HiCache: A Plug-in Scaled-Hermite Upgrade for Taylor-Style Cache-then-Forecast Diffusion Acceleration

Diffusion models have achieved remarkable success in content generation but suffer from prohibitive computational costs due to iterative sampling. While recent feature caching methods tend to accelerate inference through temporal extrapolation, these methods still suffer from severe quality loss due to the failure in modeling the complex dynamics of feature evolution. To solve this problem, this paper presents HiCache (Hermite Polynomial-based Feature Cache), a training-free acceleration framework that fundamentally improves feature prediction by aligning mathematical tools with empirical properties. Our key insight is that feature derivative approximations in Diffusion Transformers exhibit multivariate Gaussian characteristics, motivating the use of Hermite polynomials, the potentially theoretically optimal basis for Gaussian-correlated processes. Besides, we introduce a dual-scaling mechanism that ensures numerical stability while preserving predictive accuracy, which is also effective when applied standalone to TaylorSeer. Extensive experiments demonstrate HiCache's superiority: achieving $5.55$ speedup on FLUX.1-dev while exceeding baseline quality, maintaining strong performance across text-to-image, video generation, and super-resolution tasks. Moreover, HiCache can be naturally added to the previous caching methods to enhance their performance, e.g., improving ClusCa from $0.9480$ to $0.9840$ in terms of image rewards. Our code is included in the supplementary material, and will be released on GitHub.