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(1) You will be faced with the problem.
(2) You will face the problem.

Are they both natural? If so, what exactly is the difference between the two? 
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They're both natural. The question is, do you face the problem or does the problem face you? Some have recently argued that if I'm facing you then you're facing me. Obviously, it's not true literally. But is it true figuratively, as in your two examples? I would say no.

A problem may be coming toward you in the figurative sense (i.e.the problem is facing you / you're faced with the problem), but you may be unaware of it, or deliberately ignoring it. So in the figurative sense, you're looking the other way.

- A.
Comments  
Students: Are you brave enough to let our tutors analyse your pronunciation?
I would say that 'facing' a problem includes attempting to deal with it/ attack it.

Being faced with does not necessarily mean you are doing anything about it, as A explained.
Old Man GordonI would say that 'facing' a problem includes attempting to deal with it/ attack it.
Being faced with does not necessarily mean you are doing anything about it, as A explained.
That's exactly how I see the difference!
Thank you both!