Jaroslav Křivánek

Volume Path Guiding Based on Zero-Variance Random Walk Theory

Sebastian Herholz
University of Tübingen
Yangyang Zhao
McGill University
Oskar Elek
Charles University, Prague

Derek Nowrouzezahrai
McGill University
Henrik P. A. Lensch
University of Tübingen
Jaroslav Křivánek
Charles University, Prague
Chaos Czech a. s.

Path tracing of an optically dense medium (30 minutes), showing both a complete “beauty” render (S+V), and a render with only volumetric transport (V). Building on an approximate adjoint solution of the incident and in-scattered radiance, our zero variance-based path construction forms near-optimal decisions for guided collision distance sampling, directional sampling, Russian roulette, and path splitting. As such, our sampling methodology leads to significantly faster convergence compared to an unguided path tracer with standard transmittance-based collision and phase function sampling.


The efficiency of Monte Carlo methods, commonly used to render participating media, is directly linked to the manner in which random sampling decisions are made during path construction. Notably, path construction is influenced by scattering direction and distance sampling, Russian roulette, and splitting strategies. We present a consistent suite of volumetric path construction techniques where all these sampling decisions are guided by a cached estimate of the adjoint transport solution. The proposed strategy is based on the theory of zero-variance path sampling schemes, accounting for the spatial and directional variation in volumetric transport. Our key technical contribution, enabling the use of this approach in the context of volume light transport, is a novel guiding strategy for sampling the particle collision distance proportionally to the product of transmittance and the adjoint transport solution (e.g., in-scattered radiance). Furthermore, scattering directions are likewise sampled according to the product of the phase function and the incident radiance estimate. Combined with guided Russian roulette and splitting strategies tailored to volumes, we demonstrate about an order-of-magnitude error reduction compared to standard unidirectional methods. Consequently, our approach can render scenes otherwise intractable for such methods, while still retaining their simplicity (compared to, e.g., bidirectional methods).


Sebastian Herholz, Yangyang Zhao, Oskar Elek, Derek Nowrouzezahrai, Hendrik P. A. Lensch, and Jaroslav Křivánek. Volume Path Guiding Based on Zero-Variance Random Walk Theory. ACM Transactions on Graphics, 38(3), 2019.
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We want to thank the following persons and institutions for providing some of the models and scenes used in this work: Stanford 3D scanning repository (Buddha), Alvaro Luna Bautista and Joel Andersdon (Natural History), Bruce Walter (Bumpy Sphere), and Infinite Realities (InfiniteScan Head). An additional thanks goes to Robert Hildebrandt for lighting some of the scenes.