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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 what we did not already know. Influential theories suggest that both challenges are met through mechanisms that use expectations about the likely state of the world to shape perception. However, current models explaining how expectations render perception either veridical or informative are mutually incompatible. While the former propose that perceptual experiences are dominated by events we expect, the latter propose that perception of expected events is suppressed. To solve this paradox we propose a two-process model in which probabilistic knowledge initially biases perception towards what is likely and subsequently upweights events that are particularly surprising.