Previous pitch-controllable text-to-speech (TTS) models rely on directly modeling fundamental frequency, leading to low variance in synthesized speech. To address this issue, we propose PITS, an end-to-end pitch-controllable TTS model that utilizes variational inference to model pitch. Based on VITS, PITS incorporates the Yingram encoder, the Yingram decoder, and adversarial training of pitch-shifted synthesis to achieve pitch-controllability. Experiments demonstrate that PITS generates high-quality speech that is indistinguishable from ground truth speech and has high pitch-controllability without quality degradation. Code, audio samples, and demo are available at https://github.com/anonymous-pits/pits.