Unflatten an Array
JavaScript, ES6, 44 bytes
f=(a,b,i=0)=>a.map(x=>x.map?f(x,b,i):b[i++])
This creates a function f which can be called like
f([0,[1,[]],[[]],[2,3],[]],[1,6,1,8])
i.e. the nested array and the values array as input arguments. The output of the function is the converted nested array.
This question is a very nice question for recursion, that is why the answer is a neat and sweet recursion function. I create a function f which converts the first argument using the map method. For each element, if the element is an array, it calls f again, otherwise, for integers, it gets the ith item and returns that, incrementing the value of i. The value of i is passed down in each recursive call, so as to maintain the order correct.
Array vs. Integer detection is yet again done using the map method. For an array variable, map is a valid function, while for integer variables, there is no property or function called map defined for the variable.
This works in a latest Firefox browser (due to ES6).
JavaScript, ES6, 41 bytes
I was really impressed by Optimizer's answer, it was very cleverly done and I learned a lot. However on looking it over I found a way of shortening it slightly and fixing a small bug:
f=(a,b)=>a.map(x=>x.map?f(x,b):b.shift())
I took out the i variable and replaced it with a shift(). This makes it slightly shorter and fixes the problem with the fact that i is passed by value and not by reference, witch caused some numbers from the final array to repeat and some at the end not to be used.
Again, Optimizer's answer was really well thought out, better than I could have done, I just fixed it a little.
Dyalog APL, 14 characters
This is a no-brainer: (∊a)←b.
Normally, ∊a means a flattened, but when it occurs on the left-hand side of an assignment, it does precisely what this problem is asking for. To comply with the requirement of being a function, it needs a few extra squiggles: {a←⍺⋄(∊a)←⍵⋄a} (curly braces for lambda; ⍺ and ⍵ for left and right argument; ⋄ for statement separator).
Test on tryapl.org. Note that in APL the empty numeric vector is denoted by ⍬ ("zilde"). One-element vectors are constructed with (,A) because (A) would mean a scalar. In the output, this thing:
┌⊖┐
│0│
└~┘
represents an empty numeric vector. The 0 in the centre shows the "prototypical element" which is not an element of the array.