1. Neighborhood is old, run-down, inexpensive (for numerous reasons)
2. Young professionals (usually white) start moving in to save money
3. Investors/developers notice the trend and start rebuilding/redeveloping at a faster rate
4. The end result is what's frequently perceived as a bland upper-middle-class neighborhood.
Somewhere between 2 and 3, the previous residents are driven out by price increases. They take their culture with them. Between that loss of diversity and zoning restrictions (typical 5-over-2 building pattern), the result usually is pretty bland (IMO).