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

arXiv: https://arxiv.org/abs/2508.16984 · HTML: https://mlsanity.com/paper/2508.16984/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 35 of its 47 references that are in the map.
- First posted on arXiv 23 Aug 2025.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 35)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Make-A-Video: Text-to-Video Generation without Text-Video Data](https://mlsanity.com/paper/2209.14792/) (2022)
- [HunyuanVideo: A Systematic Framework For Large Video Generative Models](https://mlsanity.com/paper/2412.03603/) (2024)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [Qwen-Image Technical Report](https://mlsanity.com/paper/2508.02324/) (2025)
- [eDiff-I: Text-to-Image Diffusion Models with an Ensemble of Expert Denoisers](https://mlsanity.com/paper/2211.01324/) (2022)
- [On Distillation of Guided Diffusion Models](https://mlsanity.com/paper/2210.03142/) (2022)
- [DeepCache: Accelerating Diffusion Models for Free](https://mlsanity.com/paper/2312.00858/) (2023)
- [Q-Diffusion: Quantizing Diffusion Models](https://mlsanity.com/paper/2302.04304/) (2023)
- [Token Merging for Fast Stable Diffusion](https://mlsanity.com/paper/2303.17604/) (2023)
- [Structural Pruning for Diffusion Models](https://mlsanity.com/paper/2305.10924/) (2023)
- [Delta-DiT: A Training-Free Acceleration Method Tailored for Diffusion Transformers](https://mlsanity.com/paper/2406.01125/) (2024)
- [Accelerating Diffusion Transformers with Token-wise Feature Caching](https://mlsanity.com/paper/2410.05317/) (2024)
- [Learning-to-Cache: Accelerating Diffusion Transformer via Layer Caching](https://mlsanity.com/paper/2406.01733/) (2024)
- [FORA: Fast-Forward Caching in Diffusion Transformer Acceleration](https://mlsanity.com/paper/2407.01425/) (2024)
- [From Reusing to Forecasting: Accelerating Diffusion Models with TaylorSeers](https://mlsanity.com/paper/2503.06923/) (2025)

## Built on by (most cited first, 12 of 12)

- [FreqCa: Accelerating Diffusion Models via Frequency-Aware Caching](https://mlsanity.com/paper/2510.08669/) (2025)
- [A Survey on Cache Methods in Diffusion Models: Toward Efficient Multi-Modal Generation](https://mlsanity.com/paper/2510.19755/) (2025)
- [Efficient Video Diffusion Models: Advancements and Challenges](https://mlsanity.com/paper/2604.15911/) (2026)
- [Fast3Dcache: Training-free 3D Geometry Synthesis Acceleration](https://mlsanity.com/paper/2511.22533/) (2025)
- [FlashClear: Ultra-Fast Image Content Removal via Efficient Step Distillation and Feature Caching](https://mlsanity.com/paper/2605.09003/) (2026)
- [BRACE: Taming Sharp Irregularities via Barycentric Rational Forecasting for Fast Diffusion Transformers Inference](https://mlsanity.com/paper/2608.07572/) (2026)
- [RA-CFGCache: From Branch-Level Criteria to Guided-Risk Control under Classifier-Free Guidance](https://mlsanity.com/paper/2609.36433/) (2026)
- [The Golden Path Hypothesis: Reusable Schedules in Diffusion Caching](https://mlsanity.com/paper/2609.39343/) (2026)
- [SpectralCache: Accelerating Diffusion-Based World Models via Spectral Feature Caching](https://mlsanity.com/paper/2610.02660/) (2026)
- [Rethinking What to Cache in Few-Step Diffusion Transformers: Solver-Aware Target Selection](https://mlsanity.com/paper/2610.03577/) (2026)
- [Hybrid-Basis Feature Forecasting for Diffusion Sampling Acceleration](https://mlsanity.com/paper/2610.05254/) (2026)
- [Tikhonov-Stabilized Bezier Representation Forecasting for Training-free Diffusion Acceleration](https://mlsanity.com/paper/2610.16448/) (2026)

## Abstract (arXiv)

Diffusion models have achieved remarkable success in content generation but often incur prohibitive computational costs due to iterative sampling. Recent feature caching methods accelerate inference via temporal extrapolation, yet can suffer quality degradation from inaccurate modeling of the complex dynamics of feature evolution. We propose HiCache (Hermite Polynomial-based Feature Cache), a training-free acceleration framework that 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 as a potentially optimal basis for Gaussian-correlated processes. We further introduce a dual-scaling mechanism that ensures numerical stability while preserving predictive accuracy, and is also effective when applied standalone or integrated with TaylorSeer. Extensive experiments demonstrate HiCache's superiority, achieving 5.55x speedup on FLUX.1-dev while matching or exceeding baseline quality, and maintaining strong performance across text-to-image, video generation, and super-resolution tasks. Moreover, HiCache can be naturally added to previous caching methods to enhance their performance, e.g., improving ClusCa from 0.9480 to 0.9840 in terms of image rewards. Code: https://github.com/fenglang918/HiCache