The brain learns an internal model of the environment through sensory experiences, which is essential for high-level cognitive processes. Recent studies show that spontaneous activity reflects such a learned internal model. Although computational studies have proposed that Hebbian plasticity can learn the switching dynamics of replayed activities, it is still challenging to learn dynamic spontaneous activity that obeys the statistical properties of sensory experience. Here, we propose a pair of biologically plausible plasticity rules for excitatory and inhibitory synapses in a recurrent spiking neural network model to embed stochastic dynamics in spontaneous activity. The proposed synaptic plasticity rule for excitatory synapses seeks to minimize the discrepancy between stimulus-evoked and internally predicted activity, while inhibitory plasticity maintains the excitatory-inhibitory balance. We show that the spontaneous reactivation of cell assemblies follows the transition statistics of the model's evoked dynamics. We also demonstrate that simulations of our model can replicate recent experimental results of spontaneous activity in songbirds, suggesting that the proposed plasticity rule might underlie the mechanism by which animals learn internal models of the environment.