Constrained Dynamic Gaussian Splatting

Zihan Zheng; Zhenlong Wu; Xuanxuan Wang; Houqiang Zhong; Xiaoyun Zhang; Qiang Hu; Guangtao Zhai; Wenjun Zhang

cs.CVFeb 3, 2026

Constrained Dynamic Gaussian Splatting

Authors: Zihan Zheng, Zhenlong Wu, Xuanxuan Wang, Houqiang Zhong, Xiaoyun Zhang, Qiang Hu, Guangtao Zhai, Wenjun Zhang

Organizations: Shanghai Jiao Tong University, Shanghai, 200240, China

Abstract

While Dynamic Gaussian Splatting enables high-fidelity 4D reconstruction, its deployment is severely hindered by a fundamental dilemma: unconstrained densification leads to excessive memory consumption incompatible with edge devices, whereas heuristic pruning fails to achieve optimal rendering quality under preset Gaussian budgets. In this work, we propose Constrained Dynamic Gaussian Splatting (CDGS), a novel framework that formulates dynamic scene reconstruction as a budget-constrained optimization problem to enforce a strict, user-defined Gaussian budget during training. Our key insight is to introduce a differentiable budget controller as the core optimization driver. Guided by a multi-modal unified importance score, this controller fuses geometric, motion, and perceptual cues for precise capacity regulation. To maximize the utility of this fixed budget, we further introduce an adaptive static-dynamic allocation strategy that separates the Gaussian representation into static and dynamic branches and distributes the shared global capacity between them according to motion complexity. Furthermore, we implement a three-phase training strategy to seamlessly integrate these constraints, ensuring precise adherence to the target count. After training, a dual-mode hybrid compression scheme further reduces storage overhead. CDGS therefore not only strictly adheres to the specified Gaussian-count budget (error<2%) but also achieves favorable rate-distortion performance. Extensive experiments demonstrate that CDGS delivers optimal rendering quality under varying capacity limits and favorable rate-distortion performance, achieving over 3x model compression compared with the state-of-the-art method Ex4DGS.

Figures & tables

Fig. 1: Left : Our CDGS leverages differentiable budget control for precise Gaussian number regulation, achieving adaptive static-dynamic allocation across varying target numbers and optimal rendering quality. Middle : Visual comparison with state-of-the-art methods, highlighting advantages in visual quality, model size, and Gaussian count controllability (second row: actual/target counts). Right : Superior rate-distortion performance and precise Gaussian number control of our approach, outperforming the compared prior works (e.g., 4DGS [ 21 ] , STGS [ 22 ] , and Ex4DGS [ 23 ] ).

Fig. 2: Overview of the proposed CDGS framework. ( Top ) Three-Phase Pipeline: The training progresses from a Warm-up phase to establish foundational priors, through a Budget Enforcement phase where constraints are actively applied, to a final Fine-tuning phase that maximizes quality under the fixed count $N_{\text{target}}$ . ( Bottom Left ) Adaptive Static-Dynamic Allocation: This module analyzes the distribution of motion magnitudes to identify a distribution-adaptive separation threshold $\tau_{\text{motion}}$ . It decomposes the scene into a Static set $\mathcal{S}$ and a Dynamic set $\mathcal{D}(t)$ . ( Bottom Right ) Differentiable Budget Control: This module regulates capacity by computing a Unified Importance Score $M_{i}$ . It fuses Perceptual cues $\mathcal{F}_{\text{perceptual}}$ and Geometric/Motion cues $\mathcal{F}_{\text{geom/motion}}$ . The resulting score guides the differentiable budget loss $\mathcal{L}_{\text{budget}}$ to precisely prune or densify Gaussians towards $N_{\text{target}}$ .

Fig. 3: Illustration of the Differentiable Budget Controller. The controller aggregates geometric, motion, and perceptual cues to compute a Unified Importance Score $M_{i}$ . This score passes through a hard-sigmoid gate to estimate the effective Gaussian count $N_{p}$ , which is regulated toward the current global sub-target $N(r)$ via a quadratic budget loss $\mathcal{L}_{\text{budget}}$ . Guided by this progressively updated constraint, the closed-loop policy performs densification on high-importance Gaussians and pruning on low-importance ones until the final target $N_{\text{target}}$ is reached.

Fig. 4: Illustration of our dual-mode hybrid compression strategy, which separates outliers from both static and dynamic Gaussian data, then applies distinct compression approaches.

Method	PSNR $\uparrow$ (dB)	SSIM $\uparrow$	Size $\downarrow$ (MB)	Render $\uparrow$ (FPS)	User-Defined Gaussian-Count Control
K-Planes [ 52 ]	29.91	0.920	300	0.15	✕
ReRF [ 17 ]	29.71	0.918	231	2.0	✕
TeTriRF [ 86 ]	30.65	0.931	227	2.7	✕
StreamRF [ 83 ]	30.61	0.930	2280	8.3	✕
3DGStream [ 70 ]	31.54	0.942	2430	215	✕
4DGC [ 71 ]	31.58	0.943	150	168	✕

TABLE I: Quantitative comparison on the N3DV [ 54 ] dataset. The PSNR, SSIM, and rendering speed are averaged over all 300 frames for each scene. The reported model size is the total for the entire sequence. Ours-l and Ours-s use target Gaussian numbers of 300,000 and 100,000, respectively. Best and second-best results are highlighted.

Method	Target	PSNR	Static	Dynamic	Overall	Ratio
Ex4DGS [ 23 ]	-	28.79	292.2k	47.7k	339.9k	-
Ours	100k	28.53	72.4k	27.6k	99.9k	0.1%
	200k	28.68	156.8k	41.0k	197.8k	1.1%
	300k	28.81	244.4k	51.4k	295.8k	1.4%
	400k	28.95	316.4k	81.2k	397.6k	0.6%

TABLE II: Validation of our precise control capability over the total number of Gaussians. We report the average PSNR on the coffee_martini sequence, the number of static/dynamic/overall Gaussians, and the error ratio of Gaussian number.

Dataset	Method	PSNR $\uparrow$ (dB)	SSIM $\uparrow$	Size $\downarrow$ (MB)	Render $\uparrow$ (FPS)
MeetRoom Dataset [ 83 ]	ReRF [ 17 ]	26.43	0.911	189	2.9
	TeTriRF [ 86 ]	27.37	0.917	183	3.8
	StreamRF [ 83 ]	26.71	0.913	2469	10
	3DGStream [ 70 ]	28.03	0.921	2430	288
	4DGC [ 71 ]	28.08	0.922	126	213
	4DGCPro [ 72 ]	28.02	0.921	123	222

TABLE III: Quantitative comparison on the MeetRoom dataset [ 83 ] and Technicolor dataset [ 82 ] .

Fig. 5: Rate-distortion curves on different datasets, illustrating the superiority of our method over ReRF [ 17 ] , TeTriRF [ 86 ] , 4DGC [ 71 ] , 4DGCPro [ 72 ] , RD4DGS [ 66 ] , and Ex4DGS [ 23 ] .

Dataset	ReRF [ 17 ]	TeTriRF [ 86 ]	4DGCPro [ 72 ]	RD4DGS [ 66 ]	Ours
N3DV [ 54 ]	-1.99	-1.12	0.08	1.33	1.90
MeetRoom [ 83 ]	-1.84	-0.86	-0.02	-	1.72

TABLE IV: The BD-PSNR(dB) results of our CDGS, ReRF [ 17 ] , TeTriRF [ 86 ] , 4DGCPro [ 72 ] and RD4DGS [ 66 ] when compared with 4DGC [ 71 ] on different datasets.

Time	ReRF [ 17 ]	TeTriRF [ 86 ]	4DGC [ 71 ]	Ex4DGS [ 23 ]	Ours
Encode(s)	246	219	810	-	16
Decode(s)	18.3	16.8	28.2	-	0.5
Train(h)	>100	5.2	4.2	1.2	1.0
Render(ms)	497	372	5.6	7.8	5.4

TABLE V: Complexity comparison of our method with dynamic scene reconstruction and compression methods.

Fig. 6: Qualitative comparison of our CDGS against STGS [ 22 ] and Ex4DGS [ 23 ] on the N3DV [ 54 ] , MeetRoom [ 83 ] and Technicolor [ 82 ] datasets, demonstrating the performance of CDGS under different target Gaussian numbers.

Fig. 7: Visualization of densification strategies at Iter. 7k. Unlike the gradient-based baseline (c) which generates excessive redundant primitives in the background, our importance-driven method (d) effectively suppresses irrelevant growth, concentrating Gaussians strictly on geometric and motion boundaries.

	PSNR(dB) $\uparrow$	Size(MB) $\downarrow$	Ratio $\downarrow$
w/o Importance score	31.91	31.2	1.6%
w/o $\mathcal{F}_{\text{geom/motion}}$	31.97	31.5	1.3%
w/o $\mathcal{F}_{\text{perceptual}}$	31.99	31.3	1.4%
$\lambda_{gm}=1.5$	32.08	31.4	1.3%
$\lambda_{gm}=2.5$	32.11	31.5	1.4%
w/o Budget loss	32.15	31.7	4.8%

TABLE VI: Ablation study of differentiable budget control and adaptive static-dynamic allocation.

	N3DV [ 54 ]		MeetRoom [ 83 ]
	PSNR(dB)	Size(MB)	PSNR(dB)	Size(MB)
w/o $\nabla_{i}^{\mu}$	32.05	31.8	29.08	10.6
w/o $\alpha_{i}^{\max}$	32.07	31.5	29.07	10.3
w/o $d_{i}^{-1}$	32.09	31.5	29.12	10.7
w/o $\lambda_{\max}(\Sigma_{i})$	32.08	31.6	29.10	10.4
w/o $\mathrm{Mo}_{i}$	32.02	31.3	29.02	10.5

TABLE VII: Component-wise ablation of the Unified Importance Score on N3DV [ 54 ] and MeetRoom [ 83 ] . PSNR and model size are averaged over all scenes.

Fig. 8: Evolution of Gaussian counts under varying target budgets. The subplots correspond to target limits of $1\times 10^{5}$ ( Left ), $2\times 10^{5}$ ( Middle ), and $3\times 10^{5}$ ( Right ). The curves illustrate the growth trajectories of Static , Dynamic , and Total Gaussians. Under our constrained optimization framework, the total number steadily increases and converges precisely to the predefined Target Number .

Fig. 9: Visualization of our adaptive static-dynamic allocation strategy ( bottom ) against the pre-defined ratio approach ( top ).

Fig. 10: Normalized motion distributions and automatically selected static-dynamic thresholds for N3DV ( coffee_martini ), MeetRoom ( discussion ), and Technicolor ( birthday ), from left to right. The horizontal axis denotes the normalized motion statistic, the vertical axis denotes the Gaussian count in logarithmic scale, and red dashed lines indicate the selected thresholds.

Fig. 11: Comparison of storage distribution before ( left ) and after ( right ) applying our dual-mode hybrid compression on the flame_salmon sequence. The visualization highlights the significant reduction in model size and the explicit isolation of background and outlier components in the compressed representation.

	PSNR(dB) $\uparrow$	Size(MB) $\downarrow$
w/o Initialization	30.90	31.8
w/o Fine-tuning	31.86	31.5
w/o Compression	32.21	98.3
w/o Static Compression	32.19	65.5
w/o Dynamic Compression	32.16	64.3
w/o Regularization Loss	31.39	31.2

TABLE VIII: Evaluation results of our three-phase training strategy and dual-mode hybrid compression.

Platform	Decoding (ms)	Rendering (ms)
RTX 3090	497	5.4
iPad M2	662	15
iPhone A15	836	32

TABLE IX: Cross-device decoding and rendering efficiency of CDGS on a desktop GPU and mobile platforms. The compressed representation is decoded once before rendering.

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Abstract

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