Don't confuse this people with the later Di 氐, relatives to the Qiang 羌 and Tanguts 黨項.
Di 狄, occasionally written 翟, was an old general term for nomadic peoples living in the northwestern regions. They are the northern representants of the four categories of uncivilized "barbarians", the other being the "western barbarians" Rong 戎, the "eastern barbarians" Yi 夷, and the "southern barbarians" Man 蠻.
During the Spring and Autumn period 春秋 (770-5th cent. BCE) Chinese chronicles mention the White Di 白狄, the Red Di 赤狄, and the Tall Di 長狄 (called so because they had taller bodies). The leaders of the Red Di bore the family name of Kui 隗 which might be a hint that they are identical to the Guifang 鬼方 people mentioned in Shang period 商 (17th-11th cent. BC) oracle bone inscriptions. They lived in the area of modern Shaanxi, Gansu and Ningxia. The Confucian Classic Shangshu 尚書 "Book of Documents" mentions campaigns of the Shang kings against the Guifang people in the west.
The early kings of the Zhou dynasty 周 (11th cent.-221 BCE) also regularly waged war against the steppe peoples and often enslaved war captives of the Di tribes. The pastoral nomads often migrated into the territory of the northwestern regional states of Qin 秦 and Jin 晉 and settled down in Chinese territory. They founded some statelets and were able to defeat minor Chinese states, like Xing 邢 or Wei 衛. Their growing power stimulated the Chinese regional states to conclude military alliances against the permanent raids undertaken by the Di, and because the kings of Zhou were unable to provide an effective defense, Duke Huan of Qi 齊桓公 (r. 685-643) took over the position of the defender of the Chinese regional states against the northern barbarians.
The Di so stimulated the rise of the institution of the hegemonial lord (ba 霸) during the Spring and Autumn period. Yet the Di tribes continued harassing the regional states and even forced the king of Zhou to flee the capital Luoyang 洛陽. The hegemonial lord Duke Wen of Jin 晉文公 (r. 636-628) defeated the Di and brought back the king to the capital. Various tribes of the Red Di people advanced as far as the eastern states of Qi 齊 and Lu 魯, but their power vaned in the late Spring and Autumn period, and their polities like Lu 潞, Shenshi 申氏, Liuxu 留吁, Duochen 鐸辰, Gaoluo 皋落 and Qiangjiu 廧咎 were conquered by Jin.
The White Di who originally lived in western Shaanxi, also migrated towards the east and founded states like Xianyu 鮮虞, Fei 肥 and Gu 鼓. The White Di of Xianyu founded the state of Zhongshan 中山 and during the Warring States period 戰國 (5th cent.221 BCE) adopted the title of king. The remnants of their residence and the royal tomb were excavated during the 1970s. Archeological remnants show that the Di were no longer a "barbarian" people but had culturally merged with the Chinese regional states.
The Chang Di migrated to the region of Henan and Hebei, where they also founded a series of smaller states, but they were less belligerent and were dominated by the Red Di. The Di had vanished as a distinct people at the end of the Zhou period.