Statistical Error Reduction
for Monte Carlo Rendering

Hiroyuki Sakai, Christian Freude, Michael Wimmer, David Hahn
TU Wien
SIGGRAPH Asia 2025 Conference Paper
To be presented at SIGGRAPH Asia 2025 in Hong Kong
Time: Tuesday, December 16, 2025, 10:50–11:01 AM (GMT+8)
Location: Hong Kong Convention and Exhibition Centre (HKCEC),
Level 4, Meeting Room S426/S427
Paper Supplementary Document
Code Results (PFM) Results (PNG)

Our statistical error-reduction framework combines multi-transform (‘M’) and cascaded (‘C’) denoising with linear explained-variance correction (‘L’) to denoise both radiance and variance estimates. The latter can be used for adaptive sampling (“ASM”) to reduce image mean squared error (MSE) even further. We compare our denoiser (with and without adaptive sampling) to various state-of-the-art methods.

TL;DR

We present a statistics-based denoising framework for Monte Carlo rendering using multiple Box–Cox transformations and a linear explained-variance correction to improve statistical robustness. We also propose variance denoising, with applications to cascaded denoising and adaptive sampling. Our fast GPU implementation provides denoising quality competitive to state-of-the-art neural denoisers.

Abstract

Denoising is an important post-processing step in physically based Monte Carlo (MC) rendering. While neural networks are widely used in practice, statistical analysis has recently become a viable alternative for denoising. In this paper, we present a general framework for statistics-based error reduction of both estimated radiance and variance. Specifically, we introduce a novel denoising approach for variance estimates, which can either improve variance-aware adaptive sampling or provide additional input for image denoising in a cascaded manner. Furthermore, we present multi-transform denoising: a general and efficient correction scheme for non-normal distributions, which typically occur in MC rendering. All these contributions combine to a robust denoising pipeline that does not require any pretraining and can run efficiently on current GPU hardware. Our results show distinct advantages over previous denoising methods, especially in the range of a few hundred samples per pixel, which is of high practical relevance. Finally, we demonstrate good convergence behavior as the number of samples increases, providing predictable results with low bias that are free of hallucinated neural artifacts. In summary, our statistics-based algorithms for adaptive sampling and denoising deliver fast, consistent, low-bias variance and radiance estimates.

BibTeX

@inproceedings{sakai-2025-stater,
  author       = {Hiroyuki Sakai and
                  Christian Freude and
                  Michael Wimmer and
                  David Hahn},
  title        = {Statistical Error Reduction for {M}onte {C}arlo Rendering},
  booktitle    = {{SIGGRAPH} Asia 2025 Conference Papers, {SA} 2025, Hong Kong, Hong Kong, December 15-18, 2025},
  publisher    = {{ACM}},
  year         = {2025},
  url          = {https://doi.org/10.1145/3757377.3763995},
  doi          = {10.1145/3757377.3763995}
}

Acknowledgments

We thank Thomas Auzinger for providing LaTeX plugins, José Dias Curto for support with confidence intervals, and Markus Schütz for assistance with the CUDA implementation. We also thank the creators of the scenes we used: Benedikt Bitterli for “Veach, Bidir Room” (Figs. 1, S12), “Cornell Box” (Fig. 2), and “Fur Ball” (Fig. 12); Jay-Artist for “Country Kitchen” (Figs. 4, 5, 10, S2, S10, S16); Mareck for “Contemporary Bathroom” (Figs. 7, 14, S13); thecali for “4060.b Spaceship” (Fig. 9); piopis for “Old Vintage Car” (Fig. 13); Cem Yuksel for “Straight Hair” (Fig. S4) and “Curly Hair” (Fig. S5); UP3D for “Little Lamp” (Fig. S6); axel for “Glass of Water” (Fig. S7); MrChimp2313 for “Victorian Style House” (Fig. S8); NovaAshbell for “Japanese Classroom” (Fig. S9); and Beeple for “Zero-Day” (Fig. S11). Statistical simulation studies were conducted using the Austrian Scientific Computing (ASC) infrastructure. This work has been funded by the Vienna Science and Technology Fund (WWTF) [Grant ID: 1047379/ICT22028]. This research was funded in whole or in part by the Austrian Science Fund (FWF) [10.55776/F77]. For open-access purposes, the author has applied a CC BY public copyright license to any author-accepted manuscript version arising from this submission. The authors acknowledge TU Wien Bibliothek for financial support through its Open Access Funding Programme.