I think you can use advanced indexing for this:
C, H, W = 3, 4, 4
x = torch.arange(C*H*W).view(C, H, W)
print(x)
idx = torch.tensor([[0, 0],
                    [1, 1],
                    [2, 2],
                    [3, 3]])

print(x[list((torch.arange(x.size(0)), *idx.chunk(2, 1)))])