ParetoGS: High-Quality Continuous-Budget 3D Gaussian Splatting with Sparse Adapted Anchors

Xiaobin Deng; Changyu Diao; Min Li; Duanqing Xu

cs.CVOct 25, 2026

ParetoGS: High-Quality Continuous-Budget 3D Gaussian Splatting with Sparse Adapted Anchors

Authors: Xiaobin Deng, Changyu Diao, Min Li, Duanqing Xu

Organizations: Zhejiang University

Abstract

Scalable 3D Gaussian Splatting allows one scene representation to serve different Gaussian-count budgets, yet its quality-budget curve may lag behind models optimized separately for each budget. Reducing the number of Gaussians changes both the selected members and the reconstruction tasks carried by the survivors; parameters inherited from a high-budget model may fit a low-budget representation poorly. We propose ParetoGS, which describes member changes and parameter evolution with a small set of adapted budget anchors and decodes intermediate budgets without separate optimization at every requested count. ParetoGS alternates pruning and fixed-member adaptation to build nested anchors with persistent identities, and encodes their parameter changes relative to the full model in a compact residual atlas. At decoding, it interpolates the states of shared members and gradually introduces the rendering contributions of new members, connecting sparse anchors into a continuous-budget representation. Across 13 scenes, ParetoGS attains better average PSNR, SSIM, and LPIPS with fewer Gaussians than the compared prefix methods at 10% of each method's own full model. From a shared full model, it also outperforms FlexGS-imp at its trained 1%, 5%, and 10% budgets and NanoGS-imp at the 1% and 0.1% budgets. On Garden, its non-anchor quality approaches an empirical reference from independently optimized GNS models at higher retention ratios and exceeds it at some lower-budget points. Across 13 scenes, encoding reduces mean additional state from 390.0 to 85.7 MB with an average PSNR change of 0.01 dB. Project page: https://xiaobin2001.github.io/ParetoGS-Web/

Figures & tables

Figure 1: ParetoGS overview. (a) Alternating pruning and fixed-member adaptation builds sparse nested anchors; each adapted state seeds the next contraction. (b) Persistent identities align anchor states, whose parameter changes relative to the full model are encoded in a compact residual atlas. (c) For a requested count

K

between adjacent anchors

L

and

U

, decoding interpolates shared-member parameters and introduces

K-L

entering members from

U

with opacity gating, producing a standard

K

-Gaussian model.

	CLOD-3DGS ( $\sim$ 35 min)				MGS ( $\sim$ 74 min)				Ours ( $\sim$ 10.3 min)
Ratio	PSNR $\!\uparrow$	SSIM $\!\uparrow$	LPIPS $\!\downarrow$	Num	PSNR $\!\uparrow$	SSIM $\!\uparrow$	LPIPS $\!\downarrow$	Num	PSNR $\!\uparrow$	SSIM $\!\uparrow$	LPIPS $\!\downarrow$	Num
100%	27.54	0.847	0.197	3029	27.75	0.853	0.180	4923	27.89	0.854	0.185	1615
30%	27.24	0.834	0.222	909	27.32	0.835	0.206	1477	27.88	0.850	0.207	485
10%	25.59	0.779	0.294	303	25.74	0.757	0.301	492	27.17	0.821	0.269	162
5%	22.38	0.691	0.376	151	24.32	0.694	0.372	246	26.48	0.791	0.315	81
1%	12.86	0.383	0.581	30	20.35	0.565	0.507	49	24.40	0.697	0.422	16

Table 1: Equal retention ratios from each method’s own full model. Metrics and actual Gaussian counts are equally weighted 13-scene means; Num gives the actual count in thousands, and full-model sizes differ. Parentheses after method names give mean offline time in minutes; Ours denotes ParetoGS. Bold marks the best mean quality at each ratio.

		FlexGS-imp ( $\sim$ 81 min)			NanoGS-imp				Ours ( $\sim$ 10.3 min)
Ratio	Num	PSNR $\!\uparrow$	SSIM $\!\uparrow$	LPIPS $\!\downarrow$	PSNR $\!\uparrow$	SSIM $\!\uparrow$	LPIPS $\!\downarrow$	Conv.	PSNR $\!\uparrow$	SSIM $\!\uparrow$	LPIPS $\!\downarrow$
30%	485	21.98	0.705	0.355	23.86	0.708	0.329	48	27.88	0.850	0.207
10%	162	25.21	0.760	0.327	21.29	0.603	0.436	54	27.17	0.821	0.269
5%	81	24.03	0.712	0.386	20.34	0.564	0.486	55	26.48	0.791	0.315
1%	16	21.75	0.621	0.488	18.84	0.511	0.579	56	24.40	0.697	0.422
0.1%	2	13.54	0.392	0.641	16.37	0.470	0.637	56	21.15	0.580	0.539

Table 2: Shared full initialization at equal requested budgets. Metrics and requested Gaussian counts are equally weighted 13-scene means; Num is in thousands, and Conv. is NanoGS-imp’s offline conversion time from Full (seconds). Parentheses after method names give mean offline time in minutes; Ours denotes ParetoGS.

Figure 2: Cross-budget reconstruction of the same Garden test view. The five columns show CLOD-3DGS, MGS, FlexGS-imp, NanoGS-imp, and ParetoGS; the rows show 30%, 10%, 5%, 1%, and 0.1%. The first two columns use a fraction of each method’s own full model; the last three use a shared full model. Each panel labels its actual Gaussian count.

Figure 3: Parameter states of the same members across budgets. The Garden columns correspond to 0.8%, 12.8%, and 100% of Full. The first row selects 24K, 384K, and 3M members, respectively, while retaining Full parameters. The second row fixes the same 24K members from the upper-left panel; column headings now indicate the budget from which their parameters were taken. All panels use the same view and crop.

Figure 4: Continuous-budget quality on Garden. The full model has 3M Gaussians. SSIM and LPIPS are averaged over 24 test views against retention percentage on a log axis. Blue open circles are ParetoGS anchors and small blue dots are decoded intervals; green denotes FlexGS-imp, and orange stars are independently optimized GNS references. Line segments connect measured points over 0.1%–50%.

Table 7

Figure 5: Effect of intermediate anchors on connection quality. From the same Garden state library and common 0.4% and 6.4% endpoints, we retain five, three, or two anchors. Open circles, triangles, and squares mark their anchors; small solid points show real evaluations at 50 shared non-anchor budgets. The red star is FlexGS-imp at the 5% Garden budget from the shared full model. Each configuration calibrates its own interval exponents, and metrics average all 24 test views.

Appendix figures & tables22 assets

Supplementary material from the paper’s appendix.

Appendix

Scene	Method	100%	30%	10%	5%	1%	0.1%
Bicycle	CLOD-3DGS	25.54	25.17	23.83	22.55	16.33	10.20
Bicycle	MGS	25.50	24.73	22.35	20.88	18.76	14.28
Bicycle	ParetoGS	25.87	25.81	25.18	24.63	23.36	21.62
Flowers	CLOD-3DGS	21.87	21.47	20.16	18.96	12.23	7.73
Flowers	MGS	21.89	21.11	18.73	17.65	15.40	11.73
Flowers	ParetoGS	21.79	21.84	21.23	20.66	19.25	17.72

Appendix

Table 5: Per-scene PSNR (dB) at retention ratios from each method’s own Full.

Scene	Method	100%	30%	10%	5%	1%	0.1%
Bicycle	CLOD-3DGS	0.7926	0.7680	0.6797	0.5945	0.3539	0.0728
Bicycle	MGS	0.7939	0.7492	0.5655	0.4569	0.3460	0.2245
Bicycle	ParetoGS	0.8050	0.7988	0.7531	0.7072	0.5728	0.4388
Flowers	CLOD-3DGS	0.6381	0.6047	0.5146	0.4360	0.2184	0.0395
Flowers	MGS	0.6451	0.6022	0.4427	0.3645	0.2545	0.1596
Flowers	ParetoGS	0.6400	0.6272	0.5684	0.5165	0.3907	0.2859

Appendix

Table 6: Per-scene SSIM at retention ratios from each method’s own Full.

Scene	Method	100%	30%	10%	5%	1%	0.1%
Bicycle	CLOD-3DGS	0.1711	0.2078	0.3100	0.3859	0.5644	0.7261
Bicycle	MGS	0.1670	0.2256	0.4185	0.5281	0.6185	0.6888
Bicycle	ParetoGS	0.1613	0.1960	0.2872	0.3426	0.4634	0.5837
Flowers	CLOD-3DGS	0.2877	0.3294	0.4124	0.4763	0.6536	0.8190
Flowers	MGS	0.2659	0.3091	0.4390	0.5137	0.6453	0.7578
Flowers	ParetoGS	0.2813	0.3322	0.4176	0.4712	0.5756	0.6911

Appendix

Table 7: Per-scene LPIPS at retention ratios from each method’s own Full.

Scene	Method	30%	10%	5%	1%	0.1%
Bicycle	FlexGS-imp	20.62	23.21	22.67	21.68	15.97
Bicycle	NanoGS-imp	21.36	19.05	18.26	17.29	16.41
Bicycle	ParetoGS	25.81	25.18	24.63	23.36	21.62
Flowers	FlexGS-imp	16.99	19.45	18.87	18.00	14.41
Flowers	NanoGS-imp	18.16	16.74	16.26	15.43	14.02
Flowers	ParetoGS	21.84	21.23	20.66	19.25	17.72

Appendix

Table 8: Per-scene PSNR (dB) at requested ratios from the shared Full.

Scene	Method	30%	10%	5%	1%	0.1%
Bicycle	FlexGS-imp	0.6193	0.6643	0.5950	0.4700	0.3109
Bicycle	NanoGS-imp	0.5556	0.4102	0.3676	0.3247	0.2990
Bicycle	ParetoGS	0.7988	0.7531	0.7072	0.5728	0.4388
Flowers	FlexGS-imp	0.3761	0.4319	0.3909	0.3202	0.2314
Flowers	NanoGS-imp	0.4279	0.3258	0.2924	0.2484	0.2221
Flowers	ParetoGS	0.6272	0.5684	0.5165	0.3907	0.2859

Appendix

Table 9: Per-scene SSIM at requested ratios from the shared Full.

Scene	Method	30%	10%	5%	1%	0.1%
Bicycle	FlexGS-imp	0.3459	0.3494	0.4160	0.5423	0.6872
Bicycle	NanoGS-imp	0.3603	0.4801	0.5349	0.6497	0.7321
Bicycle	ParetoGS	0.1960	0.2872	0.3426	0.4634	0.5837
Flowers	FlexGS-imp	0.5558	0.5246	0.5619	0.6399	0.7682
Flowers	NanoGS-imp	0.4562	0.5526	0.5984	0.7128	0.7745
Flowers	ParetoGS	0.3322	0.4176	0.4712	0.5756	0.6911

Appendix

Table 10: Per-scene LPIPS at requested ratios from the shared Full.

Scene	Method	100%	30%	10%	5%	1%	0.1%
Bicycle	CLOD-3DGS	6132	1840	613	307	61	6
Bicycle	MGS	5000	1500	500	250	50	5
Bicycle	ParetoGS	3000	900	300	150	30	3
Flowers	CLOD-3DGS	3636	1091	364	182	36	4
Flowers	MGS	5000	1500	500	250	50	5
Flowers	ParetoGS	1500	450	150	75	15	2

Appendix

Table 11: Per-scene actual Gaussian counts (K) at retention ratios from each method’s own Full.

Scene	Count	30%	10%	5%	1%	0.1%
Bicycle	Requested	900	300	150	30	3
Bicycle	FlexGS actual	900	300	150	30	3
Flowers	Requested	450	150	75	15	2
Flowers	FlexGS actual	450	150	75	15	2
Garden	Requested	900	300	150	30	3
Garden	FlexGS actual	900	300	150	30	3

Appendix

Table 12: Per-scene requested and FlexGS-imp actual output counts (K) from the shared Full.

Scene	30%	10%	5%	1%	0.1%
Bicycle	99	108	110	111	110
Flowers	49	57	57	58	59
Garden	96	106	111	110	110
Stump	87	101	103	104	104
Treehill	49	56	57	58	59
Room	28	32	32	33	34

Appendix

Table 13: Per-scene NanoGS-imp offline conversion time (seconds) from the shared Full to each target PLY.

Scene	CLOD	MGS	FlexGS	Training	Encoding	Calibration	Packaging	Total
Bicycle	57.24	68.74	120.18	12.28	1.98	31.91	3.98	12.92
Flowers	38.10	71.78	74.74	9.29	1.60	26.29	2.43	9.80
Garden	56.35	72.58	123.04	13.53	1.83	33.10	3.86	14.18
Stump	46.94	68.18	119.88	12.12	1.74	29.84	3.75	12.71
Treehill	38.46	68.18	72.29	8.79	2.07	24.74	2.41	9.27
Room	29.36	82.03	69.89	9.62	1.43	33.23	1.91	10.23

Appendix

Table 14: Per-scene offline time. CLOD, MGS, FlexGS, ParetoGS training, and total are in minutes; encoding, calibration, and packaging are in seconds. ParetoGS total includes its training and all three post-processing stages.

Scene	Variant	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
Bicycle	Full method	24.16	0.6544	0.3687
Bicycle	Fixed shared state	24.04	0.6523	0.3701
Bicycle	No opacity gate	24.03	0.6522	0.3686
Bicycle	Linear progress	24.08	0.6494	0.3732
Bicycle	Full parameters	15.57	0.3871	0.4946
Flowers	Full method	20.12	0.4789	0.4894

Appendix

Table 15: Per-scene results for Table 4 . Each scene averages ten interval midpoints; the Full-parameter row uses the same member IDs.

Scene	Encoding	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	MB $\downarrow$
Bicycle	FP32	24.18	0.6550	0.3678	724.3
Bicycle	FP16	24.18	0.6550	0.3678	362.2
Bicycle	Atlas	24.16	0.6544	0.3687	158.7
Flowers	FP32	20.13	0.4792	0.4890	362.2
Flowers	FP16	20.13	0.4792	0.4890	181.1
Flowers	Atlas	20.12	0.4789	0.4894	79.6

Appendix

Table 16: Per-scene results for Table 4 . Quality averages ten interval midpoints per scene; MB is additional state storage.

Method	Median	P95	Maximum
CLOD-3DGS	0.12	3.01	7.46
MGS	0.41	7.79	8.10
FlexGS-imp	18.66	46.91	98.87
ParetoGS	0.27	2.77	5.65

Appendix

Table 17: Synchronized budget-switch parameter preparation time across 13 scenes (milliseconds), pooling 1,404 switches per method.

Panel of Figure 6 — Figure 6: Cross-budget reconstruction on Bicycle (top) and Flowers (bottom).

Panel of Figure 7 — Figure 7: Cross-budget reconstruction on Stump (top) and Treehill (bottom).

Panel of Figure 8 — Figure 8: Cross-budget reconstruction on Room (top) and Counter (bottom).

Panel of Figure 9 — Figure 9: Cross-budget reconstruction on Kitchen (top) and Bonsai (bottom).

Panel of Figure 10 — Figure 10: Cross-budget reconstruction on Train (top) and Truck (bottom).

Panel of Figure 11 — Figure 11: Cross-budget reconstruction on Playroom (top) and DrJohnson (bottom).

Figure 12: Continuous-budget quality curves for Bicycle, Flowers, Stump, and Treehill, top to bottom.

Figure 13: Continuous-budget quality curves for Room, Counter, Kitchen, and Bonsai, top to bottom.

Figure 14: Continuous-budget quality curves for Train, Truck, Playroom, and DrJohnson, top to bottom.

3D Gaussian Splatting

3D Gaussian Splatting represents scenes as optimizable 3D Gaussian primitives for fast, photorealistic rendering from new viewpoints.

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SPARE-GS: Structural Parsimony and Resource Efficiency for 3D Gaussian Splatting

3D Gaussian Splatting (3DGS) achieves high-fidelity novel view synthesis in real-time; however its training efficiency and representation compactness are hindered by excessive primitive proliferation. To address this challenge, we formulate the structural evolution of 3DGS as a global budget-constrained optimization problem and derive an optimality condition, which requires the marginal utility of structural resources to be balanced across spatial regions under a finite primitive budget. Based on this formulation, we propose SPARE-GS, a general plug-and-play framework that dynamically aligns the distribution of 3D Gaussian primitives with regional representational demand. SPARE-GS estimates capacity-normalized regional demand, assigns adaptive target quotas, and uses regional budget deviations to coordinate densification, pruning and adaptive termination toward a more balanced structural allocation. Extensive experiments across standard, accelerated, and structure-enhanced 3DGS pipelines demonstrate that SPARE-GS reduces the Gaussian count and training time by an average of 30.38% and 23.81%, respectively, while improving the average PSNR. Moreover, the resulting compact representations reduce downstream processing time and improve the rate-distortion performance of diverse compression and pruning methods, demonstrating the broad applicability of global structural budget regulation.

Zhang Chen, Shuai Wan, Fuzheng Yang +3

School of Electronics and Information, Northwestern Polytechnical University, Xi’an 710129, China · Department of Computer Science, City University of Hong Kong, Hong Kong SAR, China · School of Telecommunication Engineering, Xidian University, Xi’an 710071, China +2

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Oct 2, 2026

Budgeted-GS: Real-Time Large-Scale Gaussian Splatting via Factoring LOD

3D Gaussian Splatting achieves excellent visual quality with real-time rendering, but at the scale of entire cities it does not fit: a trained model carries millions of primitives and gigabytes of memory, and real-time rendering at high quality on a consumer GPU remains out of reach. We introduce Budgeted-GS, a post-hoc method that turns any trained 3DGS model into a factoring tree, a multi-resolution hierarchy of moment-matched aggregates. After a construction pass of a few seconds, a single quality parameter selects, for each view, the level of detail that fits the memory of the target device, so the same city-scale model serves GPUs with widely different memory capacities. When a new scene is to be trained, the same theory applies: instead of growing a full-sized model and compressing it afterwards, budget-centered training first measures how many primitives the scene needs and then trains the model directly at that size, avoiding the wasted effort of optimizing primitives that are later discarded. Both methods are grounded in a measurable capacity floor, a budget-error law derived from optimal transport in phase space; selection rules certified by recent covering theorems decide which primitives are redundant. The floor answers how many primitives a scene actually needs and how many can safely be given up. We validate the floor on 13 public scenes under a preregistered protocol, and exercise both methods from object scenes to an official city capture, rendering it at native 1920x1080, full SH, in real time on one consumer GPU.

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Oct 9, 2026

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Existing 3D Gaussian Splatting (3DGS) pruning methods primarily rely on global Top-K selection based on independent importance scores, lacking regional budget control and ignoring joint deletion effects. Consequently, they cannot ensure balanced reconstruction quality across a scene. We propose SplatQ, a combinatorial pruning algorithm that coordinates regional budget allocation and joint Gaussian selection under a fixed budget. SplatQ partitions Gaussians by spatial proximity and appearance similarity into size-limited blocks, decomposing global selection into subproblems of a specific size. It then smooths importance-based block retention quotas to prevent excessive budget concentration. Finally, it constructs a quadratic approximation of joint deletion effects using the responses of representative pixel colors to changes in Gaussian opacity. Individual responses, pairwise interactions, and quota penalties are incorporated into a quadratic unconstrained binary optimization (QUBO) objective, solved using simulated annealing (SA) or a coherent Ising machine (CIM) to jointly select Gaussians. Experiments on 5 benchmarks demonstrate that SplatQ outperforms state-of-the-art pruning methods in aggregate reconstruction quality, spatial quality balance, and rendering speed. Ablations confirm that budget smoothing improves local detail reconstruction, while interaction modeling improves Gaussian selection quality under a fixed budget.

Hongbin Ye, Haixu Liu, Shenwei Kang +13

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Abstract

3D Gaussian Splatting

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