How to check which process(es) wrote the last x GB on a filesystem without explicit setup? / Cumulated command I/O statistics

It would be great to find a solution where no explicit and resource consuming setup is necessary (e.g. like inotify requires). My use case is a problem where I'm running out of disk space because of a number of processes which seems to write small amounts of data to disk in a lot of constantly newly spawned instances (i.e. iotop doesn't help because it restarts monitoring when the process terminates).

In this situation I'd like to be able to query statistics for a command regardless of the process instances which have been created, e.g. when I started the OS I had 10 GB left, now there's only 1 GB left, so show me which process consumed how much from that last 9 GB.

It's possible to retrieve that information for certain programs, e.g. it'd be possible to check how much has been used by the latest dpkg installations and removals. I'm searching for a generic way which I can set up for a certain filesystem.