Music performances are rich in systematic temporal irregularities called "microtiming", too fine-grained to be notated in a musical score but important for musical expression and communication. Several studies have examined listeners' preference for rhythms varying in microtiming, but few have addressed precisely how microtiming is perceived, especially in terms of cognitive mechanisms, making the empirical evidence difficult to interpret. Here we provide evidence that microtiming perception can be simulated as a process of probabilistic prediction. Participants performed an XAB discrimination test, in which an archetypal popular drum rhythm was presented with different microtiming. The results indicate that listeners could implicitly discriminate the mean and variance of stimulus microtiming. Furthermore, their responses were effectively simulated by a Bayesian model of entrainment, using a distance function derived from its dynamic posterior estimate over phase. Wide individual differences in participant sensitivity to microtiming were predicted by a model parameter likened to noisy timekeeping processes in the brain. Overall, this suggests that the cognitive mechanisms underlying perception of microtiming reflect a continuous inferential process, potentially driving qualitative judgements of rhythmic feel.