I only just got around to reading this closely. Good post, very well structured, thank you for writing it.

I agree with your translation from simulators to predictive processing ontology, and I think you identified most of the key differences. I didn't know about active inference and predictive processing when I wrote Simulators, but since then I've merged them in my map.

This correspondence/expansion is very interesting to me. I claim that an impressive amount of the history of the unfolding of biological and artificial intelligence can be retrodicted (and could plausibly have been predicted) from two principles:

• Predictive models serve as generative models (simulators) merely by iteratively sampling from the model's predictions and updating the model as if the sampled outcome had been observed. I've taken to calling this the progenesis principle (portmanteau of "prognosis" and "genesis"), because I could not find an existing name for it even though it seems very fundamental.
  • Corollary: A simulator is extremely useful, as it unlocks imagination, memory, action, and planning, which are essential ingredients of higher cognition and bootstrapping.
• Self-supervised learning of predictive models is natural and easy because training data is abundant and prediction error loss is mechanistically simple. The book Surfing Uncertainty used the term innocent in the sense of ecologically feasible. Self-supervised learning is likewise and for similar reasons an innocent way to build AI - so much so that it might be done on accident initially.

Together, these suggest that self-supervised predictors/simulators are a convergent method of bootstrapping intelligence, as it yields tremendous and accumulating returns while requiring minimal intelligent design. Indeed, human intelligence seems largely self-supervised simulator-y, and the first very general and intelligent-seeming AIs we've manifested are self-supervised simulators.

A third principle that bridges simulators to active inference allows the history of biological intelligence to be more completely retrodicted and may predict the future of artificial intelligence:

• An embedded generative model can minimize predictive loss both by updating the model (perception) to match observations or "updating" the world so that it generates observations that match the model (action).

The latter becomes possible if some of the predictions/simulations produced by the model make it act and therefore entrain the world. An embedded model has more degrees of freedom to minimize error: some route through changes to its internal machinery, others through the impact of its generative activity on the world. A model trained on embedded self-supervised data naturally learns a model correlating its own activity with future observations. Thus an innocent implementation of an embedded agent falls out: the model can reduce prediction error by simulating (in a way that entrains action) what it would have done conditional on minimizing prediction error. (More sophisticated responses that involve planning and forming hierarchical subgoals also fall out of this premise, with a nice fractal structure, which is suggestive of a short program.)

The embedded/active predictor is distinguished from the non-embedded/passive predictor in that generation and its consequences are part of the former's model thanks to embedded training, leading to predict-o-matic-like shenanigans where the error minimization incentive causes the system to cause the world to surprise it less, whereas non-embedded predictors are consequence-blind. 

In the active inference framework, error minimization with continuity between perception and action is supposed to singlehandedly account for all intelligent and agentic action. Unlike traditional RL, there is no separate reward model; all goal-directed behavior is downstream of the model's predictive prior.

This is where I am somewhat more confused. Active inference models who behave in self-interest or any coherently goal-directed way must have something like an optimism bias, which causes them to predict and act out optimistic futures (I assume this is what you meant by "fixed priors") so as to minimize surprise. I'm not sure where this bias "comes from" or is implemented in animals, except that it will obviously be selected for. 

If you take a simulator without a fixed bias or one with an induced bias (like an RLHFed model), and embed it and proceed with self-supervised prediction error minimization, it will presumably also come to act agentically to make the world more predictable, but the optimization that results will probably be pointed in a pretty different direction than that imposed by animals and humans. But this suggests an approach to aligning embedded simulator-like models: Induce an optimism bias such that the model believes everything will turn out fine (according to our true values), close the active inference loop, and the rest will more or less take care of itself. To do this still requires solving the full alignment problem, but its constraints and peculiar nondualistic form may inspire some insight as to possible implementations and decompositions.

Predictors are (with a sampling loop) simulators! That's the secret of mind