Matlab, 100 bytes

I just tried my best to shorten my code in Matlab, like telegraphing it.

[m,n]=size(M); a=ones(n,1)*(1:m); A=a'+a-1;B=a'-a; C=A.^2+(-1).^A.*B+1; [~,I]=sort(C(:)); V=M(:);V=V(I)'; 

Notes:

1. M is an m×n matrix.
2. a is a matrix same size of M, each row consists of numbers equal to row number. Thus, a+a'(transpose of a) is a matrix whose element equals to sum of row and column number, i.e., matrix(p,q)=p+q.
3. Thus, A(p,q)=p+q-1; and B(p,q)=p-q.
4. C is mathematically stated as equation below. with the equation, a zigzagifiedly increasing matrix can be made like shown below.

C = 1 2 6 7 3 5 8 14 4 9 13 18 10 12 19 25 

5. C indicates the order of elements of M in zigzagified results. Then, [~,I]=sort(C(:));returns the order, i.e., I, thus, V=V(I)' is the result.