Markov chain Monte Carlo (MCMC) algorithms are indispensable when sampling from a complex, high-dimensional distribution by a conventional method is intractable. Even though MCMC is a powerful tool, it is also hard to control and tune in practice. Simultaneously achieving both rapid local exploration of the state space and efficient global discovery of the target distribution is a challenging task. In this work, we introduce a novel continuous-time MCMC formulation to the computer science community. Generalizing existing work from the statistics community, we propose a novel framework for adjusting an arbitrary family of Markov processes - used for local exploration of the state space only - to an overall process which is invariant with respect to a target~distribution. To demonstrate the potential of our framework, we focus on a simple, but yet insightful, application in light transport simulation. As a by-product, we introduce continuous-time MCMC sampling to the computer graphics community. We show how any existing MCMC-based light transport algorithm can be seamlessly integrated into our framework. We prove empirically and theoretically that the integrated version is superior to the ordinary algorithm. In fact, our approach will convert any existing algorithm into a highly parallelizable variant with shorter running time, smaller error and less variance.