Based on what you say your issue is really falling forward as you come up. A video would be helpful, btw. There may be stuff going on you haven't described contributing to your squat issues.
One fairly simple way to stop falling forward is to stick your chest up throughout the squat. Head driven into the bar, traps into the bar etc mean the same thing basically, they get you keeping your torso more upright. What do you do with your elbows? Do you pull them into your sides or do you shoot them out backwards? If you shoot them backwards, that will definitely pitch you forward. Do you initiate the squat by shooting your butt back or straight down? If you shoot backwards, try going straight down instead as that often can help you stay more upright.
If you're already using those cues and it still happens, then for my money the issue may be that you're not getting tight enough. How well do you brace yourself when you squat? Do you get big air into your belly and back and squeeze down on it? Do you drop so fast you can't stay tight?
If you're both keeping your chest up and getting tight and you still fall forward, then I would suspect your back is weak. That's an easy fix: lots of rows, pull ups if you can do them without messing your elbows up, ideally squatting with the safety squat bar for a while, good mornings and front squats. Also deadlifts. Speaking of which, how is your deadlift? If you find you're deadlifting less than you squat I'd take that as a pretty strong indicator that your back isn't strong enough. If your deadlift is higher than your squat then probably the back isn't the whole problem, but is still going to benefit from some extra work.
Also worth looking at is how wide your stance is and where the bar sits. I've found that if you have a higher bar position but naturally tend to squat with a fairly large degree of torso lean you're going to get pulled forward, so sitting the bar lower can be a big help. On the other hand, if you squat with a very upright torso, a higher bar position may work better.
Without a video I can't really tell you much about your specific case. Hopefully some of the above strikes a chord and helps you out.