  We propose a new Markov chain Monte Carlo method in which trial
configurations are generated by evolving a state, sampled from a prior
distribution, using a Markov transition matrix. We present two prototypical
algorithms and derive their corresponding acceptance rules. We first identify
the important factors controlling the quality of the sampling. We then apply
the method to the problem of sampling polymer configurations with fixed
endpoints. Applications of the proposed method range from the design of new
generative models to the improvement of the portability of specific Monte Carlo
algorithms, like configurational-bias schemes.
