Per theVerilog-AMS LRM, diode (as well as jfet, mosfet, bjt) require the use of a .model card in most Spice simulators, and thus you can't instantiate them directly.  Resistor and capacitor are allowed, not because they are Spectre primitives, but because the LRM says that these Spice primitives shall be recognized by the Verilog-AMS simulator.

I don't know how you get a model card into your circuit.  It's outside the LRM, in terms of how you direct your particular simulator to read spice/spectre library files.

Can you make up your own models?  Eg, look at how the technology-specific models are added in and add a pointer to a local file that defines your own model.

In Spectre format, something like:
model mydio diode
is probably sufficient; you can add is, cjo, etc. when you're ready.

Doing spectre -h components will give you all the list of available built in models.
Doing say spectre -h diode will give you all the default parmaters for a diode. you can do the same on the other components.

In spectre you can just add a blank model file, and it'll pick up the default values.
so you could create mydiodemodels.scs which is uses default values with:

model modelName diode

cheers
aw