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
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 us>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 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 ↑
CLIP ↑
Acceleration
Quality
VBench Quality ↑
Latency(s) ↓
Speedup ↑
PSNR ↑
SSIM ↑
LPIPS ↓
Latency(s) ↓
Speedup ↑
PSNR ↑
SSIM ↑
LPIPS ↓
50 steps †
37.681
1.00 ×
−
−
−
1.052
27.01
489.18
1.00 ×
−
−
−
84.03
25 steps
19.583
1.92 ×
17.350
0.679
0.228
0.998
27.23
252.40
1.94 ×
21.779
0.885
0.243
83.60
15 steps
12.379
3.04 ×
15.191
0.602
0.329
0.953
27.38
157.06
3.12 ×
18.894
0.796
0.382
83.47
FORA ( N=4 )
11.208
3.36 ×
14.702
0.584
0.356
0.885
27.20
153.67
3.18 ×
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 λ . (b) Robustness score under equal relative-norm perturbations injected into different FLUX representations; higher values indicate smaller final-output changes.
Table 8
Variant
PSNR ↑
SSIM ↑
LPIPS ↓
CLIP ↑
Rwd. ↑
Lat. ↓
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 ↑
SSIM ↑
LPIPS ↓
CLIP ↑
ImageReward ↑
Latency ↓
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 zs
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 ↑
SSIM ↑
LPIPS ↓
CLIP ↑
ImageReward ↑
Latency ↓
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 ↑
SSIM ↑
LPIPS ↓
CLIP ↑
ImageReward ↑
Latency / Speedup
3
17.070
0.623
0.242
27.117
0.984
7.881 / 4.78×
4
18.598
0.678
0.180
27.310
1.045
8.732 / 4.32×
5
20.010
0.724
0.135
27.414
1.046
9.383 / 4.02×
6
20.993
0.750
0.115
27.192
1.028
10.109 / 3.73×
7
22.206
0.780
0.093
27.060
1.028
10.848 / 3.47×
8
23.287
0.798
0.074
27.099
1.038
11.530 / 3.27×
Appendix
Table 7: Warm-up schedule ablation on FLUX. All rows use output-proximal BeziCast with R=6 , n=4 , Kmax=6 , and λ=0.5 .
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.
Chengjie Lu, Tianchi Deng, Zhengqi He +3
College of Electronics and Information Engineering, Shenzhen University · School of Artificial Intelligence, Shenzhen University · College of Computer Science and Software Engineering, Shenzhen University
Diffusion Transformers (DiTs) achieve high-fidelity image and video generation, but they suffer from substantial inference costs due to repeated transformer evaluations across many denoising steps. Feature caching reduces this cost by reusing features across denoising steps. Recent forecasting methods extend this idea by extrapolating features to skipped steps instead of reusing them. However, existing forecasting methods extrapolate the features they predict uniformly, even though the spatial-frequency components of these features change most at different stages of denoising. They also overlook that denoising progresses nonuniformly, so equal step intervals can correspond to very different amounts of change. These mismatches amplify forecast errors as more steps are skipped, limiting the achievable acceleration. We propose SpecKCast, a training-free method that forecasts the model output in the frequency domain. SpecKCast applies a 2D discrete cosine transform (DCT) to the output and tracks each coefficient with a lightweight Kalman filter along a band-specific time coordinate derived from the noise schedule. The filter tracks each coefficient's value and rate of change, and the transformer is evaluated only when the filter's forecast uncertainty exceeds a threshold. Experiments on FLUX.1-dev, Qwen-Image, Wan2.1-14B, and HunyuanVideo show that SpecKCast achieves a better trade-off between acceleration and fidelity than existing caching and forecasting methods, reaching up to 6x speedup with less than 0.05 GiB of additional memory.
Javad Rajabi, Hakki Can Karaimer, David B. Lindell +2
University of Toronto · Vector Institute · AI Center–Toronto, Samsung Electronics
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× latency reduction across various DiT-based image and video generation models, while incurring negligible quality degradation.
Hanshuai Cui, Zhiqing Tang, Qianli Ma +3
School of Artificial Intelligence, Beijing Normal University, Beijing, China · Institute of Artificial Intelligence and Future Networks, Beijing Normal University, Zhuhai, China · Shenzhen University of Advanced Technology, Shenzhen, China