Computational models for simulating physical phenomena during laser-based powder bed fusion additive manufacturing (L-PBF AM) processes are essential for enhancing our understanding of these phenomena, enable process optimization, and accelerate qualification and certification of AM materials and parts. It is a well-known fact that such models typically involve multiple sources of uncertainty that originate from different sources such as model parameters uncertainty, or model/code inadequacy, among many others. Uncertainty quantification (UQ) is a broad field that focuses on characterizing such uncertainties in order to maximize the benefit of these models. Although UQ has been a center theme in computational models associated with diverse fields such as computational fluid dynamics and macro-economics, it has not yet been fully exploited with computational models for advanced manufacturing. The current study presents one among the first efforts to conduct uncertainty propagation (UP) analysis in the context of L-PBF AM. More specifically, we present a generalized polynomial chaos expansions (gPCE) framework to assess the distributions of melt pool dimensions due to uncertainty in input model parameters. We develop the methodology and then employ it to validate model predictions, both through benchmarking them against Monte Carlo (MC) methods and against experimental data acquired from an experimental testbed.