  We prove the existence of symmetric diffusions and self-adjoint Laplacians on
(uniformly) hyperbolic attractors, endowed with SRB-measures. The proof is
based on Dirichlet form theory. We observe some features of such diffusions,
for instance, a quasi-invariance property of energy densities in the
$u$-conformal case and the existence of non-constant harmonic functions of zero
energy in the ergodic case.
