Continuous Multiple Importance Sampling (CMIS) is a generalization of multiple importance sampling to uncountably infinite sets of techniques, equipped with a corresponding balance heuristic and a practical estimator.

To demonstrate the practicality of CMIS, we've applied it to three problems in light transport,

Path Reuse

Path sampling entails a high computational cost whose amortization is desirable, e.g., by reusing (sub)paths across multiple pixel estimations. In prior unbiased approaches, such reuse is limited by the discrete nature of DMIS. Path and (ir)radiance filtering methods are more flexible but add bias and are hampered by simplistic weighting heuristics. We show how CMIS can ameliorate these issues.

Spectral Rendering

Spectral rendering overcomes the limitations of tri-stimulus (RGB) rendering by extending the path integral over the wavelength domain, which results in increased variance in the form of color noise. We show how our CMIS framework can be leveraged to reduce color noise via more flexible and effective wavelength importance sampling.

Photon Planes

A continuum of path sampling techniques arises naturally in some methods for volumetric light transport simulation. We show that the photon plane method of [Deng et al., 2019] can be formulated under CMIS, and derive a balance-heuristic SMIS estimator that achieves lower variance through more accurate weighting.


Multiple importance sampling (MIS) is a provably good way to combine a finite set of sampling techniques to reduce variance in Monte Carlo integral estimation. However, there exist integration problems for which a continuum of sampling techniques is available. To handle such cases we establish a continuous MIS (CMIS) formulation as a generalization of MIS to uncountably infinite sets of techniques. Our formulation is equipped with a base estimator that is coupled with a provably optimal balance heuristic and a practical stochastic MIS (SMIS) estimator that makes CMIS accessible to a broad range of problems. To illustrate the effectiveness and utility of our framework, we apply it to three different light transport applications, showing improved performance over the prior state-of-the-art techniques.

The Paper

Presentation Video

The SIGGRAPH 2020 presentation video for the paper. It covers a brief introduction to continuous MIS and stochastic MIS, and a high-level overview of how they can be applied to path-reuse, spectral path sampling, and photon planes.

Supplementary Materials

Coming soon.


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Rex West
PhD. Student

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Iliyan Georgiev

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Adrien Gruson

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Toshiya Hachisuka