In this paper, we studied the Hilbert space-valued statistical dynamical model of the instantaneous forward interest rate curves with as a regularity term, which is first considered and studied by R. Douady, M. Musiela, R. Cont and so forth. In particular, we raised the question: how to construct infinite dimension version of stochastic volatility which is a Hilbert-Schmidt operator valued stochastic process. In order to handle the SABR-type volatility operators, we purpose two kinds of models, one is a direct generalization of the classic SABR model while the other one is more general involving more non- linearity and flexibility. We showed the existence of mild solutions to our models. Our proof is based on Leray-Schauder fixed point theorem and some priori inequalities on the stochastic operator processes we construct. Further, we relaxed the assumptions and studied the regularity of the solutions to some specific models.