ZEUS: Accelerating Diffusion Models with Only Second-Order Predictor

Abstract: Denoising generative models deliver high-fidelity generation but remain bottlenecked by inference latency due to the many iterative denoiser calls required during sampling. Training-free acceleration methods reduce latency by either sparsifying the model architecture or shortening the sampling trajectory. Current training-free acceleration methods are more complex than necessary: higher-order predictors amplify error under aggressive speedups, and architectural modifications hinder deployment. Beyond 2x acceleration, step skipping creates structural scarcity -- at most one fresh evaluation per local window -- leaving the computed output and its backward difference as the only causally grounded information. Based on this, we propose ZEUS, an acceleration method that predicts reduced denoiser evaluations using a second-order predictor, and stabilizes aggressive consecutive skipping with an interleaved scheme that avoids back-to-back extrapolations. ZEUS adds essentially zero overhead, no feature caches, and no architectural modifications, and it is compatible with different backbones, prediction objectives, and solver choices. Across image and video generation, ZEUS consistently improves the speed-fidelity performance over recent training-free baselines, achieving up to 3.2x end-to-end speedup while maintaining perceptual quality. Our code is available at: https://github.com/Ting-Justin-Jiang/ZEUS.

• The paper introduces ZEUS, a training-free acceleration framework that employs a second-order predictor to enhance ODE diffusion model sampling.
• It shows that under aggressive skip schedules, second-order extrapolation outperforms higher-order methods, achieving optimal speed–quality trade-offs.
• Empirical evaluations demonstrate up to 3.2× speedup with negligible degradation, validating the framework across both image and video generative models.

ZEUS: Second-Order, Training-Free Acceleration for Diffusion ODE Sampling

Introduction

The paper "ZEUS: Accelerating Diffusion Models with Only Second-Order Predictor" (2604.01552) introduces ZEUS, a training-free acceleration framework targeting inference bottlenecks in ODE-based generative models. ZEUS is designed for maximum generality and minimal integration overhead: it is modality- and parameterization-agnostic (supporting image and video models, and all standard prediction objectives), can be integrated by modifying fewer than 20 lines of code, and imposes $\mathcal{O}(1)$ additional computational or memory cost.

ZEUS’s core insight is both technical and contrarian: Under aggressive acceleration ratios ($>2\times$ skipping of network evaluations), second-order predictors outperform both higher-order methods and simpler reuse strategies, contradicting prevalent heuristics in recent literature. The approach avoids feature caching, architectural changes, and overfitting to specific model internals, making it practically attractive for rapid deployment across diverse generative pipelines.

Figure 1: Overview of ZEUS, demonstrating training-free, modality-agnostic ODE acceleration with state-of-the-art speed–fidelity tradeoff and minimal integration effort.

Technical Motivation and Methodology

Scarcity of Full Evaluations

Aggressive skip schedules (e.g., evaluating the denoiser only every $r{+}1$ steps) induce a fundamental information scarcity: at most one "fresh" denoiser output per local window, with the rest of the trajectory approximated. The observed, causally meaningful information at each such anchor is the output and its local backward difference—termed the observed information set.

Figure 2: Under rapid acceleration, the denoising trajectory offers only sparse, causally meaningful outputs for trajectory prediction.

Second-Order Predictor: Statistical and Numerical Rationale

ZEUS employs a second-order extrapolation scheme: given an observed pair $(\psi_t, \Delta^{(1)}\psi_t)$, the denoiser output at the next skipped step is predicted as $\hat\psi_{t-1} = 2\psi_t - \hat\psi_{t+1}$. This estimator is the unique BLUE (Best Linear Unbiased Estimator) among two-point linear predictors for locally affine trajectories, as shown in rigorous theoretical analysis in the appendix. No higher-order method can improve the minimax bias rate under $C^2$ smoothness while avoiding costly variance amplification and instability.

Empirically, increasing the predictor order beyond two degrades performance under skipping-induced scarcity, as additional points used for extrapolation are themselves approximate and compound error, rather than reducing it. Conversely, reusing only a single model output sacrifices essential local trend information, incurring a higher bias.

Figure 3: Perceptual deviation (LPIPS) versus predictor order, demonstrating optimality and stability of the second-order predictor in the scarcity regime.

Interleaved Extrapolation for Stability

Naïve chaining of second-order extrapolation across multiple consecutive skipped steps leads to rapid error amplification (predictor-only scheme), while full reuse (reuse-only) degrades fine detail through bias accumulation. ZEUS mitigates these tradeoffs via an interleaved scheme: alternating between direct reuse ($\psi_t$) and a single second-order extrapolate ($2\psi_t - \hat\psi_{t+1}$) for contiguous skipped steps. This enables stable variance and preserves high perceptual fidelity even under high skipping rates.

Figure 4: Comparison of reuse-only, predictor-only, and ZEUS's interleaved reuse. ZEUS maintains trajectory stability and preserves local detail under skipping.

Theoretical Analysis: Second-Order Sufficiency and Higher-Order Pathologies

The authors formalize the limits of estimation accuracy under the information constraint imposed by aggressive step skipping. They identify that, under $C^2$ regularity, the minimax risk for the skipped-step inference problem is matched by the second-order predictor and cannot be sharpened. Further, higher-order polynomial extrapolants exhibit pathologies such as exponential variance amplification and spurious oscillations (Runge phenomenon), which are especially pronounced in uniformly spaced schedules due to lack of Chebyshev node placement.

Figure 5: Illustration of the Runge phenomenon—high-order polynomial interpolation with uniform spacing leads to severe oscillation and divergence, demonstrating the inadequacy of higher-order predictors in practice under ZEUS's skipping regime.

Empirical Evaluation

ZEUS is evaluated across multiple state-of-the-art text-to-image (SD-2.1, SDXL, FLUX) and text-to-video (Wan 2.1, CogVideoX) models, tested with popular schedulers (Euler, DPM-Solver++). Experimental results show:

• Image Generation: ZEUS achieves up to $3.2\times$ end-to-end speedup with negligible or improved LPIPS and FID scores against full evaluation. It consistently outperforms or matches strong baselines (DeepCache, SADA, AdaptiveDiffusion, TaylorSeer, DiCache) on multiple backbones and schedulers.
• Video Generation: Similar efficiency gains are observed for T2V models, demonstrating the generality of the approach.

Across all tasks, ZEUS successfully moves the Pareto frontier on speed–quality trade-offs, validating the theoretical analysis.

Implications and Future Directions

The findings challenge the consensus that predictor complexity or caching depth are prerequisites for deployment-friendly, high-performance acceleration of diffusion samplers. By establishing strict optimality of the second-order approach under information constraints and demonstrating practical generalization across prediction targets and model architectures, this work suggests an architectural decoupling between approximation order and skip-aggressiveness for ODE-based generators.

On the practical side, lowering the compute barrier for high-fidelity generative models has clear relevance for edge deployment, rapid prototyping, and democratizing access to advanced generative technology. However, the efficiency gain may contribute to increased generative output volume, potentially amplifying negative societal externalities in synthetic media, and will need to be considered alongside safe deployment and content moderation frameworks.

Theoretically, the connection between information-theoretic bounds, numerical analysis of ODE integrators, and model-agnostic trajectory prediction provides fertile ground for future research—potentially inspiring analogous approaches for training-free acceleration, step adaptation, or certification in other iterative generative domains and for broader classes of stochastic processes.

Conclusion

ZEUS provides a disciplined and robust framework for aggressively accelerating sampling in ODE-based generative models. It combines rigorous theoretical justification, engineering simplicity, and empirical validation, establishing both a practical baseline and a new direction in the design of training-free accelerators for diffusion and flow-based generation. The work decisively supports the sufficiency and optimality of second-order, locally causal predictors under high skipping rates, and cautions against complexity escalation in the absence of additional informative gradients. These insights are poised to impact future developments in efficient generative inference and model adaptation.