What type of injection/ignition system do you have? What year?

My first impulse is to think it's improper valve timing - caused by the timing belt being a tooth or two off on the cam gear (or the cam gear being a tooth or two off the alignment of the other rotating parts).

I think that the only way a backfire can come out the intake is for the intake valves to be open when the spark goes off, but I think that it can happen otherwise under the right conditions.

A bit more info will help us guess at the problem.

Good Luck