  We consider a quantum field model with exponential interactions on the
two-dimensional torus, which is called the $\exp (\Phi)_{2}$-quantum field
model or H{\o}egh-Krohn's model. In the present paper, we study the stochastic
quantization of this model by singular stochastic partial differential
equations, which is recently developed. By the method, we construct a unique
time-global solution and the invariant probability measure of the corresponding
stochastic quantization equation, and identify with an infinite-dimensional
diffusion process, which has been constructed by the Dirichlet form approach.
