It depends on what type of a diode you mean.
In most cases (rectifier, Zener, etc.) a diode is, no doubt, a PASSIVE device. Only in some special cases like with a tunnel diode, when its negative resistance region is used, it can be considered as an ACTIVE device.
Best Regards
Eric
Note:
"an activity" vs. "a passivity" of a device is exactly defined although the exact math evidence for a concrete device is not so easy. E.g. the activity of a linear N-port is determined by some particular properties of its immitance matrix (immitance = either impedance or admitance; so immitance matrices are Y, Z, H or G)
see also: Guillemin, E.A., Synthesis of Passive Networks, John Wiley & Sons, 1957
Very simplified:
passive devices only dissipate a power from an external source,
active devices have an ability of amplifying a signal at one port of the device and deliver it to another port of it, where a load is connected, ie. they have some power gain > 1 (power itself is taken from a power supply, of course)
Eric