EigenCache: Rethinking Diffusion Acceleration as Covariance-Optimal Forecasting and Submodular Information Allocation

Accelerating diffusion models via feature caching has evolved from static reuse to polynomial extrapolation, yet current "cache-then-forecast" strategies remain limited by rigid, hand-crafted approximation families (e.g., Taylor or Hermite bases) that often misalign with the complex, layer-specific non-stationarity of generative feature dynamics. This paper introduces EigenCache, a theoretically grounded framework that re-frames acceleration as a problem of covariance learning and experimental design. By modeling feature trajectories as time-indexed stochastic processes governed by learnable temporal kernels, we demonstrate that the statistically optimal feature predictor (Minimum Mean Squared Error) is the Gaussian Process posterior mean (Kriging), which strictly generalizes and outperforms previous fixed-basis expansions. Crucially, this probabilistic formulation couples prediction with uncertainty quantification via a closed-form variance certificate. Leveraging this, we derive an information-theoretic scheduling algorithm that selects computation anchors by maximizing the log-determinant of the posterior covariance—a submodular objective that admits a provably near-optimal greedy solution. EigenCache thus provides a unified, training-free foundation for efficient inference, offering not only superior reconstruction accuracy but also a rigorous mechanism for robust, uncertainty-aware compute allocation.