My quick theory:
The Hmong/Miao were originally one people, and flourished under Chiyou (Txiv Yawg) in Eastern China. After the fall of Chiyou, and the expansion of the Chinese, the Hmong/Miao were forced repeatedly to relocate. Through time, some groups stayed, while others fled. Isolation from one group to the other over the centuries lead to sub groupings of what was once one group of people. Dialects, and culture change over time, as the various subgroups intermixed with other ethnic groups.
If you explore the world just a bit further to western China, there exists people with an asian face with caucasian characteristic s in their hair, eyes, and even skin. It may be possible, that at one time, our ancestors and these people may have intermixed (given the "silk road" connected China to the west).
In my opinion, we share a common ancestor with the Miao in China more than we do with Mongols, Isrealis, etc.
The soft evidence is our similarities in:
Culture (All if not most, practice the same/similar funeral rituals (or so I've heard))
Clothing (It's all about the bling or showcasing your bling)
Lifestyle (Many use the same tools to cultivate, make clothing, prepare food, etc)
Musical Instruments (Qeej)
Language (From what I read, there are about 3 Miao dialects, Western, Central, Eastern)