The graph shows forward voltage for a 300 uS pulse, not a continuous current, so currents well above 1 amp are allowed. See the nearby graph for the "Non-repetitive Surge Current"; currents up to 30 amps are allowed.
Looking at the Absolute Maximum Ratings, you will note that the 1 Amp rating is with .375" lead length. They expect you to solder the leads to some kind of heat sink, such as a relatively large area of copper foil on the PCB, with only .375" of lead between the diode body and the solder joint, and an ambient temperature (the temp of the foil to which the diode is soldered) of no more than 75 degrees C. Under those conditions, the diode can sustain 1 amp average forward current indefinitely.
Also, you said in your first post, "...in the graph, VF = 1.1V @ IF = 2A".
Look at the graph again; it indicates a VF of 1.1V @ IF = 4A.
Crutschow's comment is relevant. The manufacturer didn't indicate which values are typical and which are max or min, so you'll have to draw your own conclusions, but the larger value may well be a maximum.