We analyze the X-ray emission of W49B, a centrally-filled galactic supernova remnant, using the Smoothed Particle Inference technique. Our method allows us to characterize the morphology and abundance distribution over the entire remnant, infer the density throughout the remnant, and compute the mass of individual elements within the plasma. Our study of the density structure confirms interaction of the remnant with a molecular cloud towards the eastern edge. We find a total mass of 130.33 (± 15.64) M⊙, with an estimated ejecta mass of 1.15 (± 0.18) M⊙. Comparison of the inferred abundances with a wide selection of supernova explosion models, including Type Ia, core-collapse, and hypernova models, favors deflagration-to-detonation transition Type Ia models. General agreement between our inferred abundances and those of previous studies suggests that prior disagreement arose mainly from comparison to a limited subset of models. While our results lean towards a Type Ia origin, other aspects of W49B can be (partially) explained by either core-collapse or Type Ia models. The origin therefore remains inconclusive, inviting further detailed study. This work was supported by NASA ADAP grant NNX15AF03G.