Place one of the two diagonals of each cell into each cell, such that there are no closed loops formed by the diagonals. Numbers represent the number of diagonals pointing into a vertex.
We can almost immediately place the diagonals in the cells in the bottom row, as the 2s on the bottom both only have two cells adjacent to them. Similarly, the diagonal in the top right corner can also be placed quickly.
To have exactly 0 diagonals pointing into a vertex, the top left cell must contain a minor diagonal, or else the 0 clue would have a diagonal pointing into it. Similarly, the cells at R3C2 and R3C3 can also be filled in this way, then the cells at R2C2 and R2C3.
Now we can complete the rest of the clues using the above two strategies. This leaves only R1C3 left. To avoid a closed loop, it must contain a minor diagonal.
This puzzle genre is also known by the names of "Gokigen Naname" and "Slalom". It is not to be confused with the other genre named Slalom.