Feature Information Dynamics in Diffusion

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.

Despite the empirical success of Diffusion Models (DMs) and Variational Autoencoders (VAEs), their generalization performance remains theoretically underexplored, especially lacking a full consideration of the shared encoder-generator structure. Leveraging recent information-theoretic tools, we propose a unified theoretical framework that provides guarantees for the generalization of both the encoder and generator by treating them as randomized mappings. This framework further enables (1) a refined analysis for VAEs, accounting for the generator's generalization, which was previously overlooked; (2) illustrating an explicit trade-off in generalization terms for DMs that depends on the diffusion time $T$; and (3) providing computable bounds for DMs based solely on the training data, allowing the selection of the optimal $T$ and the integration of such bounds into the optimization process to improve model performance. Empirical results on both synthetic and real datasets illustrate the validity of the proposed theory.

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.