 40 references that are in the map.
- First posted on arXiv 3 Sep 2026.

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

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields](https://mlsanity.com/paper/2111.12077/) (2021)
- [2D Gaussian Splatting for Geometrically Accurate Radiance Fields](https://mlsanity.com/paper/2403.17888/) (2024)
- [Deformable 3D Gaussians for High-Fidelity Monocular Dynamic Scene Reconstruction](https://mlsanity.com/paper/2309.13101/) (2023)
- [SuGaR: Surface-Aligned Gaussian Splatting for Efficient 3D Mesh Reconstruction and High-Quality Mesh Rendering](https://mlsanity.com/paper/2311.12775/) (2023)
- [Gaussian Splatting SLAM](https://mlsanity.com/paper/2312.06741/) (2023)
- [Mini-Splatting: Representing Scenes with a Constrained Number of Gaussians](https://mlsanity.com/paper/2403.14166/) (2024)
- [Taming 3DGS: High-Quality Radiance Fields with Limited Resources](https://mlsanity.com/paper/2406.15643/) (2024)
- [CityGaussian: Real-time High-quality Large-Scale Scene Rendering with Gaussians](https://mlsanity.com/paper/2404.01133/) (2024)
- [GaussianFormer: Scene as Gaussians for Vision-Based 3D Semantic Occupancy Prediction](https://mlsanity.com/paper/2405.17429/) (2024)
- [FreGS: 3D Gaussian Splatting with Progressive Frequency Regularization](https://mlsanity.com/paper/2403.06908/) (2024)
- [GaussianImage: 1000 FPS Image Representation and Compression by 2D Gaussian Splatting](https://mlsanity.com/paper/2403.08551/) (2024)
- [Speedy-Splat: Fast 3D Gaussian Splatting with Sparse Pixels and Sparse Primitives](https://mlsanity.com/paper/2412.00578/) (2024)
- [GS2Mesh: Surface Reconstruction from Gaussian Splatting via Novel Stereo Views](https://mlsanity.com/paper/2404.01810/) (2024)
- [GaussianWorld: Gaussian World Model for Streaming 3D Occupancy Prediction](https://mlsanity.com/paper/2412.10373/) (2024)
- [3DGS-LM: Faster Gaussian-Splatting Optimization with Levenberg-Marquardt](https://mlsanity.com/paper/2409.12892/) (2024)
- [FastGS: Training 3D Gaussian Splatting in 100 Seconds](https://mlsanity.com/paper/2511.04283/) (2025)
- [DashGaussian: Optimizing 3D Gaussian Splatting in 200 Seconds](https://mlsanity.com/paper/2503.18402/) (2025)
- [Large Images are Gaussians: High-Quality Large Image Representation with Levels of 2D Gaussian Splatting](https://mlsanity.com/paper/2502.09039/) (2025)
- [EfficientGS: Streamlining Gaussian Splatting for Large-Scale High-Resolution Scene Representation](https://mlsanity.com/paper/2404.12777/) (2024)
- [3DGS2: Near Second-order Converging 3D Gaussian Splatting](https://mlsanity.com/paper/2501.13975/) (2025)
- [Frequency-Aware Density Control via Reparameterization for High-Quality Rendering of 3D Gaussian Splatting](https://mlsanity.com/paper/2503.07000/) (2025)
- [VTGaussian-SLAM: RGBD SLAM for Large Scale Scenes with Splatting View-Tied 3D Gaussians](https://mlsanity.com/paper/2506.02741/) (2025)
- [HRGS: Hierarchical Gaussian Splatting for Memory-Efficient High-Resolution 3D Reconstruction](https://mlsanity.com/paper/2506.14229/) (2025)
- [From Coarse to Fine: Learnable Discrete Wavelet Transforms for Efficient 3D Gaussian Splatting](https://mlsanity.com/paper/2506.23042/) (2025)
- [Optimized 3D Gaussian Splatting using Coarse-to-Fine Image Frequency Modulation](https://mlsanity.com/paper/2503.14475/) (2025)

## Abstract (arXiv)

A key bottleneck in 3D Gaussian Splatting training is the continual growth of Gaussian primitives, which increases optimization cost and slows convergence, especially at high resolutions. We propose Laplacian Frequency Hierarchies, a simple yet efficient 3DGS scheme that combines Laplacian image decomposition with coarse-to-fine, frequency-staged training. After fitting lower-frequency structure, we archive the corresponding Gaussian field so that subsequent fields can optimize higher-frequency residuals without carrying the full primitive burden, and we compose the rendered components in the image domain via a Laplacian-style reconstruction at inference time. This design reduces the number of active Gaussians during training, thereby lowering optimization overhead and accelerating training. The proposed scheme is plug-and-play and orthogonal to prior 3DGS accelerations: it can be directly combined with strong backbones such as Taming-3DGS and FastGS to improve training speed with competitive reconstruction quality. It achieves average speedups of 1.73x and 1.21x at 1K setting, and 1.74x and 1.33x at 4K setting on Taming-3DGS and FastGS, with larger gains on more challenging scenes and increasingly pronounced benefits at higher resolutions.