The acoustic variation in language presents learners with a substantial challenge. To learn by tracking statistical regularities in speech, infants must recognize words across tokens that differ based on characteristics such as the speaker's voice, affect, or the sentence context. Previous statistical learning studies have not investigated how these types of non-phonemic surface form variation affect learning. The present experiments used tasks tailored to two distinct developmental levels to investigate the robustness of statistical learning to variation. Experiment 1 examined statistical word segmentation in 11-month-olds and found that infants can recognize statistically segmented words across a change in the speaker's voice from segmentation to testing. The direction of infants' preferences suggests that recognizing words across a voice change is more difficult than recognizing them in a consistent voice. Experiment 2 tested whether 17-month-olds can generalize the output of statistical learning across variation to support word learning. The infants were successful in their generalization; they associated referents with statistically defined words despite a change in voice from segmentation to label learning. Infants' learning patterns also indicate that they formed representations of across word syllable sequences during segmentation. Thus, low probability sequences can act as object labels in some conditions. The findings of these experiments suggest that the units that emerge during statistical learning are not perceptually constrained, but rather are robust to naturalistic acoustic variation.