When Generative Models Act as Simulators

A simulator summarizes an environment in a state that users can read and change. Generative models learn representations of the world without explicit specification, but offer no built-in way to edit that world's state. We investigate the conditions under which a generative model can act as a simulator through $\text{editability}$: whether changing a model's latent representation produces the next-step outputs we get by editing a simulator's state. Plainly stated, our goal is to find a mapping between a generative model's latent state and the simulator state, where the model is trained on observations alone and the mapping is learned afterward. We test two kinds of mappings, both learned from observations paired with simulator states. In one, we train probes to decode the simulator state from the model, then steer along them. In the other, we learn the mapping directly with an inverse map, which can succeed even where steering fails. We study both in two contrasting environments: the discrete board game Othello, and Rayworld, our own continuous world of moving discs seen through partial renderings, closer to physical scenes and video. We find that which mapping succeeds depends strongly on the environment, even though the state is decodable in every variant. In Othello, editability falls smoothly as the game is simplified, and even small rule changes have large consequences. In Rayworld, probes fail to steer along the simulator's continuous state, yet an inverse map sets the model from that state anyway. A model can therefore be driven by a simulator it may have never learned.