Stochastic Collapse: Video World Models Fail to Reproduce Outcome Frequencies

We repeatedly prompt video generation models marketed as ``world simulators'' to generate videos of rolling a fair die, and record the outcomes. The result: they almost never produce 1, 2, or 3. We term this failure mode \textbf{Stochastic Collapse}, in which a video model's large-sample outcome frequencies systematically deviate from the governing theoretical distribution, collapsing onto the visually most prevalent appearance of the object in question. In short, the model produces what a die \emph{looks like}, not what a die \emph{does}. We evaluate eight video generators across three canonical stochastic processes with closed-form theoretical distributions (coin flip, die roll, urn draw). Unlike prior video-physics benchmarks that judge whether a single clip is plausible, we ask whether the aggregate outcome frequencies match a mathematically exact reference. Because the reference is a theorem rather than any empirical dataset, the comparison is inherently dimensionless and requires no scene calibration, reference videos, or human judgment. We find that Stochastic Stochastic Collapse is pervasive: every tested model exhibits statistically significant distributional deviation. We attribute this failure to the models aligning with the visual frequency statistics of their training corpora rather than with the physical frequency statistics of the underlying processes. This finding provides empirical evidence against the prevailing assumption that visual fidelity implies physical understanding and, by extension, suitability as a world model.