  We propose a learning-based method for light-path construction in path
tracing algorithms, which iteratively optimizes and samples from what we refer
to as spatio-directional Gaussian mixture models (SDMMs). In particular, we
approximate incident radiance as an online-trained $5$D mixture that is
accelerated by a $k$D-tree. Using the same framework, we approximate BSDFs as
pre-trained $n$D mixtures, where $n$ is the number of BSDF parameters. Such an
approach addresses two major challenges in path-guiding models. First, the $5$D
radiance representation naturally captures correlation between the spatial and
directional dimensions. Such correlations are present in e.g. parallax and
caustics. Second, by using a tangent-space parameterization of Gaussians, our
spatio-directional mixtures can perform approximate product sampling with
arbitrarily oriented BSDFs. Existing models are only able to do this by either
foregoing anisotropy of the mixture components or by representing the radiance
field in local (normal aligned) coordinates, which both make the radiance field
more difficult to learn. An additional benefit of the tangent-space
parameterization is that each individual Gaussian is mapped to the solid sphere
with low distortion near its center of mass. Our method performs especially
well on scenes with small, localized luminaires that induce high
spatio-directional correlation in the incident radiance.
