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ChebBooster: A Training-Free Approach for Efficient Diffusion Transformer Inference via Chebyshev-Inspired Extrapolation

Chengjie Lu, Tianchi Deng, Zhengqi He, Chengwen Luo, Xueliang Li

arXiv:2608.23429v1cs.LGcs.AI

TL;DR

ChebBooster addresses the need to approximate future Diffusion Transformer features for training-free acceleration by using Chebyshev-inspired extrapolation with stable Barycentric evaluation. Across multiple DiT models, tasks, and resolutions, it achieves superior acceleration-quality trade-offs, including 3.679× speedup on FLUX.1-dev.

  • Problem

    Training-free acceleration requires approximating future feature tensors from a small set of known cache points during diffusion sampling.

    Source: §3.2 · p. 4

  • Method

    ChebBooster uses Chebyshev polynomial extrapolation with Barycentric evaluation, separating offline weight precomputation from lightweight online application.

    Source: §1 · p. 2, §5 · p. 9

  • Results

    Across multiple DiT-based models, tasks, and resolutions, ChebBooster achieves superior acceleration-quality trade-offs; on FLUX.1-dev it reaches 3.679× latency speedup and 4.993× FLOPs reduction.

    Source: §5 · p. 9, §4.4 · p. 9

  • Takeaways & Limitations

    ChebBooster provides stable, efficient sampling acceleration while preserving visual fidelity at high acceleration ratios.

    Source: §5 · p. 9

Abstract

from arXiv · show

Diffusion Transformers (DiTs) have shown strong performance in high-fidelity image generation, but their sampling process remains computationally intensive due to full model execution at every timestep. While cache-based acceleration has been explored to mitigate inference cost, naive reuse schemes suffer from low accuracy over long intervals, and Taylor-series-based extrapolation methods often face instability caused by Runge oscillations. In this paper, we propose ChebBooster, a training-free extrapolation framework based on Chebyshev polynomial theory that achieves stable and efficient acceleration for DiTs. Specifically, we adopt the Barycentric formulation to evaluate Chebyshev approximants with high numerical stability and minimal overhead, and further decouple the extrapolation into an offline weight precomputation phase and a lightweight online application stage. Extensive experiments across three representative DiT-based models, including DiT-XL/2, PixArt-$Σ$, and FLUX.1-dev, demonstrate that ChebBooster achieves consistent improvements in visual quality and inference efficiency, reaching up to $3.68\times$ latency speedup and $5.12\times$ FLOPs reduction, outperforming existing training-free baselines under diverse generation tasks and resolutions.

1. Introduction

DiT sampling is expensive because full model execution is required at every timestep, motivating inference-time caching and extrapolation. ChebBooster addresses the limitations of naive reuse and Taylor-series extrapolation with stable Chebyshev-inspired extrapolation and offline-precomputed barycentric weights.

Motivation

  • Full model execution at every denoising timestep makes DiT sampling computationally intensive.Source: §1 · p. 1

Existing acceleration methods

  • Inference-time caching exploits temporal redundancy, but FORA has limited correction capacity over large timestep intervals.Source: §1 · p. 2, Figure 1 · p. 2
  • TaylorSeer models future representations through Taylor-series extrapolation, yet its extrapolation errors exhibit larger mid-trajectory oscillations.Source: §1 · p. 2, Figure 2 · p. 2

ChebBooster

  • ChebBooster extends Chebyshev interpolation into extrapolation to predict future DiT features across diffusion timesteps.Source: §1 · p. 2
  • The barycentric formulation improves numerical stability and reduces interpolant-evaluation overhead, while its schedule-dependent weights enable offline precomputation and lightweight online application.Source: §1 · p. 2

2. Related Works

Diffusion models use iterative sampling methods to balance generation quality and efficiency, while recent work increasingly reuses intermediate features. ChebBooster represents a two-stage framework that combines sparse full forwards with feature extrapolation to reduce redundant computation.

ChebBooster

  • ChebBooster performs full-network computation at selected reference timesteps and replaces other expensive forwards with lightweight extrapolation from cached features.Source: Figure 3 · p. 3
  • Its two-stage design precomputes Chebyshev-inspired weights offline and applies cached activations with those weights online.Source: Figure 3 · p. 3

Sampling acceleration

  • Diffusion models use DDIM, high-order solvers, flow-based formulations, distillation, and consistency models to reduce sampling cost.Source: §2.2 · p. 3

Feature caching

  • Caching methods exploit temporal redundancy in intermediate features, but DeepCache relies on U-Net features and therefore has limited generalizability to transformer architectures.Source: §2.3 · p. 3

3. Method

ChebBooster accelerates DiT inference by extrapolating future feature tensors from cached timestep features using Chebyshev-inspired interpolation. It combines equispaced-node extrapolation, barycentric evaluation, precomputed coefficients, and lightweight online feature reuse.

Chebyshev-Inspired Extrapolation

  • Barycentric interpolation provides a numerically stable and efficient weighted representation of the interpolant using known function values.The barycentric weights are precomputed, separating interpolation coefficients from cached feature values.Source: §3.2 · p. 5
  • Chebyshev nodes can produce larger long-range extrapolation errors than equispaced nodes, so ChebBooster adopts equispaced nodes for stability.This choice is supported by the Runge-function comparison in Figure 4.Source: Figure 4 · p. 4, §3.2 · p. 5

ChebBooster

  • ChebBooster replaces selected full-network computations with extrapolation from previously cached DiT features.The method targets training-free acceleration by predicting future feature tensors across diffusion timesteps.Source: §3.3 · p. 5
  • Diffusion timesteps are normalized to τ∈[−1,1], while full-computation timesteps provide cached feature nodes for extrapolation.A query timestep is mapped to a target feature estimate using the cached values and precomputed coefficients.Source: §3.3 · pp. 5–6
  • The method separates weight precomputation from forward application, with a schedule selecting full computations and extrapolation steps.Coefficients are computed once and stored; full-step feature tensors are detached and placed in a fixed-size history buffer.Source: §3.3 · p. 6
  • Cached feature extrapolation reduces per-module computation to O(n) and can be packaged as a portable drop-in inference accelerator.At skipped timesteps, the target feature is formed through a lightweight linear combination of cached tensors.Source: §3.3 · p. 7

4. Experiments

Experiments across DiT-XL/2, PixArt-Σ, and FLUX.1-dev show that ChebBooster maintains strong visual quality while accelerating inference, including under aggressive settings.

Experimental Settings

  • ChebBooster was evaluated on DiT-XL/2, PixArt-Σ, and FLUX.1-dev across class-to-image and text-to-image tasks at 256×256, 512×512, and 1024×1024 resolutions.The evaluation used official weights and 50 sampling steps, with DDIM for the first two models and Rectified Flow for FLUX.Source: §4.1 · p. 7

Results on DiT-XL/2

  • At r=3, ChebBooster (H=3) achieved the lowest DiT-XL/2 FID of 2.25 with a 1.674× latency speedup.It was 13.6% faster than TaylorSeer and 9.8% faster than DDIM-25.Source: §4.2 · p. 8

Results on PixArt-Σ

  • At r=4, ChebBooster reached 2.018× speedup with a peak PixArt-Σ CLIP score of 33.1699 and 3.652× FLOPs reduction.Its CLIP score surpassed DDIM-50 by 0.43%, while its speed exceeded TaylorSeer by 31.5%.Source: §4.3 · p. 8
  • Under PixArt-Σ acceleration at r=6 and H=2, ChebBooster maintained Reward=1.0784, while FORA and ToCa dropped to 0.9493 and 0.9873.The corresponding decreases were Δ-16.0% for FORA and Δ-9.4% for ToCa.Source: §4.3 · p. 8

Qualitative Study

  • Qualitative comparisons showed sharper structure, finer textures, stronger prompt alignment, and better preservation of facial and object details than competing methods.The FLUX.1-dev comparisons also reported fewer hallucinations such as extra limbs or missing elements under strong acceleration.Source: §4.3 · p. 8, §4.4 · p. 9

Results on FLUX.1-dev

  • At r=5 on FLUX.1-dev, ChebBooster achieved 3.242× latency speedup with Reward=1.0070 and 4.162× FLOPs reduction.At r=6, it reached 3.679× speedup while matching the baseline CLIP score and preserving Image Reward of 0.9962.Source: §4.4 · p. 9

5. Conclusion

ChebBooster is a training-free DiT acceleration framework that uses stable Chebyshev extrapolation and lightweight feature prediction. Experiments across tasks and resolutions report superior acceleration-quality trade-offs and practical scalability for generation and large-batch inference.

Method

  • ChebBooster uses Chebyshev polynomial extrapolation to predict future DiT features and reduce redundant computation during sampling.It is presented as a training-free acceleration framework.Source: §5 · p. 9
  • Barycentric interpolation provides efficient and stable evaluation, while offline weight precomputation and lightweight online application reduce extrapolation overhead.The design addresses numerical instability and computational overhead associated with polynomial extrapolation.Source: §5 · p. 9

Results

  • Experiments across C2I and T2I tasks at varying resolutions show superior acceleration-quality trade-offs to prior cache-based methods in visual fidelity and computational efficiency.The evaluation covers multiple DiT-based models.Source: §5 · p. 9

Conclusion

  • At high acceleration ratios, ChebBooster provides a practical and scalable solution for generation and large-batch inference.The conclusion also identifies adaptive caching and hybrid extrapolation as directions for future exploration.Source: §5 · p. 9

A. Extensive Proof for Chebyshev-Inspired Extrapolation

ChebBooster justifies barycentric extrapolation with equispaced nodes for sparse, long-range predictions, prioritizing numerical stability outside the interpolation interval. The method combines mathematically derived weights with an O(N)-per-point evaluation scheme.

Barycentric Formulation

  • The barycentric formulation evaluates the interpolant using weights determined by node geometry rather than function values.Applying the constant-function identity yields the numerically stable second barycentric form.Source: A. Extensive Proof for… · p. 13

Node Selection

  • Chebyshev-node optimality for interpolation does not extend to extrapolation, where the Chebyshev polynomial grows exponentially for |x| > 1.This growth can produce large extrapolation errors despite near-optimal interpolation stability.Source: A. Extensive Proof for… · p. 14

Weight Construction

  • For equispaced nodes, alternating binomial-coefficient weights follow directly from the barycentric principle rather than an ad hoc design.The paper states that these weights correctly implement Lagrange polynomial extrapolation.Source: A. Extensive Proof for… · pp. 14–15

Barycentric Formulation

  • O(N) evaluation per point gives the barycentric formula low computational overhead.The formulation is presented as both numerically stable and computationally efficient.Source: A. Extensive Proof for… · pp. 14–15

Node Selection

  • ChebBooster uses barycentric extrapolation with equispaced nodes to improve stability for sparse predictions outside the interpolation interval.The paper argues that equispaced nodes can have more moderate nodal-polynomial growth than Chebyshev nodes during extrapolation.Source: A. Extensive Proof for… · pp. 13–15

B. Pseudocode of ChebBooster

ChebBooster separates coefficient preparation from feature extrapolation during inference. Offline coefficients are prepared for non-full-computation steps, while online inference stores full-step features and applies those coefficients.

Two-Stage Algorithm

  • ChebBooster has offline precomputation and online application stages.This separation reduces the work required during cache-based forecasting.Source: B. Pseudocode of ChebBooster · p. 15

Offline Precomputation

  • Offline precomputation defines a full-computation schedule and stores interpolation coefficients for the remaining steps.The schedule uses model and sampling parameters before inference begins.Source: B. Pseudocode of ChebBooster · p. 15

Online Application

  • Online inference records features from full-computation steps in a history buffer and uses precomputed coefficients at extrapolation steps.The resulting approximated feature proceeds with the diffusion step.Source: B. Pseudocode of ChebBooster · p. 15

C. Additional Introduction to Experiment Settings

Experiments use RTX 4090 GPUs for DiT-XL/2 and PixArt-Σ, and an A800 for FLUX.1-dev. PixArt-Σ evaluation separates repeated text embedding from sampling, while T2I settings use seed 2025.

Hardware

  • DiT-XL/2 and PixArt-Σ experiments run on Nvidia RTX 4090 GPUs, while FLUX.1-dev experiments run on an Nvidia A800 GPU.The hardware differs by model family.Source: C. Additional Introduction to… · p. 15

Evaluation Procedure

Reproducibility

D. Additional Experiments on DiT-XL/2

Additional DiT-XL/2 experiments examine quality–efficiency trade-offs, parameter roles, and configurations for quality or computational efficiency. ChebBooster maintains strong quality while substantially reducing computation relative to original sampling baselines.

Experimental Design

Results

  • ChebBooster improves the performance-efficiency frontier: Cheb (r=5, n=5) achieves FID 2.28 versus 3.27 and IS 247.27 versus 235.35 for Original (20 steps), with 10% fewer FLOPs.The experiments also report that Original sampling from 50 to 10 steps cuts FLOPs nearly 80% while worsening FID from 2.18 to 11.19.Source: D. Additional Experiments on DiT-XL/2 · p. 16

Parameter Recommendations

  • Cheb (r=3, n=5) reaches IS 247.27 and FID 2.28 while reducing computational cost by over 63% versus Original (50 steps).It is recommended when maximizing generation quality among accelerated configurations.Source: D. Additional Experiments on DiT-XL/2 · p. 17
  • Cheb (r=7, n=2) uses 4.295 GFLOPs and improves FID from 11.19 to 3.98 versus Original (10 steps) at a similar computational budget.It is recommended for resource-limited deployment.Source: D. Additional Experiments on DiT-XL/2 · p. 17

Results

E. Extensive Visual Quality Analysis of ChebBooster

ChebBooster consistently produces visually superior images across class-to-image and text-to-image comparisons, preserving sharpness, semantic fidelity, and structural coherence. These results indicate a favorable acceleration–quality trade-off across models and prompts.

  • ChebBooster consistently outperforms Δ-DiT, FORA, ToCa, and TaylorSeer in sharpness, semantic fidelity, and structural coherence across evaluated prompts and classes.The comparisons cover both class-to-image and text-to-image generation tasks.Source: E. Extensive Visual Quality Analysis… · p. 17

PixArt-Σ

  • ChebBooster preserves fine-grained textures, defined contours, vivid colors, and global consistency in PixArt-Σ outputs.TaylorSeer and Δ-DiT exhibit blurriness or semantic degradation, while ToCa and FORA often produce washed-out textures or simplified details.Source: E. Extensive Visual Quality Analysis… · pp. 17, 19

FLUX.1-dev

  • ChebBooster retains facial features, object poses, and stylistic elements in FLUX.1-dev images that other methods often lose or distort.The method is described as outperforming all other baselines in semantic correctness and visual appeal in this setting.Source: Figure 11 · p. 18, E. Extensive Visual Quality Analysis… · p. 19
  • ChebBooster achieves a better trade-off between acceleration and image quality, with robustness across different models and prompts.The qualitative results suggest generalization to diverse generative scenarios.Source: E. Extensive Visual Quality Analysis… · p. 19

F. Prompts for Demonstration

The demonstration uses prompts spanning varied subjects and artistic styles for PixArt-Σ and FLUX.1-dev. The examples include both realistic and illustrated image-generation scenarios.

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