Abstract: Efficient light transport simulation in participating media is challenging in general, but especially if the medium is heterogeneous and exhibits significant multiple anisotropic scattering. We present Principal-Ordinates Propagation, a novel finite-element method that achieves real-time rendering speeds on modern GPUs without imposing any significant restrictions on the rendered participated medium. We achieve this by dynamically decomposing all illumination into directional and point light sources, and propagating the light from these virtual sources in independent discrete propagation domains. These are individually aligned with approximate principal directions of light propagation from the respective light sources. Such decomposition allows us to use a very simple and computationally efficient unimodal basis for representing the propagated radiance, instead of using a general basis such as spherical harmonics. The resulting approach is biased but physically plausible, and largely reduces the rendering artifacts inherent to existing finite-element methods. At the same time it allows for virtually arbitrary scattering anisotropy, albedo, and other properties of the simulated medium, without requiring any precomputation.