The idea of handing out additional stunts (or aspects - to be honest, I prefer new aspects as it creates a closer tie to the narrative of the game) is the most common within Fate systems (it's the primary mechanic in Starblazer in my mind). That said, one of the game's designers, Byron Kerr, has actually opined on this topic:
Create characters as described in Chapter 3: Characters in Diaspora. Complete the five phases of life and select ten Aspects.
Instead of using the default 5 level skill pyramid (and 15 subsequent skills,) cap the character with a pinnacle skill of 3.
X X X
These characters will therefore have 9 skills (one at level 3 – their pinnacle skill, two at level 2 and three at level 1.) Characters like this represent young characters, ones fresh from the academy or older characters who have never left their planet before their moment of crisis. Newly exposed to the width and breadth of the cluster, these characters have the possibility of improving themselves, their abilities and gaining renown throughout the cluster.
Upon completion of each session, the characters shall improve a skill. This starts at level 1, each subsequent skill increase builds up the pyramid; level 2, then level 3, then level 4. After four successful adventures characters will have a new pinnacle skill level of 4. The empty skill slot could be filled during game play when a desired, but currently unselected, skill was needed for a situation during the session’s play.
X X 2
X X X 1
(Numbers represent the order that skills are added, at the conclusion of each session.)
This means they have survived and might even be starting to thrive in the cluster. Their pinnacle skill may be their original level 3 skill shifted one spot higher or any other skill they so wish. It may be something brand new that they’ve just discovered about themselves while exploring the cluster.
Upon successful completion of this level 4 pyramid, characters begin at level 1 again and as they improve can, after another five successful advancements have a 5 level pyramid. Should the players and the GM so desire, there is nothing to stop them from continuing their quest for improvement as after another six promotions the characters will have a Skill pyramid with 6 levels (by this point the characters renown should pretty much span a cluster of 6 to 10 systems.)
4 8 (13)
X 3 7 (12)
X X 2 6 (11)
X X X 1 5 (10)
(So after nine sessions the 5-cap pyramid is complete. Numbers in brackets indicate the sequence of the expansion slots if the ref wants a 6-cap.)
It is important to remember that Aspects may be changed over the course of the game, swapping one unused or no longer relevant Aspect for something new that has happened during the game is encouraged. Remember to make the shifts gradual and that characters may only have 10 Aspects at any time.
In addition to the new skills the characters add, they may shift an existing skill up or down one level at a table agreed upon time or adding a brand new skill at level 1 at the expense of an existing level 1 skill.
It is not advised to continuing advancing character since a level 7 pyramid means character would enjoy 28 skills, as the default starting skill list contains 35 skills this would mean having a 7 level pyramid would only be missing 7 of the skills.
Below is listed a bare bones chart of how to take a character starting with a Skill cap of 3 up to a character with a Skill cap of 4. Following the numbered charts beyond that to evolve into a Skill cap 5 character is numerically represented, taking that a step further to make a very powerful Skill cap 6 character should be straightforward.
The entire thread is (along with an alternate approach) is available on RPGGeek.