Fork-Ready World Models: Training Distilled World Models to Be Branchable

Tree-structured imagination relies on continuations sampled from a shared prefix, but a shared noisy cache can correlate those continuations and reduce the benefit of best-of-$k$ selection. We characterize this effect in a linear-Gaussian model and measure it in a $1.4$B distilled autoregressive video model built on Self-Forcing and Wan2.1. The shipped clean-cache recipe has zero cache-noise variance in our protocol, whereas increasing cache noise reduces the measured variance ratio from $1.0$ to $0.25$. We introduce Fork-Invariance, a training objective that compares noised-cache rollouts with clean-cache references using a shared sampling tape. Its strongest variance-ratio result ($0.964$) is misleading: full-weight training damages decoded video and reduces sensitivity to the prefix. Capping the objective's gradient norm at $0.2$ of the distillation gradient instead yields a variance ratio of $0.888$, retains prefix sensitivity, and shows no detected quality degradation under two frozen visual judges. At matched measured variance ratio, the retained best-of-$k$ search gain increases from $52\%$ to $84\%$. These results distinguish cache-noise suppression from preservation of useful conditioning and motivate evaluating branch groups through variance, selection performance, decoded quality, and prefix sensitivity together. The gradient-matched result uses one training run, and judge scores alone do not establish perceptual equivalence.