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Monte Carlo Energy Aggregation for Mobile 3D Gaussian Splatting
Xiaobiao Du, YuAn Wang, Hao Li, Bosheng Wang, Xun Sun, Xin Yu
TL;DR
Mobile 3D Gaussian Splatting is hindered by the storage and inference overhead of high-order spherical harmonics. Flux-GS compresses radiance and prunes Gaussians using multi-view guidance, achieving competitive visual fidelity with real-time mobile rendering and reduced resource use.
Problem
Method
Flux-GS combines Monte Carlo specular-energy aggregation, attribute-conditioned SH enhancement, and multi-view alpha-based densification and pruning.
Source: §3.2 · p. 10, §6 · p. 15Results
Flux-GS achieves competitive fidelity and real-time rendering speed with lower storage costs, fewer Gaussian primitives, and fast mobile inference.
Source: §5.2 · p. 13, §5.3 · p. 14, §6 · p. 15Takeaways & Limitations
Flux-GS provides a scalable, lightweight representation for real-time 3D scene rendering on resource-constrained mobile hardware.
Source: §5.2 · p. 13, §6 · p. 15Reducing to first-order SH loses capacity for highly complex mirror-like reflections, while initial training still requires peak memory comparable to standard 3DGS.
Source: §D.2 · p. 22
Abstract
from arXiv · showhide
Recent advances in 3D Gaussian Splatting have demonstrated unprecedented success in novel view synthesis. However, the substantial inference and storage overhead driven by high-order Spherical Harmonics (SH) are primary bottlenecks for mobile platforms. In this paper, we present Flux-GS, a real-time Gaussian Splatting method designed to achieve high-fidelity rendering with significantly reduced overhead for resource-constrained mobile platforms. We first propose a Monte Carlo Specular Energy Aggregator, sampling third-order radiance residuals and aggregating specular energy into a compact latent space. In this way, our method effectively preserves visually salient lighting features in lower-order bands without expensive distillation or pre-training. To mitigate the high-frequency details lost during compression, we introduce an Attribute-Conditioned SH Enhancement module. This module predicts Gaussian-aware offsets based on intrinsic Gaussian attributes, which enhance the first-order SH representation prior to inference, without extra inference costs. Furthermore, the original single-view gradient-based densification is prone to producing excessive Gaussians and overfitting to a certain view. We address these limitations by proposing a Multi-view Alpha-based Densification and Pruning strategy. By leveraging multi-view guidance, we ensure multi-view structure consistency and the precise removal of redundant primitives. Extensive experiments demonstrate that Flux-GS achieves substantial parameter reduction while maintaining competitive visual quality, offering a robust and scalable solution for real-time mobile rendering. Code: \textcolor{magenta}{\href{https://xiaobiaodu.github.io/flux-gs-project/}{https://xiaobiaodu.github.io/flux-gs-project/}}.
1 Introduction
Flux-GS targets mobile 3D Gaussian Splatting by addressing third-order Spherical Harmonics overhead and redundant Gaussian primitives. It combines compact radiance representation and fewer primitives to preserve competitive visual quality for real-time mobile rendering.
Motivation
- Third-order Spherical Harmonics impose prohibitive storage and memory-bandwidth costs when applied to millions of Gaussians.The coefficients capture complex, view-dependent radiance but increase rasterization-phase overhead.Source: §1 · p. 2
- Single-view gradient-based densification aggressively creates redundant primitives, increasing training time, storage footprints, and inference latency.The approach is also prone to overfitting to a particular view, limiting suitability for edge devices.Source: §1 · p. 3
Flux-GS
- Flux-GS is a mobile real-time Gaussian Splatting method designed for high-fidelity rendering with significantly fewer parameters.The framework combines a Monte Carlo Specular Energy Aggregator with additional technical innovations described in the introduction.Source: §1 · p. 3
Results
- Flux-GS achieves rendering quality comparable to existing baselines with fewer Gaussian primitives and faster inference than Mobile-GS.These claims are presented as outcomes illustrated in Fig. 1.Source: §1 · p. 3
- Extensive experiments show that Flux-GS provides a robust, scalable solution for mobile real-time rendering while maintaining competitive visual quality.The method uses a powerful first-order SH representation to support high-fidelity 3DGS deployment on mobile devices.Source: §1 · p. 3
2 Related work
Related work advances 3D Gaussian Splatting through faster training, Gaussian pruning, and compression. These approaches regulate primitive counts, improve multi-view consistency, remove insignificant Gaussians, and reduce storage overhead using quantization, entropy coding, structured representations, and factorization.
Gaussian Splatting
- Mini-Splatting limits primitive count through importance-driven densification, while 3DGS-MCMC models training dynamics as a Markov Chain Monte Carlo process.These methods target training acceleration in 3D Gaussian Splatting.Source: §2 · pp. 3–4
- Revisiting Densification introduces loss-driven densification, MVGS regulates training across views, and Taming 3DGS enforces a user-defined Gaussian budget.MVGS is described as improving multi-view consistency through multi-view regulated training.Source: §2 · p. 4
Gaussian Pruning
- Gaussian pruning methods remove redundant primitives using importance scores derived from ray contributions, opacity, gradient information, transmittance, or Hessian-based sensitivity.The cited examples include EAGLES and PUP 3DGS.Source: §2 · p. 4
Gaussian Compression
- Gaussian compression research uses scalar and vector quantization, entropy coding, anchor-based structures, and factorization techniques to reduce storage overhead.Vector quantization benefits from redundancy across Gaussian attributes, enabling compact encoding.Source: §2 · p. 4
3 Methodology
Flux-GS reduces Gaussian appearance modeling to first-order spherical harmonics while retaining view-dependent detail through compact Monte Carlo energy latents. It also uses attribute-conditioned enhancement and multi-view alpha-guided densification and pruning to improve fidelity and control the primitive count.
Monte Carlo Specular Energy Aggregator
- Flux-GS restricts appearance modeling to first-order spherical harmonics, requiring only 4 coefficients per channel.A Monte Carlo Specular Energy Aggregator compresses high-order radiance energy into a lower-order subspace without pretraining or distillation.Source: §3 · p. 5
- Monte Carlo aggregation preserves sparse view-dependent specular energy by encoding residual magnitude and direction instead of absolute photometric residuals.The method samples directions on the sphere, evaluates third-order versus second-order SH radiance residuals, and stores compact latents Emag and Edir.Source: §3.1 · pp. 6–7
Attribute-Conditioned SH Enhancement
- The compact high-frequency latents are mapped to first-order SH parameters, dynamically allocating restricted SH capacity to visually salient scene features.The mapping jointly adjusts Gaussian geometry and low-order appearance while avoiding expensive distillation.Source: §3.1 · p. 7
- Attribute-conditioned enhancement predicts SH offsets from normalized first-order coefficients, opacity, scales, position, and rotation, then adds them to the original coefficients.The enhanced coefficients are defined as c^out_i = c'_i + Δc_i.Source: §3.1 · p. 8
Multi-view Alpha-based Densification and Pruning
- Multi-view alpha-based densification and pruning evaluates Gaussian contributions across sampled views to improve geometry modification and avoid single-view overfitting.The strategy clones or splits Gaussians that consistently contribute to high-error regions and moderately prunes non-contributing or artifact-inducing Gaussians.Source: §3.2 · pp. 8, 10, Figure 4 · p. 8
4 Difference with Mobile-GS
Flux-GS differs from Mobile-GS by replacing distillation with Monte Carlo energy aggregation, enabling attribute-conditioned SH enhancement without dynamic view-dependent computation. It also uses multi-view alpha-guided densification and pruning to improve structural consistency and remove redundant Gaussians.
Energy Aggregation vs. Distillation-based SH
- Flux-GS replaces Mobile-GS’s teacher-student SH distillation with a Monte Carlo Specular Energy Aggregator that maps third-order radiance energy into a compact low-order subspace.This preserves high-frequency signal without requiring a distillation process.Source: §4 · p. 11
Zero-Cost SH Enhancement
- Flux-GS predicts view-independent SH offsets from Gaussian attributes instead of using Mobile-GS’s view-dependent neural enhancement strategy.The module recovers high-frequency details without adding dynamic computation to the rendering pipeline.Source: §4 · p. 11
Multi-view vs. Single-view Consistency
- Flux-GS replaces Mobile-GS’s single-view gradient densification and opacity- and scale-based pruning with multi-view alpha-weighted error guidance.This strategy addresses excessive Gaussian primitives, single-view overfitting, and redundant primitive removal.Source: §4 · p. 11
5 Experiments
Experiments on a Snapdragon 8 Gen 3 smartphone show that Flux-GS reduces storage and training costs while preserving competitive visual quality and mobile rendering efficiency. Ablations and SH decomposition further validate the contributions of its compact representation and component design.
Experimental Setup
- Experiments use offscreen benchmarking on a commercial Snapdragon 8 Gen 3 smartphone, averaging FPS across consecutive warmed-up runs to reduce display and initialization effects.The protocol removes the 120 FPS screen limit and UI overhead.Source: §5.1 · p. 12
Quantitative Evaluation and Mobile Performance
- Flux-GS is evaluated against 3DGS, Speedy-Splat, C3DGS, LocoGS, and Mobile-GS on Mip-NeRF 360, Tanks and Temples, and Deep Blending.Rendering-efficiency comparisons use a Mobile-GS variant without its inference MLP.Source: §5.2 · p. 12
- Flux-GS achieves the lowest memory footprint, compresses entire scenes to very low storage costs, and converges several times faster than Speedy-Splat and Mobile-GS.The reduced storage requirement is described as suitable for resource-constrained edge devices.Source: §5.2 · p. 13
Qualitative Results
- Qualitative comparisons show that Flux-GS preserves high-frequency details and sharp structural edges while reducing Gaussian primitives relative to high-fidelity 3DGS and avoiding Speedy-Splat’s blurring.The comparison covers rendering quality, Gaussian number, and storage costs.Source: §5.2 · p. 13, Figure 5 · p. 14
Ablation Study
- The full model provides the best reconstruction-quality and efficiency trade-off, with competitive PSNR, lower storage costs, fewer Gaussian points, and the fastest mobile FPS.The ablation progressively disables MC-SEA, enhanced SH offset ∆c, and Multi-view Alpha-based Densification and Pruning.Source: Table 3 · p. 13, §5.3 · p. 14
Analysis of Spherical Harmonic Decomposition
- SH decomposition shows that 0th-order SH reconstructs diffuse color and global illumination, whereas 1st-order and ∆1st-order components capture high-frequency structural variation and refine local context.These results validate the enhanced first-order SH representation.Source: §5.3 · p. 15, Figure 6 · p. 15
6 Conclusion · A Preliminary
Flux-GS targets real-time rendering on resource-constrained mobile platforms by reducing the memory overhead of high-order Spherical Harmonics. It combines compact radiance-energy representation, zero-overhead SH refinement, and multi-view densification and pruning with the Gaussian Splatting framework.
6 Conclusion
- Flux-GS addresses high-order Spherical Harmonics memory overhead for real-time rendering on resource-constrained mobile platforms.The method is presented as a mobile-oriented Gaussian Splatting approach.Source: §6 · p. 15
- The Monte Carlo Specular Energy Aggregator compresses radiance energy into a low-order subspace, while Attribute-Conditioned SH Enhancement refines base SH without inference overhead.The conclusion identifies these modules as complementary components of Flux-GS.Source: §6 · p. 15
- Multi-view Alpha-based Densification and Pruning eliminates redundant Gaussians as part of Flux-GS’s mobile rendering design.The supplied conclusion passage identifies this strategy as the method’s additional contribution.Source: §6 · p. 15
A Preliminary
- A 3D Gaussian represents scene geometry and appearance using anisotropic Gaussian primitives for high-quality novel view synthesis.The representation includes 3D position, covariance, opacity, and color-related parameters.Source: A Preliminary · pp. 15–16
- Rendering projects Gaussians into image space, depth-sorts them near-to-far, and computes pixel colors through alpha blending.The formulation uses accumulated transmittance and Gaussian opacity contributions.Source: A Preliminary · p. 16
- Gaussian Splatting provides a differentiable, efficient, and compact representation for complex scenes suited to real-time rendering.Its rendering process remains compatible with optimization through differentiable image formation.Source: A Preliminary · p. 16
- Spherical Harmonics represent directional appearance with an orthonormal basis whose expansion is truncated at a finite maximum degree L.The truncated representation contains (L + 1)2 coefficients.Source: A Preliminary · p. 16
- Low-order SH, such as L ≤2, are preferred for compactness and numerical stability, whereas higher-order SH capture high-frequency view-dependent effects during training.This tradeoff motivates reducing SH overhead while preserving directional detail.Source: A Preliminary · p. 16
B Additional Implementation
Flux-GS is trained for 30k iterations without pretraining or distillation, converting third-order SH to first-order SH after an initial 3k-iteration phase. The implementation specifies compact MLP modules, multi-view densification settings, Mobile-GS quantization, and RTX 4090 training.
Training
- Flux-GS trains for 30k iterations without pretraining or distillation, using third-order SH for the initial 3k iterations before first-order conversion.The Monte Carlo Specular Energy Aggregator performs the conversion from the previous third-order SH representation.Source: B Additional Implementation · p. 16
Monte Carlo Specular Energy Aggregator
- The Monte Carlo aggregator samples K = 2048 uniform points on a unit sphere and is applied once to obtain the low-order SH representation.Two MLPs with one hidden layer of 64 neurons perform the first-order SH mapping.Source: B Additional Implementation · pp. 16–17
Attribute-Conditioned SH Enhancement
- The Attribute-Conditioned SH Enhancement module uses a 4-layer ReLU MLP with hidden neurons (128, 64, 32, 12).The implementation also uses two one-hidden-layer MLPs with 64 neurons for first-order SH mapping.Source: B Additional Implementation · p. 17
Multi-view Alpha-based Densification and Pruning
- The multi-view densification strategy samples 6 cameras, using τ + = 0.1 and τ −= 0.01 as reconstruction-loss thresholds.The importance and pruning quantile is set to Q+ τ = 0.1.Source: B Additional Implementation · p. 17
Quantization and Training Environment
- Flux-GS uses the same quantization method as Mobile-GS and is trained on an RTX 4090 GPU.The authors state that code will be released to foster reproducibility.Source: B Additional Implementation · p. 17
C Additional Experiments · C.1 Monte Carlo K Sampling Point Analysis · C.2 Camera Count in Multi-view Alpha-based Densification
The additional experiments show that increasing Monte Carlo sampling points improves PSNR until saturation at K = 2048, while more camera views improve reconstruction quality and reduce Gaussian counts. These results support efficient, high-fidelity multi-view densification and sampling choices.
C.1 Monte Carlo K Sampling Point Analysis
- PSNR improves monotonically as K increases from 64 to 2048.The experiment evaluates K ∈{64, . . . , 4096}.Source: §C.1 · p. 17
- Lower sampling rates, K < 2048, produce sub-optimal integral approximations because Monte Carlo estimator variance remains higher.Increasing sampling density significantly reduces estimator variance.Source: §C.1 · p. 17
C.2 Camera Count in Multi-view Alpha-based Densification
- Increasing input camera views from 2 to 6 yields a significant PSNR improvement in multi-view densification.The ablation varies camera counts from 2 to 12.Source: §C.2 · p. 17
- As camera count increases, the total Gaussian count drops significantly, indicating improved representation efficiency.The results show a synergistic relationship between viewpoint coverage and representation efficiency.Source: §C.2 · p. 17
C.1 Monte Carlo K Sampling Point Analysis
- K = 2048 marks the saturation point for reconstruction fidelity as Monte Carlo sampling density increases on Mip-NeRF 360.Performance follows an upward trend before saturation.Source: Figure 7 · p. 18
C.2 Camera Count in Multi-view Alpha-based Densification
- PSNR steadily improves and stabilizes with additional views while Gaussian primitives decrease significantly.This demonstrates densification that avoids aggressive primitive growth while maintaining high-fidelity reconstruction.Source: Figure 8 · p. 18
C.3 Densification and Pruning Quantile Analysis
The quantile analysis shows that densification and pruning thresholds control the trade-off between Gaussian count and rendering quality. Larger densification quantiles reduce primitives but worsen results, whereas larger pruning quantiles retain more primitives and improve PSNR; the selected pruning quantile is Q−τ = 0.1.
Densification quantile analysis
- Larger densification quantiles hinder Gaussian splitting and cloning, producing fewer primitives and worse rendering performance.The analysis evaluates densification quantile Q+τ on the Mip-NeRF 360 dataset.Source: §C.3 · pp. 18–19
Pruning quantile analysis
- Larger pruning quantiles reduce pruning, yielding more primitives and better PSNR results.The analysis evaluates pruning quantile Q−τ on the Mip-NeRF 360 dataset.Source: §C.3 · p. 19
- Smaller pruning quantiles prune more aggressively, remove more Gaussians, and consequently harm rendering performance.This reflects the compactness–quality trade-off in the pruning strategy.Source: §C.3 · p. 19
- The selected pruning quantile is Q−τ = 0.1, providing a better trade-off between model compactness and rendering quality.The value is chosen based on the quantile analysis.Source: §C.3 · p. 19
C.4 Per-Scene Results … D.1 Discussion
Flux-GS maintains competitive rendering quality with reduced training overhead and favorable subjective evaluations, while compressing appearance into first-order SH and improving multi-view efficiency for mobile and cross-platform rendering.
C.4 Per-Scene Results
- Flux-GS achieves comparable per-scene performance to 3DGS and other lightweight Gaussian Splatting variants on Mip-NeRF 360.The evaluation covers Tables 6–8, while Table 9 compares training time.Source: §C.4 · p. 19
- Flux-GS uses substantially less training time while retaining competitive rendering performance on Mip-NeRF 360.Training-time comparisons are reported in Table 9.Source: §C.4 · p. 19, Table 9 · p. 20
C.5 User Study
- Thirty volunteers rated novel-view synthesis videos across Mip-NeRF 360, Tanks & Temples, and Deep Blending in a comparison with Mobile-GS, Speedy-Splat, and quantized 3DGS.The study evaluated subjective rendering quality using videos produced by each method.Source: §C.5 · p. 20, Figure 9 · p. 21
- The user-study results indicate a clear preference for Flux-GS in subjective rendering quality.Figure 9 summarizes the comparison against previous advanced methods.Source: §C.5 · p. 20, Figure 9 · p. 21
D Discussion and Limitations
- Flux-GS addresses mobile hardware constraints by compressing appearance representation from third-order to first-order Spherical Harmonics.This reduces the memory-bandwidth and storage overhead associated with traditional 3DGS.Source: §D.1 · p. 21
D.1 Discussion
- The Monte Carlo Specular Energy Aggregator preserves first-order directional moments, energy magnitude, and direction of high-frequency specular residuals in a compact latent space.The approach avoids expensive distillation and heavy pre-training typically used by lightweight methods.Source: §D.1 · p. 21
- Attribute-Conditioned SH Enhancement predicts Gaussian-aware offsets to improve the first-order SH representation without extra inference costs.The mechanism is presented as part of the method’s compact appearance representation.Source: §D.1 · p. 21
- Multi-view Alpha-based Densification and Pruning improves multi-view consistency, mitigates single-view overfitting, and reduces the primitive budget while preserving structural integrity.Stratified camera sampling provides multi-view guidance for scalable mobile and WebGL-based rendering.Source: §D.1 · p. 21
D.2 Limitations · D.3 Future Works
Flux-GS remains limited by reduced capacity for highly complex specular reflections and by an initially expensive third-order SH training phase. Future work targets lower storage, low-bandwidth streaming, dynamic-scene support, and temporal redundancy handling on mobile platforms.
D.2 Limitations
- First-order SH loses some capacity to model highly complex, mirror-like specular reflections that third-order SH can naturally capture.The limitation remains despite preservation of visually salient lighting features through the Monte Carlo Specular Energy Aggregator.Source: §D.2 · p. 22
- Flux-GS optimizes full third-order SH for the initial 3,000 iterations before transitioning to the lower-order representation.Thus, the final model is lightweight, but the initial training phase remains computationally expensive.Source: §D.2 · p. 22
- The final model is remarkably lightweight despite the initial third-order SH optimization phase.This passage contrasts final-model efficiency with the cost incurred during early training.Source: §D.2 · p. 22
D.3 Future Works
- Multi-view guidance in codebook-based compression or entropy coding could further reduce storage requirements.The proposed direction builds on Flux-GS’s existing reduction in primitive count and SH footprint.Source: §D.3 · p. 22
- Further storage reduction could enable instantaneous streaming over low-bandwidth networks.The passage identifies low-bandwidth streaming as a potential benefit of stronger compression.Source: §D.3 · p. 22
- Extending Flux-GS to dynamic scenes, including 4D Gaussian Splatting, is proposed for mobile platforms.The stated goal is to support dynamic-scene rendering on mobile devices.Source: §D.3 · p. 22
- Adapting Multi-view Densification to temporal redundancies could enable real-time mobile playback of volumetric content.The passage connects temporal redundancy handling with future real-time playback capabilities.Source: §D.3 · p. 22