In a circuit connected to a DC voltage source, the current direction is from the positive terminal to the negative terminal of the source; therefore, Kirchhoff Current Law requires that the current in the voltage source flows from its negative terminal to its positive terminal. Your simulation measures the current SRC1 through the source (equal to a minus current through the diode according to KCL) against the voltage VCC across the swept source, so the current values are negative in the positive voltage range of your simulation plot.
For your simulation, you selected the Schottky diode (HSMS2850). The "knee" voltage of Schottky diodes is around 0.2 - 0.4 V, you can see it in your graph. For silicon diodes (like 1N400X), the "knee" voltage is about 0.6-0.7 V.