  We consider SDEs driven by two different sources of additive noise, which we
refer to as intrinsic and common. We establish almost sure existence and
uniqueness of pullback attractors with respect to realisations of the common
noise only. These common noise pullback attractors are smooth probability
densities that depend only on (the past of) a common noise realisation and to
which the pullback evolution of a corresponding stochastic Fokker-Planck
equation converges. Common noise pullback attractors have a natural motivation
in the context of particle systems with intrinsic and common noise, describing
the distribution of the system conditioned on (the past of) a common noise
realisation.
