Diffusion transformers generate high-quality videos but remain computationally expensive. Sparse attention and temporal caching reduce computation within and across denoising steps, respectively, offering a natural composition. However, predictions produced with sparse attention become sources for temporal reuse, coupling their errors along the sampling trajectory. We observe that improving the accuracy of these sources recovers fidelity without changing the reuse schedule, and that sparsification errors remain directionally aligned across nearby steps, suggesting that correction information can be shared rather than recomputed. These observations motivate RECAP, a training-free method that couples sparse attention with hierarchical caching through reciprocal correction, adaptively coordinated by online error feedback. Cached dense refinement corrects omitted interactions in current sparse estimates, while fresh sparse statistics track input changes and regulate the aging correction. The resulting predictions then renew the sources for whole-step prediction reuse, allowing prediction history to advance between dense refreshes. We evaluate RECAP on multiple video diffusion models against sparse-attention methods, caching methods, and their direct compositions. On HunyuanVideo at 720p 5-second generation, RECAP achieves a 3.05x speedup and outperforms all tested direct compositions in both fidelity and inference speed.

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