This paper proposes a probabilistic extension of SimSiam, a recent self-supervised learning (SSL) method. SimSiam trains a model by maximizing the similarity between image representations of different augmented views of the same image. Although uncertainty-aware machine learning has been getting general like deep variational inference, SimSiam and other SSL are insufficiently uncertainty-aware, which could lead to limitations on its potential. The proposed extension is to make SimSiam uncertainty-aware based on variational inference. Our main contributions are twofold: Firstly, we clarify the theoretical relationship between non-contrastive SSL and multimodal variational inference. Secondly, we introduce a novel SSL called variational inference SimSiam (VI-SimSiam), which incorporates the uncertainty by involving spherical posterior distributions. Our experiment shows that VI-SimSiam outperforms SimSiam in classification tasks in ImageNette and ImageWoof by successfully estimating the representation uncertainty.