  We study Markov Chain Monte Carlo (MCMC) methods operating in primary sample
space and their interactions with multiple sampling techniques. We observe that
incorporating the sampling technique into the state of the Markov Chain, as
done in Multiplexed Metropolis Light Transport (MMLT), impedes the ability of
the chain to properly explore the path space, as transitions between sampling
techniques lead to disruptive alterations of path samples. To address this
issue, we reformulate Multiplexed MLT in the Reversible Jump MCMC framework
(RJMCMC) and introduce inverse sampling techniques that turn light paths into
the random numbers that would produce them. This allows us to formulate a novel
perturbation that can locally transition between sampling techniques without
changing the geometry of the path, and we derive the correct acceptance
probability using RJMCMC. We investigate how to generalize this concept to
non-invertible sampling techniques commonly found in practice, and introduce
probabilistic inverses that extend our perturbation to cover most sampling
methods found in light transport simulations. Our theory reconciles the
inverses with RJMCMC yielding an unbiased algorithm, which we call Reversible
Jump MLT (RJMLT). We verify the correctness of our implementation in canonical
and practical scenarios and demonstrate improved temporal coherence, decrease
in structured artifacts, and faster convergence on a wide variety of scenes.
