Conventional forward models advance a physical state under a specified action. In real-world physical systems under operation, however, the true state is rarely observable: important fields and internal variables are only partially observed, and stochasticity drives the system away from its nominal description. Prediction of such systems thus requires a model that infers a "belief distribution" over plausible physical states, given what has been observed and what is enacted; propagates that belief under a proposed action; and represents the resulting uncertainty. This construction supports inverse control by allowing alternative actions to be evaluated through their predicted consequences. Moreover, direct optimization through a fixed-horizon rollout – "backpropagation through imagination" – can identify a course of action that maximizes a desired objective. We introduce Leviathan, a world model [Ha and Schmidhuber, 2018] that factorizes these tasks. A belief transformer summarizes the preceding observations into a belief state. Rectified flow models [Liu et al., 2023], conditioned on this belief and a given action, generate distributions over possible observations. We demonstrate the framework on laser powder bed fusion using the Peregrine dataset [Scime et al., 2023]: 67 builds containing visible imagery, three-channel near-infrared measurements, anomaly masks, and scan programs. Each modality is represented at its natural spatial resolution, and the preceding 16 layers are used to predict observations at the next layer. Leviathan reduces next-layer prediction error by up to approximately 40% compared to persistence, with the largest improvements in near-infrared channels. Predicted spread correlates with realized error, and the model supports closed-loop multi-layer rollouts. Its spatial conditioning also reproduces a localized near-infrared signature associated with an overlapping scan path, evidence that the model links the prescribed action to its predicted consequence, a common failure mode in similar AI approaches. Backpropagation through imagination is demonstrated on the CartPole benchmark problem [Barto et al., 1983], and its extension to risk-aware scan control is discussed.