  We study the diffusion of a Brownian probe particle of size $R$ in a dilute
dispersion of active Brownian particles (ABPs) of size $a$, characteristic swim
speed $U_0$, reorientation time $\tau_R$, and mechanical energy $k_s T_s =
\zeta_a U_0^2 \tau_R /6$, where $\zeta_a$ is the Stokes drag coefficient of a
swimmer. The probe has a thermal diffusivity $D_P = k_B T/\zeta_P$, where $k_B
T$ is the thermal energy of the solvent and $\zeta_P$ is the Stokes drag
coefficient for the probe. When the swimmers are inactive, collisions between
the probe and the swimmers sterically hinder the probe's diffusive motion. In
competition with this steric hindrance is an enhancement driven by the activity
of the swimmers. The strength of swimming relative to thermal diffusion is set
by $Pe_s = U_0 a /D_P$. The active contribution to the diffusivity scales as
$Pe_s^2$ for weak swimming and $Pe_s$ for strong swimming, but the transition
between these two regimes is nonmonotonic. When fluctuations in the probe
motion decay on the time scale $\tau_R$, the active diffusivity scales as $k_s
T_s /\zeta_P$: the probe moves as if it were immersed in a solvent with energy
$k_s T_s$ rather than $k_B T$.
