Systems, methods and articles of manufacture for rendering three-dimensional virtual environments using reversible jumps are disclosed herein. In one embodiment, mappings from random numbers to light paths are modeled as an explicit iterative random walk. Inverses of path construction techniques are employed to turn light transport paths back into the random numbers that produced them. In particular, such inverses may be used to extend the Multiplexed Metropolis Light Transport (MMLT) technique to perform path-invariant perturbations that produce a new path sample using a different path construction technique but preserve the path's geometry. To render an image, a rendering application in one embodiment may trace light paths through a virtual scene, with some path samples being generated by probabilistically selecting one or more techniques through technique perturbation and using inverses of the selected technique(s) to invert existing path(s), and with new paths being obtained by mutating or perturbing existing paths.