LEAP: Accelerating ODE-based Diffusion Sampling with Optimal Linear Leaps

Haowei Zheng; Zhenyu Zhou; Jiawei Chen; Can Wang; Defang Chen

cs.CVOct 19, 2026

LEAP: Accelerating ODE-based Diffusion Sampling with Optimal Linear Leaps

Authors: Haowei Zheng, Zhenyu Zhou, Jiawei Chen, Can Wang, Defang Chen

Organizations: State Key Laboratory of Blockchain and Data Security, Zhejiang University. · Hangzhou High-Tech Zone (Binjiang) Institute of Blockchain and Data Security. · University of California, Berkeley, California, United States

Abstract

Diffusion models primarily rely on general-purpose ODE-based numerical methods for training-free accelerated sampling, but performance degrades with coarse time discretization. In this paper, we propose optimal linear leaps (LEAP), a specialized method grounded in theoretical and empirical investigations of sampling trajectory geometry. Built upon low-dimensionality and cross-trajectory consistency, LEAP formulates a supervised least-squares optimization problem within the local trajectory subspace, achieving a precise approximation of future states without model evaluations. Extensive experiments demonstrate that LEAP outperforms previous methods across diverse modalities, including text-to-image (Stable Diffusion 3.5, FLUX.1-dev) and image-to-3D (TRELLIS.2) generation. Furthermore, LEAP can be seamlessly integrated into existing solver-based methods, offering a plug-and-play enhancement for modern diffusion models. Code is available at https://github.com/zju-pi/LEAP.

Figures & tables

Figure 1. Overview of the proposed LEAP. A linear predictor (blue boxes) extrapolates the subsequent score from a sliding history buffer of size $r$ (dashed boxes), yielding an approximated state $\hat{\mathbf{x}}$ (grey circles) without model evaluations. To prevent error drift, a model evaluation subsequently refines this approximation into a corrected state $\tilde{\mathbf{x}}$ (yellow circles). Overview of the proposed prediction-correction sampling. A linear predictor (blue boxes) extrapolates the next score from a sliding history buffer of size $r$ (dashed boxes), yielding an approximated state $\hat{\mathbf{x}}$ (grey circles) without model evaluations. To prevent error drift, an actual model evaluation subsequently refines this approximation into a corrected state $\tilde{\mathbf{x}}$ (yellow circles).

Figure 2. Visualizing the trajectory regularity of diffusion models. Following the visualization protocol in ( Chen et al., 2024 ) , we project 100 sampling trajectories generated with distinct noise and prompt initializations using SD3.5-Medium ( Esser et al., 2024 ) .

Figure 3. Relative prediction error vs. noise level $\sigma_{t}$ . We quantify the projection error of each score onto the subspace spanned by its corresponding historical buffer. The relative error is strictly bounded, using a small window size of $r=3$ .

Steps	Method	SD3.5-Medium			FLUX.1-dev
Steps	Method	HPSv2 $\uparrow$	ImageReward $\uparrow$	CLIPScore $\uparrow$	HPSv2 $\uparrow$	ImageReward $\uparrow$	CLIPScore $\uparrow$
10	Euler	25.8866	0.6653	32.7920	28.3538	0.8110	30.6939
	DPM++	26.4565	0.7178	32.9027	28.6365	0.8331	30.7257
	iPNDM	26.4041	0.7063	32.7579	28.8272	0.8956	30.9178
	UniPC	26.4450	0.7122	32.6428	28.8193	0.8839	31.0634
	LTC-Accel	26.2546	0.7324	33.1578	28.9543	0.9193	31.1217

Table 1. Quantitative results on SD3.5-Medium and FLUX.1-dev. The best and second-best results are marked in bold and underlined , respectively. Our proposed method (LEAP) is highlighted with a gray background.

Method	PSNR $\uparrow$					CLIP Score $\uparrow$
Method	10	15	20	25	30	10	15	20	25	30
Euler	7.250	7.396	7.235	7.361	7.405	0.8638	0.8654	0.8682	0.8650	0.8658
LEAP (Euler)	7.414	7.537	7.337	7.410	7.408	0.8677	0.8674	0.8693	0.8678	0.8709

Table 2. Quantitative comparison of image-to-3D generation on the GSO dataset via TRELLIS.2.

Panel of Figure 4 — Figure 4. Text-to-image generation on SD3.5-Medium using 10 inference steps across diverse prompts.

Panel of Figure 5 — Figure 5. Image-to-3D generation on TRELLIS.2 using 10 inference steps across different image prompts.

Panel of Figure 6 — Figure 6. Ablation studies on key hyperparameters in Stable Diffusion 3.5-Medium. We evaluate the impact of (a) Window Size, (b) Penalty Strength, and (c) Number of Tokens on the HPSv2 score across different NFEs. The default configuration is indicated by the dashed vertical line.

Figure 7. Ablation study on basis construction in Stable Diffusion 3.5-Medium. Our proposed different basis effectively addresses the issue of ill-conditioning.

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

Solver + Method	HPSv2 $\uparrow$	ImageReward $\uparrow$	CLIPScore $\uparrow$
Euler	27.4725	0.8416	33.4644
LEAP (Euler)	28.1826	0.9522	33.6817
DPM++	27.8642	0.8438	33.4704
LEAP (DPM++)	28.2152	0.9806	33.5617
iPNDM	27.9220	0.8770	33.4416
LEAP (iPNDM)	28.2204	0.9642	33.6601

Appendix

Table 3. LEAP combined with different base solvers in SD3.5-Medium. All results use the same 15-step schedule and

r=5

in LEAP’s setting.

NFE	P:C	HPSv2 $\uparrow$	ImageReward $\uparrow$	CLIPScore $\uparrow$
10	$1{:}1$	26.8419	0.7692	33.2982
10	$1{:}2$	26.3182	0.7224	33.1515
15	$1{:}1$	28.1826	0.9522	33.6817
15	$1{:}2$	27.9594	0.9004	33.7109
20	$1{:}1$	28.5727	0.9701	33.7192
20	$1{:}2$	28.3575	0.9499	33.8125

Appendix

Table 4. Ablation on the prediction-to-correction (P:C) schedule on SD3.5-Medium.

Metric	Method	Anime	ConceptArt	Paintings	Photo
HPSv2	Euler	30.14	28.63	28.99	26.56
	LEAP (Euler)	31.22	30.15	30.14	27.37
ImageReward	Euler	1.10	1.02	1.06	0.80
	LEAP (Euler)	1.18	1.15	1.16	0.96
CLIPScore	Euler	35.18	33.61	33.41	32.28
	LEAP (Euler)	35.19	33.96	33.69	32.79

Appendix

Table 5. Ablation study on prompt distributions (NFE

=15

). Reference prompts are sampled from DrawBench, while evaluation prompts are sampled from the HPSv2 benchmark.

Transfer setting	Method	HPSv2 $\uparrow$	ImageReward $\uparrow$	CLIPScore $\uparrow$
Cross-model	Euler	25.89	0.67	32.79
	LEAP (FLUX coeffs.)	26.97	0.75	33.26
Cross-solver	DPM++	26.46	0.72	32.90
	LEAP (Euler coeffs.)	27.01	0.80	33.48
Cross-step	Euler	27.47	0.84	33.46
	LEAP (10-NFE coeffs.)	28.17	0.91	33.69

Appendix

Table 6. Transferability of the coefficient bank. Cross-model and cross-solver results use 10 NFE; cross-step results use 15 NFE.

Panel of Figure 8 — Figure 8. Reference images adopted in image-3D qualitative experiments.

Figure 9. Additional qualitative comparison on the FLUX model (Part 1).

Figure 10. Additional qualitative comparison on the FLUX model (Continued).

Figure 11. Additional image-3D qualitative results. Columns from left to right show the input conditions, generation results from the baseline solver (NFE=10), and results from our proposed LEAP method (NFE=10).

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Sampling from a diffusion model typically requires many forward passes through a large neural network, making generation computationally expensive. While much work has focused on efficient solvers and samplers, comparatively little attention has been paid to selecting the sampling timesteps themselves. A recent line of work optimizes theoretically derived surrogates for sample quality rather than the quality metric itself. We propose Optimizing Your Sampling (OYS), which instead treats timestep selection as a black-box optimization problem, optimizing the target metric directly with Bayesian optimization. OYS outperforms both the default schedules and those of Align Your Steps on text-to-image generation, and improves over the default schedules on inpainting and other image tasks, in both quantitative and human evaluations. OYS requires no additional training, is applicable even to distilled models, and improves both simple and sophisticated samplers such as Euler and DPM-Solver++. A 5-step OYS schedule retains 89%-94% of the quality of a 50-step schedule while reducing inference cost by 10x.

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