Keep other columns when doing groupby

Method #1: use idxmin() to get the indices of the elements of minimum diff, and then select those:

>>> df.loc[df.groupby("item")["diff"].idxmin()]
   item  diff  otherstuff
1     1     1           2
6     2    -6           2
7     3     0           0

[3 rows x 3 columns]

Method #2: sort by diff, and then take the first element in each item group:

>>> df.sort_values("diff").groupby("item", as_index=False).first()
   item  diff  otherstuff
0     1     1           2
1     2    -6           2
2     3     0           0

[3 rows x 3 columns]

Note that the resulting indices are different even though the row content is the same.

You can use DataFrame.sort_values with DataFrame.drop_duplicates:

df = df.sort_values(by='diff').drop_duplicates(subset='item')
print (df)
   item  diff  otherstuff
6     2    -6           2
7     3     0           0
1     1     1           2

If possible multiple minimal values per groups and want all min rows use boolean indexing with transform for minimal values per groups:

print (df)
   item  diff  otherstuff
0     1     2           1
1     1     1           2 <-multiple min
2     1     1           7 <-multiple min
3     2    -1           0
4     2     1           3
5     2     4           9
6     2    -6           2
7     3     0           0
8     3     2           9

print (df.groupby("item")["diff"].transform('min'))
0    1
1    1
2    1
3   -6
4   -6
5   -6
6   -6
7    0
8    0
Name: diff, dtype: int64

df = df[df.groupby("item")["diff"].transform('min') == df['diff']]
print (df)
   item  diff  otherstuff
1     1     1           2
2     1     1           7
6     2    -6           2
7     3     0           0