Verified answer

The wings are creating lift upwards and with no pilot to correct it, it stalls and happens all over again.

It's hard to make a perfect paper plane. And on top of that, you have to give the right amount of force for a perfect paper plane to fly straight until stalling. It curves up and down because of either imperfections or too much or too little lift. It would curve from side to side for imperfections. And factors like wind effect both. I hope that's what you meant by curve.

you build the aircraft with inbuilt control inputs... one way or another.

then it's all about trading the altitude for speed and vice versa. the paperplane will be flying in the so called second regime, unstable flight under its "economic" speed. in this part of flight envelope, the decreasing speed creates a requirement for even MORE thrust.. or dive, in sail planes. so, without pilot input the speed continues its decrease until the nose drops at the stall speed. the nose drop acts as a pilot input of some sort, and sailplane trades off altitude for speed. as the higher speed is reached, the ballance of the plane will eventually raise the nose again, as it is built as "tail heavy", in most cases.