Tikhonov-Stabilized Bezier Representation Forecasting for Training-free Diffusion Acceleration

Lei Zhu; Mujie Lin; Ruochong Zheng; Guangyi Wang; Hao Li; Peng Jin; Chang Liu; Jie Chen

cs.CVOct 12, 2026

Tikhonov-Stabilized Bezier Representation Forecasting for Training-free Diffusion Acceleration

Authors: Lei Zhu, Mujie Lin, Ruochong Zheng, Guangyi Wang, Hao Li, Peng Jin, Chang Liu, Jie Chen

Organizations: School of Electronic and Computer Engineering, Peking University · School of Informatics, Xiamen University · Department of Automation and BNRist, Tsinghua University

Abstract

Diffusion models, particularly Diffusion Transformers, achieve strong image and video generation quality but remain expensive at inference time due to repeated denoiser evaluations. Feature caching offers a deployment-friendly acceleration strategy by reusing or predicting intermediate representations without retraining the generator or modifying the sampler. However, existing cache-then-forecast methods often rely on Taylor-style finite-difference extrapolation, which can become unstable over longer cache intervals, and typically predict local module outputs whose errors may accumulate through subsequent denoiser blocks. We propose BeziCast, a training-free diffusion acceleration framework that forecasts output-proximal denoising representations using low-order B'ezier trajectories. BeziCast estimates B'ezier control points via Tikhonov-stabilized fitting, providing a smooth, capacity-controlled temporal parameterization that avoids explicit high-order derivative estimation and decouples trajectory capacity from cache-query density. To moderate aggressive extrapolation, we further derive equivalent forecasting weights and introduce a convex-hull-inspired guardrail that detects high-risk predictions and softly pulls them toward a conservative simplex-projected estimate. Extensive evaluations across advanced image and video diffusion models demonstrate the effectiveness of BeziCast. In particular, BeziCast accelerates FLUX.1 by up to (4.79\times) and HunyuanVideo by up to (4.11\times), while preserving substantially better generation quality than competing acceleration baselines.

Figures & tables

Figure 1: Stable, Fast, and Accurate Diffusion Acceleration. Left : PC1 projections of output-proximal representation in denoising step. Right : Speedup and PSNR comparison, where $N$ is the cache interval. BeziCast achieves faster inference while better quality.

Figure 2: Overview of BeziCast. (a) A local cubic Bernstein/Bézier trajectory is fitted from cached full-step representations and evaluated at cache queries $u_{s}>1$ , providing a low-order alternative to Taylor-style extrapolation. (b) BeziCast detects risky extrapolation via equivalent history weights, constructs a simplex-projected prediction inside the cached-representation convex hull, and softly blends it with the raw forecast to obtain the guarded prediction.

Figure 3: BeziCast sampling pipeline. In the cache-then-forecast paradigm, selected full steps run the denoiser backbone and cache output-proximal representations, while intermediate cache steps skip the backbone and forecast the missing representation from history. BeziCast forecasts $\tilde{z}_{s}$ with Tikhonov-stabilized Bézier fitting and then uses the unchanged output head and sampler update.

Method	FLUX.1 [dev] / DrawBench							HunyuanVideo / VBench
	Acceleration		Quality			Image Reward $\uparrow$	CLIP $\uparrow$	Acceleration		Quality			VBench Quality $\uparrow$
	Latency(s) $\downarrow$	Speedup $\uparrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	Image Reward $\uparrow$	CLIP $\uparrow$	Latency(s) $\downarrow$	Speedup $\uparrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	VBench Quality $\uparrow$
50 steps †	37.681	1.00 $\times$	$-$	$-$	$-$	1.052	27.01	489.18	1.00 $\times$	$-$	$-$	$-$	84.03
25 steps	19.583	1.92 $\times$	17.350	0.679	0.228	0.998	27.23	252.40	1.94 $\times$	21.779	0.885	0.243	83.60
15 steps	12.379	3.04 $\times$	15.191	0.602	0.329	0.953	27.38	157.06	3.12 $\times$	18.894	0.796	0.382	83.47
FORA ( $\mathcal{N}=4$ )	11.208	3.36 $\times$	14.702	0.584	0.356	0.885	27.20	153.67	3.18 $\times$	17.892	0.740	0.421	83.21

Table 1: Benchmark results on text-to-image generation with FLUX.1 and text-to-video generation with HunyuanVideo. We use 50 steps as the reference ( † ). Our BeziCast achieves higher speedup while maintaining better sample quality across two speedup scenarios consistently.

Figure 4: Qualitative comparison on text-to-image generation using FLUX.1. BeziCast delivers the highest speedup while preserving prompt alignment, text readability, and visual fidelity.

Figure 5: Qualitative comparison on text-to-video generation using HunyuanVideo. BeziCast closely follow the 50-step reference, whereas TaylorSeer is slower and introduces visible artifacts.

Figure 6: Ablation on Tikhonov regularization and different forecasting targets. (a) Effect of the Tikhonov coefficient $\lambda$ . (b) Robustness score under equal relative-norm perturbations injected into different FLUX representations; higher values indicate smaller final-output changes.

Table 8

Variant	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	CLIP $\uparrow$	Rwd. $\uparrow$	Lat. $\downarrow$
None	20.993	0.750	0.115	27.192	1.028	10.109
PCA hull	20.930	0.750	0.115	27.214	1.031	10.150
Simplex	21.229	0.753	0.112	27.229	1.032	10.137

Table 4: Effect of equivalent-weight convex-hull guardrails in the Flux.1.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Forecasting target	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	CLIP $\uparrow$	ImageReward $\uparrow$	Latency $\downarrow$
Block-wise forecasting	22.993	0.793	0.075	27.091	1.035	15.208
Residual forecasting	23.289	0.798	0.074	27.097	1.026	14.016
Output-proximal forecasting $z_{s}$	23.287	0.798	0.074	27.099	1.038	11.530

Appendix

Table 5: Ablation on forecasting targets on FLUX. All variants use the same pretrained denoiser, sampler, cache schedule, history length, Bernstein order, Tikhonov coefficient, and guardrail configuration.

Output-proximal switch step	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	CLIP $\uparrow$	ImageReward $\uparrow$	Latency $\downarrow$
25	23.199	0.797	0.074	27.100	1.031	13.146
20	23.229	0.797	0.074	27.111	1.030	12.622
15	23.243	0.797	0.075	27.101	1.027	12.176
10	23.274	0.798	0.075	27.081	1.026	11.749
0 / before first cache step	23.287	0.798	0.074	27.099	1.038	11.530

Appendix

Table 6: Ablation on when to switch to output-proximal forecasting. Steps are 0-indexed; the first 8 steps are always full denoiser evaluations. Switching at the first cache step gives the best latency and overall fidelity in this setting.

Warm-up $W$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	CLIP $\uparrow$	ImageReward $\uparrow$	Latency / Speedup
3	17.070	0.623	0.242	27.117	0.984	7.881 / $4.78\times$
4	18.598	0.678	0.180	27.310	1.045	8.732 / $4.32\times$
5	20.010	0.724	0.135	27.414	1.046	9.383 / $4.02\times$
6	20.993	0.750	0.115	27.192	1.028	10.109 / $3.73\times$
7	22.206	0.780	0.093	27.060	1.028	10.848 / $3.47\times$
8	23.287	0.798	0.074	27.099	1.038	11.530 / $3.27\times$

Appendix

Table 7: Warm-up schedule ablation on FLUX. All rows use output-proximal BeziCast with

R=6

n=4

K_{\max}=6

, and

\lambda=0.5

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Diffusion Transformers achieve high-fidelity image and video generation, but their iterative sampling remains expensive, for each denoising step requires large matrix operations. Existing cache-based acceleration reduces redundant computation yet increases the VRAM footprint by storing intermediate states, which can directly constrain inference batch size. In this work, we propose a training-free acceleration method that performs stepwise forecasting for DiT sampling using a Barycentric Extrapolator. By leveraging barycentric extrapolation, our predictor is numerically stable and alleviates oscillatory artifacts analogous to the Runge phenomenon during forward forecasting. Across extensive experiments on both image and video generation, our approach provides a favorable trade-off between memory usage and perceptual quality, while delivering up to 3.30x end-to-end sampling speedup compared with baseline DiT inference.

Abstract

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