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Path guiding is a promising tool to improve the performance of path tracing algorithms. However, not much research has investigated what target densities a guiding method should strive to learn for optimal performance. Instead, most previous work pursues the zero-variance goal: The local decisions are guided under the assumption that all other decisions along the random walk will be sampled perfectly. In practice, however, many decisions are poorly guided, or not guided at all. Furthermore, learned distributions are often marginalized, e.g., by neglecting the BSDF. We present a generic procedure to derive theoretically optimal target densities for local path guiding. These densities account for variance in nested estimators, and marginalize provably well over, e.g., the BSDF. We apply our theory in two state-of-the-art rendering applications: a path guiding solution for unidirectional path tracing [Müller et al. 2017] and a guiding method for light source selection for the many lights problem [Vévoda et al. 2018]. In both cases, we observe significant improvements, especially on glossy surfaces. The implementations for both applications consist of trivial modifications to the original code base, without introducing any additional overhead.

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