Koopman Observers for Diffusion Acceleration: Correcting Feature Forecasts with Shallow Measurements

Training-free feature forecasting accelerates diffusion sampling by predicting features at skipped denoising steps. Recent work has mainly focused on designing stronger forecasters. Yet forecast error varies sharply across steps, and open-loop caches trust the forecast in full at every skipped step. This fixed trust is what breaks as acceleration turns aggressive. The missing question is not only how to forecast better, but when and how much to trust a forecast. We show that reliability can be observed from the cache itself. Two forecasts agree where the feature trajectory is smooth, and they diverge where prediction turns hard. Their disagreement is a cheap runtime signal, and it costs no extra denoiser evaluation. Based on this signal, we introduce RACER, a training-free closed-loop controller with two responses. It continuously shrinks uncertain forecasts toward the last computed feature. At the riskiest steps, RACER refreshes the feature and repays the added evaluation by skipping a later scheduled one. We derive a deterministic error bound for the shrinkage and empirically evaluate its validity and tightness across acceleration regimes. At the same number of denoiser evaluations, RACER improves the strongest open-loop baseline across SD3.5-Large, FLUX.1-dev, Wan2.1-14B, and HunyuanVideo on DrawBench, VBench, and COCO. On SD3.5, we further show that RACER samples faster at equal quality. RACER generalizes across forecasting designs as well. For example, it recovers much of the quality lost on a Taylor base. These results show that reliable diffusion acceleration also depends on how forecasts are used. Code is available at https://github.com/LiZaiyuan0619/RACER

Diffusion models are widely used to generate high-quality images and videos, but their iterative denoising process remains computationally intensive. A growing class of training-free accelerators reduces this cost by reusing cached intermediate features or forecasting future ones. To control draft drift, these methods sometimes compute an exact block feature for verification. Yet the resulting exact feature is typically used only to measure discrepancy or guide a later decision and is then discarded. We find that this previously computed feature can instead be reused for correction. Forwarding it at the verification site resets the local draft residual and reduces downstream feature error. Based on this observation, we introduce FeatFix, a local exact-feature correction method for cached diffusion inference. FeatFix operates at a fixed sparse set of layer--timestep sites. At each selected site, it replaces the complete draft block output with the exact output computed from the same incoming state, avoiding token- or channel-level partial replacement and full-timestep recomputation. Experiments across four image and video backbones show that FeatFix consistently accelerates generation, achieving a speedup of up to $6.70\times$ over Vanilla while maintaining competitive output quality.

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$\times$ speedup on FLUX.1 and 4.67$\times$ speedup on Wan2.1-14B, while maintaining much higher sample quality compared with the baselines.