From the noisy information bombarding our senses our brains must construct percepts that are veridical – reflecting the true state of the world – and informative – conveying the most important information for adjusting our beliefs and behaviour. Influential theories in the cognitive sciences suggest that both of these challenges are met through mechanisms that use expectations about the likely state of the world to shape what we perceive. However, current models explaining how expectations render perception either veridical or informative are mutually incompatible. Given the multitude of domains applying these conflicting models, it is essential that we consider whether and how this paradox can be resolved. We contend that ideas from the research on learning and inference may offer a resolution.