What's the difference between notorious and infamous?

Are these two words synonymous or is there any nuance between these two words? Though they are used synonymously in sentences and also followed by the same preposition "for". I want to be expertly responded to these nuances with reference to their adequate collocations.

Infamous is strictly negative. Even if it is about fame, this is always negative fame. It's almost never used figuratively, or tongue-in-cheek. It's negative fame, be it due to bad failures, or due to evil conduct.

Notorious is more often than not used as a more neutral "famous" - used in contexts, where you want to limit the positive connotation be it not to sound overly flattering or as tongue-in-cheek expression of limited praise. You can be a DJ notorious in clubs of your city, a notorious speaker at Sci-Fi conventions, a notorious hacker with three hundred security advisories published to your name. These don't strictly imply what you do is wrong, they just say you are widely recognized, and simultaneously don't try to trump up your achievements.

Notoriety is more about insistence, being known for repeating your activity, without actually creating anything very notable, while fame or infamy may be about popularity possible to gain with a single truly spectacular performance. Notorious is often used humorously, due to lack of inherent positivity (presenting a positive fame in mock sinister light) and implied insistence, stubbornness (becoming known despite failure to achieve genuine fame, implying poor quality of "production", insufficient to be called "famous".)

As result, fame and infamy are "stronger" than notoriety, and notoriety is more neutral.

Edit: an example of this usage for Mary-Lou.

The notorious Robert Downey Jr. known for his role of Iron Man, takes the character of Tony Stark, the incorrigible playboy genius philantropist billionaire out of the stage and adopts it as his own. Asked by a reporter, "Tony, could you... sorry, Robert..." - answers, oozing humility, "No, Tony is fine. Tony is perfectly fine." He hides snacks all over the movie stage and pulls them out during filming, taking wild liberties with the script and causing woe both to other actors and the director (and allegedly not just for "artistic license", but simply because he doesn't bother to learn his proper script!) Take the scene from "Avengers" when he serves peanuts to other members of the team, it's completely spontaneous.

[now, there is no doubt Robert Downey Jr. is simply a famous actor, but his antics, ego, and style make the word 'famous' simply miss the point - he's not loved for being a famous actor, but for being the notorious Tony Stark.]

Etymologically, notorious has (had) no negative connotations at all.

notorious (adj.)
1540s, "publicly known," from Medieval Latin notorius "well-known, commonly known," from Latin notus "known," past participle of noscere "come to know" ….

As etymonline notes, the "Negative connotation arose 17c. from frequent association with derogatory nouns." [ibid.]

Even today, the negative connotation comes explicitly from the context, as ODO notes:

Famous or well known, typically for some bad quality or deed:
Los Angeles is notorious for its smog
he was a notorious drinker and womanizer

Infamous on the other hand is a "natural" antonym of 'famous.'