Create instance of implementation of generic class based on type of Class

I have the following class layout:

abstract class GenericClass<TArgs> where TArgs : ArgsBaseClass { }
abstract class ArgsBaseClass { }

class RandomArgs : ArgsBaseClass { }
class RandomClass : GenericClass<RandomArgs> { }

Now I want to be able to create an instance of RandomClass from an instance of RandomArgs, without knowing that it should be RandomClass. I.e. somehow I need to derive the fact that RandomClass implements GenericClass<RandomArgs>.

I'm able to create an instance of GenericClass<RandomArgs> using:

void CreateSpecificInstance(ArgsBaseClass args)
{
    Type genericType = typeof(GenericClass<>).MakeGenericType(typeof(args));
    var genericInstance = Activator.CreateInstance(genericType, typeof(args));
    // But then I need help for the following step:
    Type specificType = ...  // in this case RandomClass, but should be derived from 'args'.
    var specificInstance = (specificType)genericInstance;
}

Any help is appreciated.