ZEUS: Accelerating Diffusion Models with Only Second-Order Predictor

Yixiao Wang; Ting Jiang; Zishan Shao; Hancheng Ye; Jingwei Sun; Mingyuan Ma; Jianyi Zhang; Yiran Chen

cs.LGApr 2, 2026

ZEUS: Accelerating Diffusion Models with Only Second-Order Predictor

Authors: Yixiao Wang, Ting Jiang, Zishan Shao, Hancheng Ye, Jingwei Sun, Mingyuan Ma, Jianyi Zhang, Yiran Chen,

Organizations: Department of Computer Science, Duke University, Durham, NC, USA · Department of Statistical Science, Duke University, Durham, NC, USA · Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA

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.

Figures & tables

Figure 1: Overview of ZEUS. ZEUS is a training-free acceleration framework for ODE-based generative models with four key properties: (i) modality-agnostic—applicable to image, video generation; (ii) parameterization-agnostic—compatible with $\epsilon$ -, $v$ -, and flow-prediction objectives; (iii) state-of-the-art speed–fidelity tradeoff—outperforming more complex methods with minimal overhead; (iv) minimal integration effort—fewer than 20 lines of code. See Section 4 for details.

Figure 2: Scarcity of full evaluations. Under an aggressive acceleration ratio, we have limited denoiser evaluations, creating a scarcity of real information. In this paper, we find that the (executed) denoising trajectory yields the observed, path-wise information set

\{\psi_{t},\ \Delta^{(1)}\psi_{t}\}

, where

\Delta^{(1)}\psi_{t}=\psi_{t}-\hat{\psi}_{t+1}

Panel of Figure 3 — Figure 3: ZEUS ablations on SDXL. We generate 1,000 samples from random MS-COCO 2017 prompts using DPM-Solver++ (50 steps). (a,b) Predictor order under a uniform $1{:}1$ schedule. (c,d) Stability from reusing the observed information set under a uniform $1{:}3$ schedule. This shows that ZEUS remains stable as the reduced-step run length increases.

	r=1	r=2	r=3
2nd-order lagrange	0.1115	0.1907	0.2246
3rd-order lagrange	0.1283	0.2431	0.2593
ZEUS (ours)	0.119	0.1745	0.2034
speedup	1.80 $\times$	2.41 $\times$	2.81 $\times$

Table 1: Ablation on numerical predictor order and input information. Second- and third-order Lagrange baselines extrapolate directly on the true previous full denoiser evaluation, whereas ZEUS (ours) exploits local solver information. Results are reported for different acceleration ratios

r

and predictor order

k

. This shows that (i) a higher-order numerical predictor does not necessarily come with higher accuracy and (ii) incorporating true but stale evaluation increases error under aggressive acceleration. The training-free strategy should exploit local information.

Figure 4: Three approximation schemes. We compare reuse-only, predictor-only, and ZEUS (reuse of the observed information pair). Dark gray: reference trajectory $\psi^{\star}$ . Light gray: solver-computed outputs $\psi_{t}$ . Crimson: approximated segments. Left–Reuse only: numerically stable but limited in expressivity; fine details erode (bottom). Middle–Predictor only: chaining second-order extrapolations overshoots without re-anchoring, producing artifacts (bottom). Right–Reuse observed information (ZEUS): alternating reuse of $\{\psi_{t},\ \psi_{t}+\Delta^{(1)}\psi_{t}\}$ prevents overshoot and preserves detail, yielding the best perceptual quality.

Model	Scheduler	Method	PSNR $\uparrow$	LPIPS $\downarrow$	FID $\downarrow$	Speedup $\uparrow$
SD-2	DPM++	DeepCache	17.70	0.271	7.83	$1.43\times$
		AdaptiveDiffusion	24.30	0.100	4.35	$1.45\times$
		SADA	26.34	0.094	4.02	$1.80\times$
		ZEUS-Medium	25.72	0.104	4.46	$1.85\times$
	Euler	DeepCache	18.91	0.239	7.40	$1.45\times$
		AdaptiveDiffusion	21.94	0.173	7.58	$1.89\times$

Table 2: Image quality vs. speed on SD-2, SDXL, and FLUX. Higher is better for PSNR/Speedup; lower is better for LPIPS/FID. Per model+scheduler block, best is bold , second best is underlined .

Strategy	Bias	Variance
Predictor-only	$\mathcal{O}(j^{2}\Delta^{2})$	$\Theta(j^{2})\sigma^{2}$
Reuse-only	$\mathcal{O}(j\Delta)$	$\sigma^{2}$
ZEUS	$\mathcal{O}(\Delta^{2})$ at $j{=}1$ ; $\mathcal{O}(j\Delta)$ else	$\leq 5\sigma^{2}$

Table 3: Bias and variance for consecutive reduced steps.

\Delta

: step size;

\sigma^{2}

: noise variance.

Model	Method	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	Speedup $\uparrow$
Wan 2.1
	SpargeAttn	20.52	0.623	0.343	1.44 $\times$
	SVG	22.99	0.785	0.199	1.58 $\times$
	SVG2	25.81	0.854	0.138	1.58 $\times$
	SVG2-Turbo	23.68	0.789	0.196	1.89 $\times$
	Ours	29.00	0.846	0.117	1.76 $\times$

Table 4: Quality & efficiency on video generation. Higher is better for PSNR/SSIM/Speedup; lower is better for LPIPS. Per- model best is bold , second-best is underlined .

Flux
Scheduler	Steps	LPIPS $\downarrow$	FID $\downarrow$	Speedup
Euler	50	0.047	1.53	2.09 $\times$
	25	0.040	2.65	1.58 $\times$
	15	0.036	2.47	1.22 $\times$
SDXL
Euler	50	0.095	3.87	1.85 $\times$

Table 5: Ablation study on few-step sampling across schedulers. Results on MS-COCO 2017.

Solver	PSNR $\uparrow$	LPIPS $\downarrow$	FID $\downarrow$	Speedup $\uparrow$
Euler-1	$28.66$	$0.095$	$3.87$	1.85 $\times$
DPM++-2	$29.17$	$0.084$	$3.59$	1.87 $\times$
DPM++-3	$29.05$	$0.079$	$3.28$	1.88 $\times$

Table 6: Ablation on higher-order solvers.

Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

Prediction mode	Target $\psi_{0}(\mathbf{x}_{0},\epsilon,s)$	Reconstruction $\hat{\mathbf{x}}_{0}^{(s)}$
$\epsilon$ -prediction	$\epsilon$	$\hat{\mathbf{x}}_{0}^{(s)}=\tfrac{1}{\alpha_{s}}\mathbf{x}_{s}-\tfrac{\sigma_{s}}{\alpha_{s}}\,\psi^{*}(\mathbf{x}_{s},s)$
$\mathbf{x_{0}}$ -prediction	$\mathbf{x}_{0}$	$\hat{\mathbf{x}}_{0}^{(s)}=\psi^{*}(\mathbf{x}_{s},s)$
$v$ -prediction	$v=\alpha_{s}\epsilon-\sigma_{s}\mathbf{x}_{0}$	$\hat{\mathbf{x}}_{0}^{(s)}=\tfrac{\alpha_{s}}{\alpha_{s}^{2}+\sigma_{s}^{2}}\mathbf{x}_{s}-\tfrac{\sigma_{s}}{\alpha_{s}^{2}+\sigma_{s}^{2}}\,\psi^{*}(\mathbf{x}_{s},s)$
$s$ -prediction	$\nabla_{\mathbf{x}_{s}}\log q_{s}(\mathbf{x}_{s})=-\tfrac{1}{\sigma_{s}}(\mathbf{x}_{s}-\tfrac{\alpha_{s}}{\alpha_{s}^{2}+\sigma_{s}^{2}}\mathbf{x}_{0})$	$\hat{\mathbf{x}}_{0}^{(s)}=\tfrac{1}{\alpha_{s}}\mathbf{x}_{s}+\tfrac{\sigma_{s}^{2}}{\alpha_{s}}\,\psi^{*}(\mathbf{x}_{s},s)$
Flow matching	$\epsilon-\mathbf{x}_{0}$	$\hat{\mathbf{x}}_{0}^{(s)}=\mathbf{x}_{s}-s\,\psi^{*}(\mathbf{x}_{s},s)$

Appendix

Table A.1 : Unified view of common parameterizations. Each training target

\psi_{0}

corresponds to a conditional regression, and the clean data

\mathbf{x}_{0}

is exactly reconstructed via ( A.12 ).

Parameterization	$\phi(s)=\mathbb{E}[\psi_{t}\mid s_{t}=s]$
$\epsilon$ -prediction	$0$
$\mathbf{x_{0}}$ -prediction	$\mathbb{E}[\mathbf{x_{0}}]$
$v$ -prediction	$-\,\sigma_{s}\,\mathbb{E}[\mathbf{x_{0}}]$
Score-prediction	$0$
Flow-prediction	$\alpha_{s}^{\prime}\,\mathbb{E}[\mathbf{x_{0}}]$

Appendix

Table A.2 : Summary of different parameterizations.

Figure A.1 : Illustration of the Runge phenomenon. Left: polynomial interpolation with only 2 nodes. Right: interpolation with 10 nodes, which exhibits severe oscillations and divergence near the boundary.

Setting	Speedup $\uparrow$	Peak Mem (MB) $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
ZEUS (Medium)	$2.07\times$	23370	31.593	0.938	0.029
ZEUS (Turbo)	$3.34\times$	23370	23.115	0.811	0.114

Appendix

Table A.3 : Memory footprint ablation on FLUX-2-dev (64B) with 4-bit quantization. ZEUS preserves the peak GPU memory budget while increasing speedup.

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Diffusion Transformers (DiT) have emerged as a widely adopted backbone for high-fidelity image and video generation, yet their iterative denoising process incurs high computational costs. Existing training-free acceleration methods rely on feature caching and reuse under the assumption of temporal stability. However, reusing features for multiple steps may lead to latent drift and visual degradation. We observe that model outputs evolve smoothly along much of the diffusion trajectory, enabling principled predictions rather than naive reuse. Based on this insight, we propose PrediT, a training-free acceleration framework that formulates feature prediction as a linear multistep problem. We employ classical linear multistep methods to forecast future model outputs from historical information, combined with a corrector that activates in high-dynamics regions to prevent error accumulation. A dynamic step modulation mechanism adaptively adjusts the prediction horizon by monitoring the feature change rate. Together, these components enable substantial acceleration while preserving generation fidelity. Extensive experiments validate that our method achieves up to

5.54\times

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Abstract

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