SteadySplats: Resampling of Low-Variance Gaussians for High-Fidelity Stochastic Rendering

Felix Windisch; Thomas Köhler; Lukas Radl; Chris Wyman; Georgios Kopanas; Bernhard Kerb; Markus Steinberger

cs.CVOct 4, 2026

SteadySplats: Resampling of Low-Variance Gaussians for High-Fidelity Stochastic Rendering

Authors: Felix Windisch, Thomas Köhler, Lukas Radl, Chris Wyman, Georgios Kopanas, Bernhard Kerb, Markus Steinberger

Organizations: Graz University of Technology · University of Copenhagen

Abstract

Stochastic order-independent transparency enables efficient and elegant rendering of primitive-based radiance fields like 3D Gaussian Splatting models, but remains impractical due to the inherent visible noise in the output. We propose a principled approach to minimize high-frequency noise, addressing its sources at the representation and image synthesis level. During stochastic rendering, our history-based spatial resampling scheme drastically accelerates image convergence, while temporal importance resampling ensures coherence under camera movement. During training, a color regularizer implicitly reduces the variance along view rays in the 3DGS models. With these properties, our optimized, Vulkan-based renderer effectively mitigates output noise at low and high sample counts, achieving a substantial 13~dB PSNR increase in quality over previous stochastic methods at 1 sample per pixel and quickly converging to sorted 3DGS with an average L1 error of less than $10^{-4}$ .

Figures & tables

Figure 1 : Through optimized training and inference, our stochastic OIT renderer achieves significantly better image quality than prior art with the same number of random samples. Our approach makes single-sample rendering a viable candidate for applications that demand high quality, as well as extremely high frame rates. Measurements were performed using each method’s original implementation.

Figure 2 : Illustration of deterministic and stochastic rendering of 3D Gaussians.

Figure 3 : By default, 3DGS optimization blends disparate colors to match the ground truth. With $\lambda_{\text{var}}>0$ , the blended colors align to reduce color variance.

Panel of Figure 4 — Figure 4 : Overview of spatial and temporal sample reuse.

Panel of Figure 5 — Figure 5 : Average quality metrics on the Mip-NeRF 360 dataset for varying $\lambda_{\text{var}}$ with deterministic ( Fig. 5(a) ) and stochastic ( Fig. 5(b) ) blending.

					PSNR (dB) $\uparrow$
Method	Avg. PSNR (dB) $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	tPSNR (dB) $\uparrow$	Indoor	Outdoor
StochasticSplats [ 13 ]	18.336	0.293	0.667	15.235	19.562	16.701
StochasticSplats + Temporal [ 13 ]	21.954	0.552	0.524	19.450	23.313	20.141
Ours	31.437	0.845	0.345	28.410	32.978	29.381
Ours + Temporal	35.085	0.937	0.209	32.449	37.161	32.318

Table 1: Quantitative comparison on the camera path benchmark (21 trajectories, 3,152 frames across 7 Mip-NeRF 360 scenes). We ablate progressive pipeline components against the 1-sample StochasticSplats baseline (

\lambda_{\text{var}}=0

), temporal reuse (CMA,

\tau=0.20

), our variance loss (

\lambda_{\text{var}}=1

) with spatial reuse, and our full spatio-temporal model ( Ours + Temporal ,

\bar{\delta}=0.7

). All variants are evaluated against sorted

\alpha

-blending ground truth.

Figure 6 : Average residual of test quality metrics on the Mip-NeRF 360 dataset trained with

\lambda_{\text{var}}=1

, comparing static blur kernels against spatial reuse weights with varying

K

. Log-scale is used to visualize small differences.

Figure 7 : Average frame time for rendering all test views of the Mip-NeRF 360 dataset. We average the frame time for 200 frames per view.

Panel of Figure 8 — Figure 8 : Excess Quality Factor on the test views of the Mip-NeRF 360 dataset for PSNR and SSIM quality metrics.

Figure 9 : Average residual of test PSNR on the Mip-NeRF 360 dataset trained with

\lambda_{\text{var}}=1

rendered with and without STBN compared against sorted rendering. Log-scale is used to visualize small differences.

Panel of Figure 10 — Figure 10 : Visual Ablations.

$\bm{\mathcal{L}}_{\textbf{var}}$	Spatial Reuse	Temporal Reuse	tPSNR (dB) $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	Avg. PSNR (dB) $\uparrow$
—	—	—	15.235	0.293	0.667	18.336
—	✓	—	21.720	0.586	0.498	24.774
—	—	✓	22.204	0.619	0.522	25.227
—	✓	✓	27.188	0.817	0.365	29.946
✓	—	—	22.423	0.613	0.525	25.561
✓	✓	—	28.410	0.845	0.345	31.437

Table 2: Component ablation on camera path benchmark. We ablate

\mathcal{L}_{\text{var}}

, Spatial Reuse, and Temporal Reuse combinations across 21 camera trajectories on the Mip-NeRF 360 dataset (3 per scene) against sorted rendering. For Spatial Reuse we set

K=4

, and Temporal Reuse evaluates EMA filtering with our soft history rejection at fixed

\bar{\delta}=0.70

. STBN was used for all evaluations.

Figure 11 : Log-scale histogram of primitive counts with respect to activated opacity over all Mip-NeRF 360 scenes trained with various values of $\lambda_{\text{var}}$ .

Figure 12 : Histogram of primitive counts with respect to Gaussian size (log-scale) over all Mip-NeRF 360 scenes trained with various values of $\lambda_{\text{var}}$ .

Panel of Figure 13 — Figure 13 : Test view of the bicycle scene, rendered deterministically with models trained with varying $\lambda_{\text{var}}$ .

Figure 14 : Increasing $\lambda_{\text{var}}$ also reduces variance in stochastically rendered depth. Images were rendered at 1 sample per pixel.

Panel of Figure 15 — Figure 15 : Distribution of primitive base colors in RGB space for scenes of Mip-NeRF 360 trained with and without variance loss.

Panel of Figure 16 — Figure 16 : Effect of $\mathcal{L}_{\text{var}}$ on alpha-blending.

Figure 17 : Comparison of quality metrics and variance for trained models with varying

\lambda_{\text{var}}

on scenes from the Mip-NeRF 360 dataset.

Figure 18 : Average residual of L1 score and values for LPIPS on the Mip-NeRF 360 dataset trained with

\lambda_{\text{var}}=1

, comparing static blur kernels against spatial reuse weights with varying

K

. Log-scale is used for L1 to visualize small differences.

Figure 19 : Excess Quality Factor on the test views of the Mip-NeRF 360 dataset for the L1 quality metric.

Panel of Figure 20 — Figure 20 : Heatmaps of quality metrics over sample counts and buffer sizes on Mip-NeRF 360.

Panel of Figure 21 — Figure 21 : Pareto-optimal combinations of sample count and $K$ for L1, PSNR, SSIM, and LPIPS. Stoch denotes stochastic rendering without spatial reuse and blur denotes stochastic rendering with a Gaussian cross-blur kernel.

Figure 22 : Average residual of test quality metrics on the Mip-NeRF 360 dataset trained with

\lambda_{\text{var}}=1

, comparing spatial reuse of 4- and 8-neighborhood kernels with varying

K

. Log-scale is used to visualize small differences.

Figure 23 : Average quality comparison of StochasticSplats and Gaussian Point Splatting with and without spatial reuse on the Mip-NeRF 360 dataset. Models were trained with

\lambda_{\text{var}}=1

Panel of Figure 24 — Figure 24 : Comparison of uniform random noise sampling (PCG32) against per-primitive spatio-temporal blue noise sampling.

Standard 3DGS ( $\lambda_{\text{var}}=0$ )
Configuration	Bicycle	Bonsai	Counter	Garden	Kitchen	Room	Stump	Overall Mean
No Reuse	13.230	16.230	15.780	13.343	15.610	18.183	14.267	15.235
Spatial Reuse	19.140	23.077	22.643	19.080	22.377	25.083	20.640	21.720
Temporal Reuse	19.767	23.020	22.427	20.390	22.857	25.757	21.210	22.204
Spatio-Temporal Reuse	23.757	28.140	27.963	24.650	28.377	31.513	25.913	27.188
Variance Regularized ( $\lambda_{\text{var}}=1$ )

Table 3: Per-scene temporal consistency tPSNR (dB). Evaluated on 7 Mip-NeRF 360 scenes (3 trajectories each).

Standard 3DGS ( $\lambda_{\text{var}}=0$ )
Configuration	Bicycle	Bonsai	Counter	Garden	Kitchen	Room	Stump	Overall Mean
No Reuse	16.340	19.307	18.880	16.397	18.750	21.313	17.367	18.336
Spatial Reuse	22.217	26.120	25.697	22.063	25.490	28.157	23.673	24.774
Temporal Reuse	22.727	25.980	25.590	23.410	25.957	28.803	24.123	25.227
Spatio-Temporal Reuse	26.453	30.837	30.867	27.440	31.287	34.273	28.463	29.946
Variance Regularized ( $\lambda_{\text{var}}=1$ )

Table 4: Per-scene PSNR (dB). Evaluated on 7 Mip-NeRF 360 scenes (3 trajectories each).

Standard 3DGS ( $\lambda_{\text{var}}=0$ )
Configuration	Bicycle	Bonsai	Counter	Garden	Kitchen	Room	Stump	Overall Mean
No Reuse	0.272	0.293	0.301	0.276	0.297	0.344	0.265	0.293
Spatial Reuse	0.538	0.612	0.607	0.538	0.601	0.646	0.559	0.586
Temporal Reuse	0.579	0.625	0.614	0.609	0.640	0.684	0.582	0.619
Spatio-Temporal Reuse	0.767	0.832	0.826	0.791	0.843	0.872	0.785	0.817
Variance Regularized ( $\lambda_{\text{var}}=1$ )

Table 5: Per-scene SSIM

\uparrow

. Evaluated on 7 Mip-NeRF 360 scenes (3 trajectories each).

Standard 3DGS ( $\lambda_{\text{var}}=0$ )
Configuration	Bicycle	Bonsai	Counter	Garden	Kitchen	Room	Stump	Overall Mean
No Reuse	0.636	0.693	0.690	0.584	0.677	0.687	0.701	0.667
Spatial Reuse	0.478	0.531	0.518	0.417	0.499	0.523	0.522	0.498
Temporal Reuse	0.504	0.569	0.542	0.421	0.514	0.538	0.564	0.522
Spatio-Temporal Reuse	0.363	0.420	0.380	0.282	0.331	0.382	0.398	0.365
Variance Regularized ( $\lambda_{\text{var}}=1$ )

Table 6: Per-scene LPIPS

\downarrow

. Evaluated on 7 Mip-NeRF 360 scenes (3 trajectories each).

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Conventional 3D Gaussian Splatting (3DGS) requires depth sorting and ordered alpha blending to correctly render overlapping Gaussian primitives. Stochastic transparency enables sorting-free rendering by replacing fractional alpha contributions with discrete stochastic visibility samples, but produces substantial spatial and temporal noise at low sample counts. We refer to this conversion from continuous Gaussian splats to discrete visibility samples as \textit{Gaussian Stippling}. Based on this, we present an efficient order-independent rendering and reconstruction framework that operates directly on unmodified 3DGS assets. Our method adaptively integrates primitive-based and fragment-based stippling, leveraging their complementary strengths across different rendering regimes to significantly improve rendering throughput. To recover high-quality images from sparse stochastic samples, we further introduce a lightweight Gaussian-aware spatiotemporal reconstruction network. By exploiting the Gaussian attributes retained by each stipple, the network aggregates structured stochastic clues across both space and time, effectively suppressing stippling noise. Experiments show that our hybrid Gaussian stippling method, coupled with a spatiotemporal reconstruction network trained on diverse scenes, generalizes to unseen scenes and enables interactive, temporally stable, and visually plausible rendering on mobile devices without retraining or preprocessing. With scene-specific training and appropriately scaled sampling and network capacity, our method further outperforms the baselines in visual quality, offering a high-fidelity configuration for quality-prioritized applications.

Abstract

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