Yinzhi was born of the ManchuAisin Gioro clan as the third son of the Kangxi Emperor. His mother was Consort Rong (榮妃; d. 28 March 1727) from the Magiya (馬佳) clan and was the daughter of Gaishan (蓋山), who served as an Imperial Examination Examiner (員外郎). Yinzhi was granted the title of "Prince Cheng of the Second Rank" (誠郡王) in 1698.
Yinzhi was known to be studious as a child and was versed in literary arts. His talents earned him the appreciation of his father. French Jesuit Joachim Bouvet once mentioned in a letter to King Louis XIV that the Kangxi Emperor personally taught Yinzhi geometry. When the Kangxi Emperor opened a school in Changchun Gardens (暢春園), he placed Yinzhi in charge of compiling a book titled Lü Li Yuan Yuan (律歷淵源), which included the shi-er-lü, calendrical calculations, and mathematics. Yinzhi was also known for his skill in calligraphy, and was tasked with writing the inscriptions on the memorial tablet at the Kangxi Emperor's tomb in Jingling Mausoleum, Eastern Qing Tombs.
Yinzhi showed little interest in the conflict among his brothers for succession to the throne. He did not take any sides in the contention and preferred to spend time compiling and writing books. In 1706 the encyclopedia Gujin Tushu Jicheng was completed by Chen Menglei (陳夢雷), a scholar and associate of Yinzhi.
In 1722 the Kangxi Emperor died and was succeeded by his fourth son Yinzhen, who became known as the Yongzheng Emperor. Yinzhi changed his name to "Yunzhi" to avoid naming taboo because the Chinese character for "Yin" (胤) in "Yinzhi" is the same as the one in the Yongzheng Emperor's personal name "Yinzhen" (胤禛). After his ascension to the throne, the Yongzheng Emperor ordered Yunzhi to remain at the Jingling Mausoleum to watch over their father's tomb on an excuse that "Yinzhi was closely affiliated to the crown prince (Yinreng)". Yunzhi was unhappy with this arrangement and complained behind the Yongzheng Emperor's back. When Yinxiang, one of Yongzheng's closest half brothers, died in 1730, Yunzhi expressed little grief and sorrow. Yongzheng was angry when he heard of Yunzhi's reaction, so he stripped Yunzhi of his title and had him confined in the Yong'an Pavilion, Jingshan, Beijing. Yunzhi died in 1732 during his incarceration.