Rolling Sink: Bridging Limited-Horizon Training and Open-Ended Testing in Autoregressive Video Diffusion

Autoregressive (AR) video diffusion models in the Self Forcing family generate a video chunk by chunk, each conditioned on the ones before it, so they can keep rolling out with no preset length. In practice they are trained on short, fixed clips ($\text{e.g.}$, 5s). Once a rollout passes this training horizon, the cache fills with self-generated chunks the model never saw in training, and quality degrades: colors oversaturate, identities drift, structures collapse, and motion fades. We frame this failure as a $\text{cache-behavior mismatch}$, a domain shift between the within-horizon caches seen in training and those produced by open-ended testing, and address it with $\text{Rolling Sink}$, a training-free inference-time cache policy. Within the base model's fixed cache budget, Rolling Sink holds the cache close to its stable within-horizon behavior: it restores low-drift content, sliding temporal indices, and evolving semantics, and keeps a small recent context. Attention sink and temporal re-indexing are existing mechanisms. Our contribution is the mismatch formulation, the joint bounded-cache policy, and the Rolling Semantics schedule. On two 5s-trained bases, Self Forcing and Causal Forcing, Rolling Sink attains the best averaged rank on $\text{VBench-Long}$ at both 1- and 5-minute rollouts under the same inference setting, at about 0.56% throughput change, and holds GPU memory constant. It also sustains a 30-minute qualitative rollout, $360\times$ its training horizon. We validate at 1- and 5-minute rollouts and do not claim guaranteed quality at arbitrary duration.