Abstract: Autoregressive (AR) video diffusion models generate streaming video of arbitrary length by conditioning each new chunk of frames on those already generated. However, they suffer from exposure bias, where a model trained on clean context must continue from its own imperfect outputs, and errors compound until quality collapses within seconds (drift). Existing methods either require cluster-scale base retraining, apply training-free inference corrections with inconsistent results, or train frozen-base correctors for sampling and cache errors. We instead find that drift is largely deterministic and therefore learnable, as holding the noisy state fixed while varying only the history reveals a counterfactual velocity gap that is ~95% systematic across noise seeds. Based on this observation, we introduce Clean Forcing, which trains a 5.9M-parameter LoRA corrector on the frozen base model to regress this gap, with a closed-loop stage that adds DAgger-style aggregation and a drift-contraction objective to expose the corrector to its own rollouts. Because the clean histories can be the base model's own single-shot generations, training needs no real videos, and the merged corrector adds no inference cost. In 50 s text-to-video generation, Clean Forcing reduces Δ-drift from +11.3 to +1.65 without real video and to -0.16 with 40 real clips, improving on the best published result of +3.57 with over 150x less data. Extensive experiments demonstrate that Clean Forcing outperforms prior methods in aesthetic quality and data efficiency with reduced drift for long-horizon video generation.