Once had a snubber diode application. Very brief transient, 100ns range, but with some 200A+ behind it. Duty cycle very low, <1%. Tried a 6A diode: failed. Didn't get hot. Ran for at least a few cycles. But not forever.
Hmm.
Tried a 12A diode. Ran for a few minutes, then same story. Hmm.
Tried a 30A diode. Ran just fine.
What's going on? Best guess, electromigration. It's probably not a thermal failure mode: even with the transient applied voltage being ~50V (yes, a real +50V across the diode junction, in the forward direction -- forward recovery is very much a real thing), the peak power isn't extraordinary, and at those currents, internal resistance ensures even current sharing -- this is well outside the range of thermal hot spots.
What's in an I_fsm rating?
Several things: thermal limits, bond wire ampacity, die ratings, electromigration -- whatever the worst of each of these contributes.
For a typical 8.3 or 10ms "half sine" pulse, the limit is mostly thermal, and the thermal time constant lies between the die itself (~100s us) and the heatsink pad (~10s ms). It does not involve much from the package, leads or external heatsinking (~seconds).
Where the limit is thermal, one expects the peak current to scale roughly as sqrt(t). Or, more precisely, as the applied waveform, combined with the V(I) curve, combined with the transient thermal impedance curve.
For a short duration pulse (usually around 1-10us square), the limit is largely device physics, and the maximum peak current levels off.
For extremely short pulses, capacitance dominates, I suppose; you might not get anything from the junction, anyway (in the 10ns range, a power PN junction diode will barely begin to conduct, even at fairly high applied voltages). Lead inductance limits dI/dt in this range, anyway.
For 1.5kA, I would expect needing, well, about a half dozen beefy diodes in parallel -- or a module or puck type diode.
Otherwise, you might try to reduce the peak current. (Ask me how I solved my snubber problem...)
Tim