🤖 machine learning

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

The paper introduces ChebBooster, a training-free framework that leverages numerically stable Chebyshev polynomial extrapolation via Barycentric formulation to significantly accelerate Diffusion Transformer inference, achieving up to 3.68× latency speedup and 5.12× FLOPs reduction while maintaining high visual quality across multiple models.

Original authors: Chengjie Lu, Tianchi Deng, Zhengqi He, Chengwen Luo, Xueliang Li

Published 2026-08-25

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Chengjie Lu, Tianchi Deng, Zhengqi He, Chengwen Luo, Xueliang Li

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the world of artificial intelligence, a specific type of computer program has recently become the gold standard for creating images from scratch. These programs, known as diffusion models, work by starting with a screen full of random static noise and gradually cleaning it up, step by step, until a clear picture emerges. To make this process faster and more capable, researchers have begun using a powerful architectural style called the Transformer, which is excellent at understanding long-range connections within data. However, this power comes with a heavy price: to generate a single high-quality image, the computer must perform a massive number of calculations, often running the entire complex model dozens of times in a row. This makes generating images slow and energy-intensive, creating a bottleneck for anyone who wants to use these tools quickly or on standard hardware.

The core challenge lies in the repetitive nature of the process. As the image evolves from noise to clarity, the internal calculations the computer performs at one moment are often very similar to those performed a moment later. For years, scientists have tried to speed things up by remembering these previous calculations and reusing them, hoping to skip the heavy lifting. Yet, this approach has been a gamble. Simply reusing old data often leads to blurry or distorted images because the details drift too far from the truth over time. Other methods that try to predict the next step based on a mathematical curve have suffered from a different problem: they become unstable, causing the predicted image to wobble or oscillate wildly, much like a bridge swaying in the wind. The result has been a trade-off where saving time meant sacrificing the quality of the art.

A team of researchers has now introduced a new method called ChebBooster, which aims to break this trade-off without requiring the model to be retrained or relearned. Instead of guessing the next step with a simple curve or blindly copying old data, this new system uses a sophisticated mathematical strategy to look at a series of past steps and predict the future ones with high precision. The researchers realized that while some prediction methods are prone to wild swings and errors when looking far ahead, a specific type of mathematical smoothing technique could remain steady. By carefully selecting how they measure the distance between past steps and applying a stable weighting system, they created a way to skip the heavy calculations entirely for many of the intermediate steps.

The process works in two distinct phases. First, before the image generation even begins, the system prepares a set of instructions based on the schedule of how often it will check its work. It calculates a specific set of weights that determine how much importance to give to each of the last few known steps when predicting the next one. This preparation happens only once and can be saved for later use. Then, during the actual creation of the image, the computer runs the full, heavy calculation only at specific, spaced-out intervals. For all the steps in between, it simply combines the results from the last few full calculations using the pre-saved weights. This is not a guess; it is a precise reconstruction of what the computer would have calculated if it had done the hard work, allowing it to skip the heavy lifting while staying on the correct path.

The researchers tested this approach on three of the most advanced image-generating models currently available, covering tasks that range from creating images from simple text descriptions to generating highly detailed pictures at various resolutions. They found that the method consistently delivered images that were just as sharp and accurate as those produced by the standard, slower methods, but with a significant reduction in time and energy. In some tests, the new method made the process nearly four times faster and reduced the computational work by more than five times. Crucially, unlike previous attempts that tried to speed up the process by skipping steps, this method did not introduce the strange distortions or loss of detail that often plague accelerated generation. The images remained coherent, with fine textures and correct structures preserved, even when the computer was skipping the majority of its usual calculations.

What makes this discovery particularly notable is that it achieves these results without needing to teach the models anything new. The system works as a plug-in layer that sits on top of existing, pre-trained models, making it a practical tool that can be adopted immediately. The researchers demonstrated that by using this stable prediction technique, it is possible to generate high-fidelity images in a fraction of the time previously thought necessary. This suggests a future where powerful image generation becomes accessible on a wider range of devices, removing the barrier of massive computing costs while maintaining the high quality that users expect. The work confirms that by understanding the mathematical behavior of these models more deeply, it is possible to find shortcuts that are both safe and efficient, turning a slow, grinding process into a swift and reliable one.

Technical Summary: ChebBooster

1. Problem Statement

Diffusion Transformers (DiTs) have established state-of-the-art performance in high-fidelity image generation (e.g., class-to-image and text-to-image tasks). However, their inference process is computationally intensive because the full model must be executed at every timestep. While various acceleration strategies exist, they face significant limitations:

Naïve Caching: Methods that simply reuse intermediate features (e.g., FORA) suffer from low accuracy over long intervals, failing to align with the original feature trajectory and degrading generation quality.
Taylor-Series Extrapolation: Approaches like TaylorSeer model feature evolution via Taylor series expansion. While effective for short-range prediction, they are prone to numerical instability, specifically Runge oscillations, which cause large errors and deviations in long-range predictions.
Retraining Requirements: Many optimization strategies (e.g., quantization, VAE-based tuning) require retraining or finetuning, limiting their applicability to pre-trained models.

The core challenge is to achieve training-free acceleration that maintains high visual fidelity while avoiding the numerical instability of polynomial extrapolation and the accuracy loss of simple caching.

2. Methodology: ChebBooster

The authors propose ChebBooster, a training-free framework that leverages Chebyshev-inspired extrapolation to predict future features in DiTs. The method is built on three technical pillars:

A. Chebyshev-Inspired Extrapolation with Equispaced Nodes

While standard Chebyshev interpolation uses Chebyshev nodes to minimize the Runge phenomenon within an interval, the authors observe that for extrapolation (predicting outside the known domain), Chebyshev nodes can lead to explosive error growth.

Strategy: ChebBooster adopts equispaced nodes for the extrapolation task. Empirical evidence and theoretical analysis (Appendix A) suggest that for sparse data and long-range prediction, equispaced nodes provide more stable and accurate extrapolation than Chebyshev nodes, as the growth of the nodal polynomial is more controlled outside the interval.

B. Barycentric Formulation

To evaluate the extrapolation efficiently and stably, the method utilizes the Barycentric interpolation formula.

Mechanism: This formulation expresses the interpolant as a rational function using precomputed weights ( $\rho_j$ ).
Benefit: It offers high numerical stability and reduces computational overhead. Crucially, it separates the weights (dependent only on node locations) from the function values (the feature tensors).

C. Decoupled Two-Stage Framework

The authors decouple the extrapolation process into two distinct stages to minimize runtime overhead:

Offline Weight Precomputation: The barycentric weights are precomputed based on the caching schedule (refresh ratio $r$ ) and stored in a structured weight table. This step is independent of the specific feature values and can be reused for repeated inferences under the same schedule.
Online Forward Application: During inference:
- Full model computations are performed at sparse "reference" timesteps.
- Intermediate features are skipped and instead approximated using a lightweight linear combination of cached features from the history buffer, weighted by the precomputed coefficients.
- The complexity per module is reduced from a full network pass to $O(n)$ , where $n$ is the history size.

3. Key Contributions

Training-Free Acceleration: A method that accelerates DiT inference without requiring model retraining or finetuning.
Stable Extrapolation: The novel application of equispaced nodes within a Barycentric framework to mitigate Runge oscillations, addressing the instability issues found in Taylor-series-based methods.
Efficient Decoupling: A design that separates weight precomputation from inference, enabling significant latency reduction and making the method portable for large-batch inference.
Comprehensive Evaluation: Validation across three diverse DiT architectures (DiT-XL/2, PixArt-Σ, FLUX.1-dev) and multiple resolutions (256px to 1024px).

4. Experimental Results

Experiments demonstrate that ChebBooster achieves superior trade-offs between inference speed and generation quality compared to baselines like DDIM, FORA, ToCa, and TaylorSeer.

DiT-XL/2 (256×256): Achieved up to 1.674× latency speedup and 2.771× FLOPs reduction (with $r=3, H=3$ ) while maintaining an FID of 2.25 (superior to TaylorSeer's 2.34 and DDIM-25's 2.75). Under extreme acceleration ( $r=5$ ), it reached 1.894× speedup with an FID of 2.44.
PixArt-Σ (512×512): Reached 2.018× speedup with a peak CLIP score of 33.1699 (at $r=4, H=4$ ), outperforming TaylorSeer by 31.5% in speed. Under aggressive settings ( $r=6, H=2$ ), it achieved 2.513× speedup with an Image Reward of 1.0784, significantly outperforming competitors in both speed and fidelity metrics.
FLUX.1-dev (1024×1024): Achieved a record 3.679× speedup (7.078s runtime) with an Image Reward of 0.9962 (at $r=6$ ), significantly outperforming TaylorSeer (3.365× speedup) and maintaining structural integrity. At $r=5$ , it achieved 3.242× speedup with a superior Image Reward of 1.0070.
Qualitative Analysis: Visual studies indicate ChebBooster preserves fine-grained textures, semantic alignment, and object structure better than competing methods, avoiding artifacts like hallucinated limbs or blurred details common in aggressive acceleration regimes.

5. Significance and Claims

The paper claims that ChebBooster provides a practical and scalable solution for accelerating Diffusion Transformers. Its significance lies in:

Overcoming the Accuracy-Speed Trade-off: It achieves higher acceleration ratios than existing training-free methods without the catastrophic quality drop associated with naïve caching or the instability of Taylor extrapolation.
Generality: The method is model-agnostic regarding the specific DiT architecture, working effectively across C2I and T2I tasks with varying resolutions.
Efficiency: By decoupling weight computation, it offers a "drop-in" accelerator that is particularly beneficial for large-batch inference scenarios where precomputation costs are amortized.

The authors conclude that ChebBooster opens avenues for future exploration into adaptive caching and hybrid extrapolation strategies, establishing a new baseline for efficient generative modeling.