Because of the slow IGBT turn off, the idea is to have the current briefly flow through something else, almost always a capacitor.
Because of the whole circuit's symmetry, it's only necessary to take notice of the top half sometimes.
For the top group of capacitors to start passing current through the bottom RH diode at the instant that the top IGBTs start turning off, the capacitors have to be already charged to almost full HVDC, negative on their the top terminals.
This charge is established shortly after the IGBTs are turned on, assuming zero initial charge voltage.
At the instant the IGBTs turn on, full HVDC is applied across the inductor which then does a half cycle of resonance with the capacitors, terminated by the top RH diode.
The 1K resistors and 220pF would be to damp the self resonance of the inductor after it has transferred all of its energy to the capacitors and left open circuited by the diode.
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Added: To help visualizes the circuit operation, imagine that the inductor has a center tap that is tied to half HVDC. And another series diode at the bottom end of the inductor.
Yes, it is a two switch forward converter.