When combining information across different senses, humans need to flexibly select cues of a common origin while avoiding distraction from irrelevant inputs. The brain could solve this challenge using a hierarchical principle by deriving rapidly a fused sensory estimate for computational expediency and, later and if required, filtering out irrelevant signals based on the inferred sensory cause(s). Analyzing time- and source-resolved human magnetoencephalographic data, we unveil a systematic spatiotemporal cascade of the relevant computations, starting with early segregated unisensory representations, continuing with sensory fusion in parietal-temporal regions, and culminating as causal inference in the frontal lobe. Our results reconcile previous computational accounts of multisensory perception by showing that prefrontal cortex guides flexible integrative behavior based on candidate representations established in sensory and association cortices, thereby framing multisensory integration in the generalized context of adaptive behavior. •Flexible use of multisensory information follows Bayesian inference•Sensory fusion emerges earlier than causal inference•Multisensory inference is represented in the frontal lobe•Inferior frontal regions guide perception in discrepant environments Humans combine multisensory information sharing a common cause while avoiding distraction from irrelevant sources. Cao et al. show how this flexible sensory inference is guided by prefrontal cortex and unfolds as sequential neural computations comprising functionally distinct multisensory representations.