  Dyson's model in infinite dimensions is a system of Brownian particles that
interact via a logarithmic potential with an inverse temperature of $ \beta =
2$. The stochastic process can be represented by the solution to an
infinite-dimensional stochastic differential equation. The associated unlabeled
dynamics (diffusion process) are given by the Dirichlet form with the sine$ _2$
point process as a reference measure. In a previous study, we proved that
Dyson's model in infinite dimensions is irreducible, but left the ergodicity of
the unlabeled dynamics as an open problem. In this paper, we prove that the
unlabeled dynamics of Dyson's model in infinite dimensions are ergodic.
