Parallelization limits of commitment in generative rollouts

Determine how far commitment can be parallelized in generative rollout schedules while preserving exact continuation accuracy, particularly across dynamics for which committing several frames per call may either maintain or reduce accuracy.

Background

The paper studies causal freezing, in which predicted frames are generated and settled sequentially before later frames use them, as a remedy for temporal-instability failures in diffusion-based cellular-automaton rollouts. In the plain denoiser experiments, committing several frames per call preserved accuracy for the Game of Life but reduced accuracy for free billiards, indicating that the appropriate degree of sequential commitment may depend on the underlying dynamics.

The unresolved issue is to characterize the maximum safe degree of parallel commitment: whether multiple future frames can be generated simultaneously without sacrificing exact rollout fidelity, and how this limit varies with the dependency structure of the dynamics. The authors explicitly leave this issue unresolved rather than establishing a universal one-frame-at-a-time or parallel-generation rule.