you can use pandas.Series.diff
>>> df['Diff'] = df.index.to_series().diff()
value Diff
Date
2015-05-04 1 NaT
2015-05-06 1 2 days
2015-05-07 1 1 days
2015-05-11 1 4 days
2015-05-11 1 0 days
elegant way to convert to float is
df['Diff'] = df.index.to_series().diff().dt.days
>>df
value Diff
Date
2015-05-04 1 NaN
2015-05-06 1 2.0
2015-05-07 1 1.0
2015-05-11 1 4.0
2015-05-11 1 0.0
more faster way is to typecast to days
df.index.to_series().diff().astype('timedelta64[D]')
to convert to Integer (pandas verson >= 0.24)
df.index.to_series().diff().astype('timedelta64[D]').astype('Int64')
>>df
value Diff
Date
2015-05-04 1 NaN
2015-05-06 1 2
2015-05-07 1 1
2015-05-11 1 4
2015-05-11 1 0
Note : Int64 is Pandas Nullable Integer Data Type (not int64)