I've noticed that when I play runs across and down the fretboard that I tend to pull off as a travel across each string, so I end up with alot of open string noise.

how do you guys recommend I got about correcting this?

If you don't know what I mean, it's mostly licks like this (from Over The Mountain by Ozzy)



I have trouble with string noise, unless I palm mute it, but that's limiting.
I'm mainly concerned with the beginning of the first riff, that's the one I get the most noise out of

I guess this is similar to deadening the previous strings when sweeping
And we will weave in and out of sanity unnoticed
Swirling in blissfully restless visions of all our bleary progress
Glowing in radiant madness
it looks like you already identified the problem, which is you pulling off the strings.

practice this SLOWLY, and by slow, i mean as slow as 30 bpm, or even lower if that's what it takes for you to be doing it correctly. Once you have COMPLETE control of what's happening, you can start working in a good habit to avoid accidentally pulling off. Once you get it down, you can bump up the speed a few bpm, repeat process until desired speed is reached.
Your picking hand should be muting all strings above where you are playing, and your fretting hand should be muting everything below where you are playing. It sounds to me like your picking hand isn't doing its job.

Practice playing regular scales staccato - there should be zero noise from anything but the string you are playing.
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