gradual, slow
leftward, rightward
He criticized the rightward drift of the party.

continental

drift (away) from
the drift of people away from rural areas into urban slums

drift (back) to
As the strike went on, there was a gradual drift back to work.

drift into
his drift into crime

drift towards/toward

general, main

catch, follow, get
I didn't follow the speech exactly, but I caught the main drift of what was being said.

deep
sand, snow (usually snowdrift)

slowly
helplessly
Cold and hungry, they drifted helplessly closer to the Arctic.

downstream
The boat drifted slowly downstream.

along, back, down, out, up, etc.
Smoke drifted up from the campfire.

from, to, towards/toward, etc.
They were drifting out to sea.

with
We drifted with the current.

aimlessly
gradually, slowly
Her gaze gradually drifted to the bookshelf.

quietly, silently
eventually, finally
He finally drifted back to his home town.

about (esp. BrE), around, back, down, round (esp. BrE), up, etc.
Voices drifted up through the floorboards.

apart, away, off
Over the years the two friends drifted apart.

begin to
seem to
allow sth to, let sth
He allowed his thoughts to drift back to his conversation with Carrie.

about (BrE), around, round (esp. BrE)
He spent the day drifting aimlessly around the house.

across
She drifted across the room to where we were standing.

between
She began to drift between sleep and wakefulness.

from
We seem to be drifting away from the point.

into
He drifted into teaching, but never really enjoyed it.

out of
He drifted in and out of consciousness.

gradually, slowly

into
He drifted off into a deep slumber.

drift off to sleep
She closed her eyes and slowly drifted off to sleep.

Drift is used with these nouns as the subject:
attention, boat, breeze, cloud, continent, conversation, eye, fog, gaze, mind, mist, music, scent, smell, smoke, snow, snowflake, word