If the diodes are all matched Vout should look like Vin because all diodes are conducting and are fwd biased DC wise.
for e.g. if you take the D3 and D4 path, Sine wave coming in will get DC level shifted down by D3 and DC level shifted up by D4. if you take the D1 and D2 path, the sine wave will get DC level shifted up by D1 and down by D2.