The talk is devoted to present the transient dynamics of diffusion processes driven by a class of Markov processes, which is absorbed by the absorption set in finite time with probability one. Our primary concern is to analyze quasi-stationary distributions (QSDs) which characterize the long term behavior before absorption. Due to the irreversibility of the absorbed diffusion processes in this paper, probability methods are used to analyze the sub-Markovian semigroup generated by the absorbed diffusion processes. We provide the Lyapunov type criteria for the existence, uniqueness of the quasi-stationary distribution and show the exponential convergence to this QSD in the weighted total variation distance. Finally, the criteria is applied to stochastic ecological systems subject to both demographic and environmental stochasticity, and sufficient conditions are given for the existence, uniqueness and convergence of the quasi-stationary distribution. This work is jointed with Yu Zhu.