Rethinking Diffusion Caching: From Historical Extrapolation to Current-Observation Completion

Training-free diffusion caching reconstructs skipped features from historical evaluations. Its accuracy depends on whether the cached directions can represent the current residual motion. We identify a representation bottleneck: on Wan2.1, the latest input secant captures $98.9\%$ of input displacement energy, while the latest residual secant captures $2.7\%$ of the deployed CFG-weighted residual displacement energy. We characterize the motion that a fixed historical basis cannot represent and use oracle reconstruction to measure this limitation. This motivates MoorCache, which combines historical prediction with current-observation completion. History propagates persistent motion, and an affordable current observation supplies complementary directions through a projected displacement update. Same-cost ablations demonstrate the value of this completion, while projection controls test how current information should be combined with history. Across Wan2.1, HunyuanVideo, DiT-XL/2, and FLUX.1-dev, MoorCache improves quality–efficiency trade-offs with observation and reconstruction costs. On HunyuanVideo, it achieves $2.784\times$ measured speedup with $38.506$ dB reference PSNR, connecting the representation analysis to practical diffusion acceleration.