It does sound DPF related. Problem is, as I learnt through experience, DPF faults are a nightmare and you just end up chasing ghosts swapping out parts until its resolved.
DPF issues can also be symptoms of another issue like injectors etc
A DPF regen should produce a little bit of smoke, certainly not a huge cloud! Most drivers wouldn't even notice the puff of smoke from the end of a DPF regen, nevermind seeing it several times and thinking their car was broken.