  The diffusion in two dimensions of non-interacting active particles that
follow an arbitrary motility pattern is considered for analysis. Accordingly,
the transport equation is generalized to take into account an arbitrary
distribution of scattered angles of the swimming direction, which encompasses
the pattern of motion of particles that move at constant speed. An exact
analytical expression for the marginal probability density of finding a
particle on a given position at a given instant, independently of its direction
of motion, is provided; and a connection with a generalized diffusion equation
is unveiled. Exact analytical expressions for the time dependence of the
mean-square displacement and of the kurtosis of the distribution of the
particle positions are presented. For this, it is shown that only the first
trigonometric moments of the distribution of the scattered direction of motion
are needed. The effects of persistence and of circular motion are discussed for
different families of distributions of the scattered direction of motion.
