FIRM-WM: State-factorized factual-interventional recurrent modeling for reward-free visual planning

Reward-free latent world models can learn from offline videos and solve new image--goal tasks by optimizing actions through predicted latent futures. This setting places two demands on the planning state: its coordinates must be comparable with a goal image. Moreover, its dynamics must retain velocity, motion trend, contact, and other history--dependent information beyond those goal coordinates. Offline training creates a second mismatch: each recorded trajectory reveals one factual future, whereas a sampling--based planner compares many actions that were not taken from the same state. We introduce FIRM-WM (Factual--Interventional Recurrent World Model), a compact pixel world model designed around these two gaps. Its recurrent state separates a typed, goal--comparable configuration from a 128-dimensional dynamic fiber used for prediction but excluded from the terminal goal cost. Broad factual trajectories provide state coverage, while common--reset intervention branches provide observed outcomes for alternative action sequences. Before executing each branch, we reset the environment and restore the same recorded values exposed by the environment's state--setting interface. Under matched CEM planning and three independent full-pipeline seeds, FIRM-WM reaches 99.0±1.0% on TwoRoom, 92.7±2.1% on Reacher, and 88.0±3.0% on OGBench-Cube, compared with 89.0%, 88.0%, and 70.0% for LeWM. The deployed model uses 2.98--3.42M parameters and records 2.13--11.60× lower planning time on these tasks.