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

Stochastic quantization associated with the $\exp(\Phi)_2$-quantum field model driven by space-time white noise on the torus