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Acquiring a precise model is a challenging task for many important robotic tasks and systems - including in-hand manipulation using underactuated, adaptive hands. Learning stochastic, data-driven models is a promising alternative as they provide not only a way to propagate forward the system dynamics, but also express the uncertainty present in the collected data. Therefore, such models en- able planning in the space of state distributions, i.e., in the belief space. This paper proposes a planning framework that employs stochastic, learned models, which ex- press a distribution of states as a set of particles. The integration achieves anytime behavior in terms of returning paths of increasing quality under constraints for the probability of success to achieve a goal. The focus of this effort is on pushing the efficiency of the overall methodology despite the notorious computational hardness of belief-space planning. Experiments show that the proposed framework enables reaching a desired goal with higher success rate compared to alternatives in sim- ple benchmarks. This work also provides an application to the motivating domain of in-hand manipulation with underactuated, adaptive hands, both in the case of physically-simulated experiments as well as demonstrations with a real hand.