  Understanding the transport behavior of quantum many-body systems constitutes
an important physical endeavor, both experimentally and theoretically. While a
reliable classification into normal and anomalous dynamics is known to be
notoriously difficult for a given microscopic model, even the seemingly simpler
evaluation of transport coefficients in diffusive systems continues to be a
hard task in practice. This fact has motivated the development and application
of various sophisticated methods and is also the main issue of this paper. We
particularly take a barely used strategy, which is based Lanczos coefficients,
and demonstrate that this strategy allows for the accurate calculation of
diffusion coefficients for different paradigmatic examples, including
magnetization transport in nonintegrable spin-1/2 chains and ladders as well as
energy transport in the mixed-field Ising model in one dimension.
