How is dynamic resistance of a diode modeled for large voltage variations?

The concept of dynamic resistance is a derivative:

\$ r = \frac{dv}{di} \$

As such, it only applies to variations of current and voltage that are small enough to allow us to neglect the non-linearity and use a linear model for the diode.

But if the voltage across the diode varies a lot like in a AC to DC rectifying diode,

In this case, a linear model can't be used to model the diode's behavior over the whole waveform, and the concept of "dynamic resistance" which is a part of this linear model does not exist, so you'll have to use the diode equation.

If you only look at a specific point in time on the waveform, then you can calculate dynamic resistance at this point, depending on the value of the current at this point.

You can model the DC I-V characteristics with the Shockley diode equation over a fairly wide range of currents, especially if you include an accurate ideality factor and some series resistance. It's nonlinear but still very simple and easy to solve numerically.

The diode model used in SPICE has more than a dozen parameters.

Yes, for slow enough changes in bias, a diode can be modeled as a nonlinear resistor. For faster changes you must also consider the diode's capacitance, which is also bias-dependent.

Simplifying a lot, the simulator has to keep updating the value for the dynamic resistance as the simulation evolves.