Implicit Worldline Constraint Models: Joint Trajectory Energy Optimization Without Autoregressive Rollout

Learned world models based on autoregressive rollout suffer from compounding prediction errors that accumulate over long planning horizons. This paper introduces Implicit Worldline Constraint Models (IWCM), a constraint-based world modeling framework that represents future trajectories through joint optimization problems over latent worldlines rather than sequential predictions. Instead of generating states autoregressively, IWCM learns a differentiable energy function over complete trajectories and performs planning through gradient-based constraint satisfaction. The paper presents experiments on synthetic grid-world environments and continuous-control tasks from DM Control, including comparisons with autoregressive rollout baselines, initialization ablations, recovery from degraded rollouts, and a self-supervised pixel pipeline (TAMG) that replaces oracle state representations with learned object-centric slot representations. Code, training pipelines, and reproduction scripts are provided to facilitate reproducibility.