# Hybrid-Basis Feature Forecasting for Diffusion Sampling Acceleration

arXiv: https://arxiv.org/abs/2610.05254 · HTML: https://mlsanity.com/paper/2610.05254/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 38 of its 39 references that are in the map.
- First posted on arXiv 4 Oct 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 30 of 38)

- [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)
- [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)
- [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)
- [Stable Video Diffusion: Scaling Latent Video Diffusion Models to Large Datasets](https://mlsanity.com/paper/2311.15127/) (2023)
- [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)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [PixArt-α: Fast Training of Diffusion Transformer for Photorealistic Text-to-Image Synthesis](https://mlsanity.com/paper/2310.00426/) (2023)
- [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)
- [Post-training Quantization on Diffusion Models](https://mlsanity.com/paper/2211.15736/) (2022)
- [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)
- [Accelerating Diffusion Transformers with Token-wise Feature Caching](https://mlsanity.com/paper/2410.05317/) (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)
- [DiTFastAttn: Attention Compression for Diffusion Transformer Models](https://mlsanity.com/paper/2406.08552/) (2024)
- [SpeCa: Accelerating Diffusion Transformers with Speculative Feature Caching](https://mlsanity.com/paper/2509.11628/) (2025)
- [Forecast then Calibrate: Feature Caching as ODE for Efficient Diffusion Transformers](https://mlsanity.com/paper/2508.16211/) (2025)
- [SmoothCache: A Universal Inference Acceleration Technique for Diffusion Transformers](https://mlsanity.com/paper/2411.10510/) (2024)
- [UniCP: A Unified Caching and Pruning Framework for Efficient Video Generation](https://mlsanity.com/paper/2502.04393/) (2025)
- [AB-Cache: Training-Free Acceleration of Diffusion Models via Adams-Bashforth Cached Feature Reuse](https://mlsanity.com/paper/2504.10540/) (2025)

## Abstract (arXiv)

We propose Hybrid-Basis Feature Forecasting (HybridFF), a training-free, plug-and-play framework for accelerating diffusion sampling. To capture local smoothness, long-range trends, and complex non-monotonic variations when modeling feature evolution, HybridFF first estimates coefficients using moving least squares (MLS) for each of multiple complementary basis families and then combines the corresponding predictors using fusion weights. In addition to the choice of basis functions, the fusion weights also play a critical role. We introduce two strategies to balance quality and speedup. HybridFF (Fixed) prioritizes efficiency with model-specific fusion weights calibrated on a small set and held constant during inference. HybridFF (Adaptive) updates the fusion weights online using branch reliability scores computed from an exponential moving average of full-step prediction errors, improving prediction fidelity and generation quality under aggressive caching while retaining substantial acceleration. Experiments across DiT-XL/2, FLUX.1-dev, SD3.5-Large, and HunyuanVideo demonstrate a favorable speedup--quality trade-off over representative single-basis forecasters and caching baselines.