When we face ambiguous images, the brain cannot commit to a single percept; instead, it switches between mutually exclusive interpretations every few seconds, a phenomenon known as bistable perception. While neuromechanistic models, e.g., adapting neural populations with lateral inhibition, may account for the dynamics of bistability, a larger question remains unresolved: how this phenomenon informs us on generic perceptual processes in less artificial contexts. Here, we propose that bistable perception is due to our prior beliefs being reverberated in the cortical hierarchy and corrupting the sensory evidence, a phenomenon known as "circular inference". Such circularity could occur in a hierarchical brain where sensory responses trigger activity in higher-level areas but are also modulated by feedback projections from these same areas. We show that in the face of ambiguous sensory stimuli, circular inference can change the dynamics of the perceptual system and turn what should be an integrator of inputs into a bistable attractor switching between two highly trusted interpretations. The model captures various aspects of bistability, including Levelt's laws and the stabilizing effects of intermittent presentation of the stimulus. Since it is related to the generic perceptual inference and belief updating mechanisms, this approach can be used to predict the tendency of individuals to form aberrant beliefs from their bistable perception behavior. Overall, we suggest that feedforward/feedback information loops in hierarchical neural networks, a phenomenon that could lead to psychotic symptoms when overly strong, could also underlie perception in nonclinical populations.