Replacing parts of a Matrix with lists

ReplacePart[{{1, 0}, {0, 1}}, Thread[{{1, 1}, {1, 2}} -> {13, 14}]]

so

ReplacePart[m, Thread[li -> lr]]

in general.

But a CompiledFunction will probably do the job quicker because Thread[li -> lr] unpacks arrays. Let's see.

cReplacePart = 
  Compile[{{A0, _Real, 2}, {pos, _Integer, 2}, {val, _Real, 1}},
   Block[{A = A0},
    If[
      1 <= Max[pos[[All, 1]]] <= Dimensions[A0][[1]] && 
      1 <= Max[pos[[All, 2]]] <= Dimensions[A0][[2]],
     Do[
      A[[Compile`GetElement[pos, i, 1], 
        Compile`GetElement[pos, i, 2]]] = Compile`GetElement[val, i],
      {i, 1, Min[Length[pos], Length[val]]}
      ]
     ];
    A
    ],
   CompilationTarget -> "C",
   RuntimeOptions -> "Speed"
   ];

And indeed, it's 100 times as fast:

n = 1000;
m = 1000000;
A = RandomReal[{-1, 1}, {n, n}];
li = RandomInteger[{1, n}, {m, 2}];
lr = RandomReal[{-1, 1}, m];

B = ReplacePart[A, Thread[li -> lr]]; // AbsoluteTiming // First
cB = cReplacePart[A, li, lr]; // AbsoluteTiming // First
Max[Abs[B - cB]]

4.91402

0.047307

0.

One may also use SparseArray; this is only a tiny bit slower than the compiled approach:

spB = A SparseArray[li -> 0., Dimensions[A], 1.] + 
     SparseArray[Reverse@li -> Reverse@lr, Dimensions[A], 0.]; // 
  AbsoluteTiming // First
Max[Abs[B - spB]]

0.086657

0.

ReplacePart has a undocumented four variables form that permits this :

oldValuesList = {{1, 0}, {0, 1}}
newValuesList = {13, 14}
modifiedPositionsList = {{1, 1}, {1, 2}}
newValuesPositions = (* gives the origin of the new data *)
 List /@ Range[Length[newValuesList]] (* simply {{1},{2}} *)

ReplacePart[oldValuesList
 , newValuesList
 , modifiedPositionsList
 , newValuesPositions]   

{{13, 14}, {0, 1}}

I have retrieved this information in Michael Trott' s book "Mathematica Guidebook for Programming" page 628.

According to this It was documented until Version 5.2.

EDIT

ReplacePart is known to be often not memory/speed optimal. It may be slow and memory consuming with large data sets.

Henrik Schumacher's comments below confirm this in this particular case.