  Complex visual effects such as caustics are often produced by light paths
containing multiple consecutive specular vertices (dubbed specular chains),
which pose a challenge to unbiased estimation in Monte Carlo rendering. In this
work, we study the light transport behavior within a sub-path that is comprised
of a specular chain and two non-specular separators. We show that the specular
manifolds formed by all the sub-paths could be exploited to provide coherence
among sub-paths. By reconstructing continuous energy distributions from
historical and coherent sub-paths, seed chains can be generated in the context
of importance sampling and converge to admissible chains through manifold
walks. We verify that importance sampling the seed chain in the continuous
space reaches the goal of importance sampling the discrete admissible specular
chain. Based on these observations and theoretical analyses, a progressive
pipeline, manifold path guiding, is designed and implemented to importance
sample challenging paths featuring long specular chains. To our best knowledge,
this is the first general framework for importance sampling discrete specular
chains in regular Monte Carlo rendering. Extensive experiments demonstrate that
our method outperforms state-of-the-art unbiased solutions with up to 40x
variance reduction, especially in typical scenes containing long specular
chains and complex visibility.
