According to Halberstam's "The Coldest Winter" page 49

"Stalin was playing a delicate game, flashing a half-green, half-amber light on the invasion."

Halberstam later states that Stalin gave Kim permission, but kept his involvement to a minimum and told Kim to rely on China for any material support. There's later an assertion on page 345 that Stalin had promised air cover to Chinese troops, but reneged on his promise.

This sounds like the mainstream theory, I'm unaware of any alternate theories.

EDIT: Spelling