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

arXiv: https://arxiv.org/abs/2610.10366 · HTML: https://mlsanity.com/paper/2610.10366/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 5 of its 18 references that are in the map.
- First posted on arXiv 7 Oct 2026.

## Placed in

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

## Builds on (most cited first, 5 of 5)

- [FastCache: Fast Caching for Diffusion Transformer Through Learnable Linear Approximation](https://mlsanity.com/paper/2505.20353/) (2025)
- [Adaptive Spectral Feature Forecasting for Diffusion Sampling Acceleration](https://mlsanity.com/paper/2603.01623/) (2026)
- [Beyond Fixed Formulas: Data-Driven Linear Predictor for Efficient Diffusion Models](https://mlsanity.com/paper/2604.26365/) (2026)
- [WorldDynCache: Risk-Controlled Latent Dynamics Approximation for Diffusion World Model](https://mlsanity.com/paper/2608.01845/) (2026)
- [Disagree to Accelerate: Closing the Loop on Diffusion Feature Forecasts](https://mlsanity.com/paper/2608.01740/) (2026)

## Abstract (arXiv)

Feature caching accelerates diffusion sampling by replacing expensive network evaluations with predictions from previously computed activations. However, forecasts based only on past features cannot directly incorporate changes in the current denoising state. We investigate whether inexpensive, freshly computed features can serve as observations for correcting these predictions. We introduce an observation-corrected Koopman framework for accelerating frozen diffusion models. Using calibration trajectories, we identify finite-dimensional, time-dependent Koopman approximations that jointly describe the increments of shallow and deep network features. During accelerated sampling, these operators predict the evolution of expensive deep features, while innovations in the observed shallow features correct the predicted state. Periodic full evaluations refresh the observer, and all generative-model parameters remain unchanged. This formulation enables controlled comparisons of temporal prediction and observation correction. Across three 10,000-image runs per dataset, our method reduces paired Inception-feature MSE by 19.9% on CIFAR-10 and 11.9% on a ten-class ImageNet subset relative to channelwise affine prediction under the same four-partial-step schedule. Matched ablations attribute additional reductions of 4.54% and 4.67% to observation correction. The observer achieves 1.89× and 1.85× measured speedups over DDIM-50, supporting improved reference-sampler fidelity without retraining the denoiser.