PokéBase - Pokémon Q&A
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No they don't. Sorry.

If you catch a Ditto in the Pokemon village its IVs will be random, just like any other Pokemon there. However, like with all Pokemon found in the wild, you could try to chain for a Ditto. If you have a chain of:

  • 40+ you get one perfect IV!
  • 50+ you get two perfect IVs!!
  • 60+ you get three perfect IVs!!!

(Thanks to fondant for the chaining information)

In order to obtain a Ditto with 2 perfect IVs instantly, you must catch it from the Friend Safari

Source: Knowledge

edited by
If you chain Dittos, you can get 1 perfect IV chain 40+, 2 perfect IVs from chain 50+, & 3 perfect IVs chain 60+.
I put it in the answer incase people skim read the answer without reading the comments. Please don't feel offended for using your information.
This way is it possible to get a perfect IV AND Shiny (40 is the magic number after which shinies become easier to find).