# Adaptive Spectral Feature Forecasting for Diffusion Sampling Acceleration arXiv: https://arxiv.org/abs/2603.01623 · HTML: https://mlsanity.com/paper/2603.01623/ ## Key facts - Cited by 7 papers in the map (data through 14 Oct 2026). - Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. - Builds on 54 of its 57 references that are in the map. - First posted on arXiv 2 Mar 2026. ## Placed in - Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/) ## Builds on (most cited first, 30 of 54) - [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) - [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014) - [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020) - [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020) - [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015) - [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) - [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022) - [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024) - [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019) - [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022) - [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022) - [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022) - [Wan: Open and Advanced Large-Scale Video Generative Models](https://mlsanity.com/paper/2503.20314/) (2025) - [CLIPScore: A Reference-free Evaluation Metric for Image Captioning](https://mlsanity.com/paper/2104.08718/) (2021) - [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) - [VBench: Comprehensive Benchmark Suite for Video Generative Models](https://mlsanity.com/paper/2311.17982/) (2023) - [HunyuanVideo: A Systematic Framework For Large Video Generative Models](https://mlsanity.com/paper/2412.03603/) (2024) - [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022) - [ImageReward: Learning and Evaluating Human Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2304.05977/) (2023) - [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023) - [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022) - [Improved Distribution Matching Distillation for Fast Image Synthesis](https://mlsanity.com/paper/2405.14867/) (2024) - [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025) - [Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion](https://mlsanity.com/paper/2310.02279/) (2023) - [Improved Techniques for Training Consistency Models](https://mlsanity.com/paper/2310.14189/) (2023) - [Simplifying, Stabilizing and Scaling Continuous-Time Consistency Models](https://mlsanity.com/paper/2410.11081/) (2024) - [Q-Diffusion: Quantizing Diffusion Models](https://mlsanity.com/paper/2302.04304/) (2023) ## Built on by (most cited first, 7 of 7) - [Disagree to Accelerate: Closing the Loop on Diffusion Feature Forecasts](https://mlsanity.com/paper/2608.01740/) (2026) - [Interpreting the Synchronization Gap: The Hidden Mechanism Inside Diffusion Transformers](https://mlsanity.com/paper/2603.20987/) (2026) - [Kolmogorov-Arnold Reservoir Computing](https://mlsanity.com/paper/2606.19984/) (2026) - [ReAL: Accelerating Flow Matching through Segment Advancement with Shared Lookahead](https://mlsanity.com/paper/2609.33202/) (2026) - [Hybrid-Basis Feature Forecasting for Diffusion Sampling Acceleration](https://mlsanity.com/paper/2610.05254/) (2026) - [Koopman Observers for Diffusion Acceleration: Correcting Feature Forecasts with Shallow Measurements](https://mlsanity.com/paper/2610.10366/) (2026) - [Tikhonov-Stabilized Bezier Representation Forecasting for Training-free Diffusion Acceleration](https://mlsanity.com/paper/2610.16448/) (2026) ## Abstract (arXiv) Diffusion models have become the dominant tool for high-fidelity image and video generation, yet are critically bottlenecked by their inference speed due to the numerous iterative passes of Diffusion Transformers. To reduce the exhaustive compute, recent works resort to the feature caching and reusing scheme that skips network evaluations at selected diffusion steps by using cached features in previous steps. However, their preliminary design solely relies on local approximation, causing errors to grow rapidly with large skips and leading to degraded sample quality at high speedups. In this work, we propose spectral diffusion feature forecaster (Spectrum), a training-free approach that enables global, long-range feature reuse with tightly controlled error. In particular, we view the latent features of the denoiser as functions over time and approximate them with Chebyshev polynomials. Specifically, we fit the coefficient for each basis via ridge regression, which is then leveraged to forecast features at multiple future diffusion steps. We theoretically reveal that our approach admits more favorable long-horizon behavior and yields an error bound that does not compound with the step size. Extensive experiments on various state-of-the-art image and video diffusion models consistently verify the superiority of our approach. Notably, we achieve up to 4.79× speedup on FLUX.1 and 4.67× speedup on Wan2.1-14B, while maintaining much higher sample quality compared with the baselines.