We present an extension of the fast beam-tracing method presented in the work of Antonacci et al. (2008) for the simulation of acoustic propagation in reverberant environments that accounts for diffraction and diffusion. More specifically, we show how visibility maps are suitable for modeling propagation phenomena more complex than specular reflections. We also show how the beam-tree lookup for path tracing can be entirely performed on visibility maps as well. We then contextualize such method to the two different cases of channel (point-to-point) rendering using a headset, and the rendering of a wave field based on arrays of speakers. Finally, we provide some experimental results and comparisons with real data to show the effectiveness and the accuracy of the approach in simulating the soundfield in an environment.