I grew Passiflora edulis from seed a few years back. As far as I remember, I just saved some seed from a fruit, washed it, sowed it in multipurpose compost and put it in a heated propagator. This might not be the quickest method but it worked.

I've grown some P. Alata from seed just a few weeks ago. They were of the Thompson and Morgan / Eden Project range. I took 7 of the 15 seeds provided, and soaked them overnight in what started as warm water, but I didn't try to keep it warm.

All the water does is start soaking through the hard seed coat to get water to the embryo seed inside. Another method is to carefully chip off some of the seed coat with a knife, but this can be tricky, and those alata seeds were damn tough!

Then, I just sowed them in a mix of 20% vermiculite to 80% peat-based compost, with a scattering of vermiculite on top.

It said expect 1 to 6 months germination, but I had 2 within a week, and about 2 months later (now), have 5 of them in desperate need of repotting since they're now about 8 inches high already!