I was wondering how much of the manga does the anime version of one week friends cover? I'm also wondering if the ending of the anime diverged from the manga?
If you've just watched the anime and want to get into the manga without repeating material, you can probably start with Volume 5. It might also help to read Volume 4. Volume 5 seems to be the cutoff point where the anime ends, but there are some differences in how the material of Volumes 4 and 5 is presented in the anime versus the original manga.
It's shocking how hard it is to find info in English on anything other than mega-hits like Naruto. For that reason, this answer isn't perfectly definitive, but this question deserves some kind of answer, so here's what my efforts produced.
I just finished watching the anime and I did a little poking through some scanlations to try and establish the timeframe. Based on my random sampling, nhahtdh is correct that the anime version ends in Volume 5 of the manga; Chapter 22 is the first chapter of Volume 5, and it contains a version of the scene from Episode 11 when Yuki and Hajime meet at the family restaurant to discuss the incident from sixth grade.
However, this chart from Japanese Wikipedia claims that Episodes 11 and 12 are covered in Volume 4. Some scenes in the anime seem to be composites of scenes from the manga, so that might make it more of a "Well, yeah, XX from the anime was in Volume 5, but the bulk of material from those episodes was in Volume 4" sort of thing. For example, the scene with Hajime and Yuki ends totally differently from the anime; they don't meet up with the girls who
bullied Kaori, causing her to run into the street and get hit and triggering her memory loss
Kaori show up and hear the reason for her memory loss
as happened in the anime; instead, they go to Yuki's house and play video games together. Also, the scene at the crepe shop from Episode 11 when
Kaori tells Hajime she probably can't remember him because he was her friend, then sees her "friends" from her past who bullied her for "stealing" Hajime and gets a tiny flash of memory, causing her to run away, after which Yuki confronts Hajime
happens in Chapter 18 (Volume 4) under different circumstances.
The anime timeline seems to run ahead of the manga timeline, and as far as I can tell, the pace of the manga is consistently slower than the anime.
According to the Wikipedia page (sourced from this Anime News Network posting), the manga hasn't ended yet and the final volume will be released in April of 2015, so we don't yet know just how how much the anime actually diverges from the manga. However, the main plot points of the manga up to Chapter 22 seem to be the same as the anime:
Hajime shows up, causing Kaori to lose all her hard-earned memories of Yuki. Yuki gets to work rebuilding those memories while trying to get to the bottom of what happened between Hajime and Kaori in the past.
Also, if we look at the dates of release on the Wikipedia page, Volume 6 didn't come out until the time the anime was already airing. Volume 5 came out around the time the anime started airing, so assuming the anime production took about six months, the material in Volume 5 was probably the most recent the animators would have had access to when they were creating the series.
Based on all of this, my educated guess is that Episodes 11 and 12 contained anime-original material, but were based on material from the manga wherever possible. Episode 12 just wrapped up too neatly to think otherwise, while also avoiding a conclusive ending and leaving things open for a second season to finish the manga plotline. Notably,
Kaori and Yuki are still just friends when the anime concludes, and Kaori still loses her memories every week, though she's fought her way back to remembering tidbits about Yuki.
So if you want to cut in to the manga without repeating material, I would start at Volume 5. According to the MangaFox page, the manga has been licensed (though I can't find any info on which company has it), so we might be seeing an official English release soon.