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Shangwen Zhu\*, Han Zhang\*, Zhantao Yang\*, Qianyu Peng\*, Zhao Pu Huangji Wang, Fan Cheng†
Shanghai Jiao Tong University, Shanghai, China
zhushangwen6,hzhang9617,ztyang196@gmail.com karry2020@alumni.sjtu.edu.cn
wanghuangji,pz-23dy@sjtu.edu.cn chengfan85@gmail.com
# Abstract
Text-based diffusion models have made significant breakthroughs in generating high-quality images and videos from textual descriptions. However, the lengthy sampling time of the denoising process remains a significant bottleneck in practical applications. Previous methods either ignore the statistical relationships between adjacent steps or rely on attention or feature similarity between them, which often only works with specific network structures. To address this issue, we discover a new statistical relationship in the transition operator between adjacent steps, focusing on the relationship of the outputs from the network. This relationship does not impose any requirements on the network structure. Based on this observation, we propose a novel training-free acceleration method called LTC-AccEL, which uses the identified relationship to estimate the current transition operator based on adjacent steps. Due to no specific assumptions regarding the network structure, LTC-AccEL is applicable to almost all diffusion-based methods and orthogonal to almost all existing acceleration techniques, making it easy to combine with them. Experimental results demonstrate that LTC-AccEL significantly speeds up sampling in text-to-image and text-to-video synthesis while maintaining competitive sample quality. Specifically, LTC-AccEL achieves a speedup of $1.67 \times$ in Stable Diffusion v2 and a speedup of $1.55 \times$ in video generation models. When combined with distillation models, LTC-AccEL achieves a remarkable $10 \times$ speedup in video generation, allowing real-time generation of more than 16FPS. Our code (include colab version) is available on Project Page.
# 1. Introduction
Recent advancements in text-based generation, particularly with diffusion models [6, 9, 27, 29, 30], have sig-
Figure 1. Comparison between LTC-ACCEL with DPM-Solver++ when implemented on Stable Diffusion v3.5 under the same number of steps and speedup framework. Results show that LTC-ACCEL significantly outperforms DPM-Solver++.
nificantly improved the generation of high-fidelity images [1, 7, 19, 43, 49, 57], audio [14, 17, 18, 24, 34, 45, 46], and video [4, 11, 16, 20, 28, 31, 52, 53] from textual descriptions, achieving remarkable advancements in visual fidelity and semantic alignment. By iteratively refining a noisy input until it converges to a sample that aligns with the given text prompt, these models capture intricate details and complex compositions previously unattainable with other approaches. Despite their impressive capabilities, a major drawback of diffusion models, particularly in video generation, is their high computational complexity during the denoising process, leading to prolonged inference times and substantial computational costs. For instance, generating a 5-second video at 8 frames per second (FPS) with a resolution of 720P using Wan2.1-14B [44] on a single H20 GPU takes approximately 6935 seconds, highlighting the significant resource demands of high-quality video synthesis. This limitation poses a considerable challenge for real-time applications and resource-constrained environments [1, 41].
(a) Combing LTC-AccEL with Deepcache (Cache).
(b) Combing with Distillation Model (Distill).
Figure 2. Qualitative results of LTC-AccEL integrated with existing training-free and training-based methods. Fig. 2a: Integration of LTC-AccEL with caching-based methods using DDIM on Stable Diffusion v2. Fig. 2b: Integration of LTC-AccEL with Animated-Diff-Lightning (distilled version of Animated-Diff). Results show that LTC-AccEL can be combined with previous methods well and achieve additional speedup without compromise on the quality of the generated images.
To accelerate diffusion models, various approaches have been proposed, including training-based and training-free strategies. Training-based methods enhance sampling efficiency by modifying the training process [12, 25, 38, 40, 42, 54, 59] or altering model architectures [15, 33, 39, 55], but they require additional computation and extended training. In contrast, training-free methods improve sampling efficiency without modifying the trained model by optimizing the denoising process [5, 10, 32, 37, 51] or introducing more efficient solvers [22, 23, 58]. Additionally, caching-based methods such as DeepCache [26, 47] exploit temporal redundancy in denoising steps to store and reuse intermediate features, thus achieving the reduction of redundant computations. However, these methods require a redesign of the caching strategy when the network architecture changes, limiting their flexibility across different models and configurations. Furthermore, they usually necessitate extra memory overhead to store intermediate representations, imposing constraints on resource-constrained deployment scenarios.
Unlike previous methods that rely on attention mechanisms or feature similarity within the network, we identify the phenomenon of Local Transition Coherence, which refers to the strong correlation between the transition operators $(\Delta x_{t + 1,t})$ of neighboring steps. Based on this insight, we propose LTC-AccEL, a novel training-free acceleration method that approximates the current step's transition operator using those from adjacent steps. As a result, it does not depend on any specific network architecture, making it broadly applicable to various diffusion models and compatible with both training-based and training-free acceleration methods.
We conducted extensive experiments demonstrating the effectiveness of our method and its compatibility with other approaches. LTC-Accel achieves a $1.67 \times$ speedup on Stable Diffusion v2 [35], and when combined with Deep-Cache [26], accelerates the process to $2.34 \times$ . It also integrates with Align Your Steps [37], achieving the equivalent of 10 steps of Align Your Steps in just 8 steps on Stable Diffusion v1.5 [35], with minimal impact on generation quality. Additionally, we achieve a $1.67 \times$ speedup on the Animated-Diff model [4], and by combining it with the distilled version, Animated-Diff-Lighting [20], we achieve a $10 \times$ speedup in video generation, enabling three-step generation. These results collectively illustrate that our proposed approach not only significantly reduces the computational load but also synergizes effectively with other optimization methods, facilitating highly efficient inference even under stringent resource constraints.
The core contributions of our work are:
- We have identified the phenomenon of Local Transition Coherence. Unlike previous approaches that rely on attention mechanisms or feature similarity within the network, this phenomenon reveals the inherent consistency of update trajectories, which is a broader consistency independent of any specific network architecture and pervasive throughout the diffusion sampling process.
- We propose LTC-AccEL, a training-free, highly generalizable method applicable to various diffusion models and orthogonal to both training-based and training-free acceleration methods, providing significant acceleration without sacrificing performance.
- We conducted extensive experiments to validate the ef
(a) Angle variation example.
(b) Acceleration error.
Figure 3. Variation of angle, error, and weight across sampling steps on Stable Diffusion v2 using DDIM with 20 steps and 20 unique prompt-latent pairs. (a) Angle variation per step. (b) Error between LTC-AccEL and the original process, with acceleration $(r = 2)$ applied over [12, 38], quantified by the 2-norm difference in latents. (c) $w_{g}$ variation, showing initial oscillations followed by rapid convergence.
(c) Convergence of $w_{g}$ .
fectiveness of our method and its compatibility with other approaches. LTC-AccEL significantly accelerates the generation process of models including Stable Diffusion, CogVideoX and Animated-Diff, and enhances performance when combined with existing acceleration methods.
# 2. Related Work
# 2.1. Training-Based Acceleration Methods
Traditional acceleration methods for diffusion models typically modify the model architecture or the sampling process during training for faster inference speed. Several typical approaches include mixed precision training and lightweight architectures [39, 55]. Recently, distillation [12, 25, 38, 40, 42, 54, 59] has gained popularity, focusing on reducing inference steps without significant quality loss. However, these methods require additional training, which can be both time-consuming and resource-intensive.
# 2.2. Training-Free Acceleration Methods
In certain scenarios where training resources are limited, training-free acceleration methods [5, 10, 32, 51] can outperform the training-based ones since they don't require any additional training, but are still capable of acceleration with little compromise to the performance. Thus, many successful training-free methods have been proposed and achieved promising effects. Optimized from the DDPM formulation, DDIM [41] is one of the typical attempts that has reduced the number of inference steps by introducing non-Markov process. The DPM-Solver [22, 23, 58] has also achieved significant reduction in the number of inference steps, while the implementation is focused on applying the specific high-order solver to solve diffusion ODEs [8, 56, 60]
equivalent to the denoising process. Besides, more recent approaches pay attention to preserving and reusing features from earlier steps, significantly reducing the computational load for subsequent steps. For example, DeepCache [26, 47] has performed exceptionally by reusing cacheable high-level features from consecutive steps and only updating low-level features, thus achieving nearly lossless acceleration. Moreover, optimizations on the sampling schedules have proved to be effective as well. Align Your Steps [37] has broadened its application scenarios by leveraging methods from stochastic calculus and applying optimal schedules specific to various solvers, pre-trained models and datasets.
# 3. LTC-Accel for Faster Diffusion Sampling
In this section, we first introduce the newly observed phenomenon called Local Transition Coherence in Sec. 3.1, which reveals the statistical correlation between the outputs of adjacent transition operations in the diffusion process. Next, in Sec. 3.2, we introduce our method, LTC-AccEL, which takes advantage of the transition operators of neighboring steps to approximate and replace the transition operator of the current step. Finally, in Sec. 3.3, we analyze the errors introduced by LTC-AccEL, which is negligible.
# 3.1. Local Transition Coherence
In this section, we introduce the newly observed phenomenon called Local Transition Coherence: During certain phases of the diffusion process, the transition operators of consecutive steps exhibit significant similarity. To quantify the difference between steps $t$ and $t + 1$ , we define the transition operator as $\Delta \mathbf{x}_{t+1,t} = \mathbf{x}_t - \mathbf{x}_{t+1}$ . Additionally, we define the angle between the transition operators at successive steps as follows:
Definition 3.1. The angle $\theta$ between $\Delta \mathbf{x}_{t + 1,t}$ and $\Delta \mathbf{x}_{t + 2,t + 1}$ is defined as
$$
\theta = \arccos \left(\frac {\Delta \mathbf {x} _ {t + 1 , t} \cdot \Delta \mathbf {x} _ {t + 2 , t + 1}}{\| \Delta \mathbf {x} _ {t + 1 , t} \| ^ {2} \| \Delta \mathbf {x} _ {t + 2 , t + 1} \| ^ {2}}\right). \tag {1}
$$
Note that when the angle $\theta$ approaches 0, the update trajectories of the two transition operators are nearly identical, and can be replaced by each other. As shown in Sec. 2, we observe that the angles are relatively small from steps 12 to 38, suggesting the update trajectories are highly similar during this period. This allows us to reduce unnecessary computations by approximating the current transition operator with that of the adjacent steps, thereby speeding up the sampling process significantly and effectively.
In practice, we define a threshold $\tau$ to identify the interval where $\theta$ remains relatively small, referred to as the acceleration interval and formally defined as follows:
Definition 3.2. The acceleration interval is defined as the range $[a, b]$ , where $a \geq 1$ , $b \leq T$ , and the value of $\theta$ for all $t \in [a, b]$ satisfies the following condition:
$$
\theta_ {t} < \tau , \quad \forall t \in [ a, b ]. \tag {2}
$$
During the acceleration interval, we approximate the update trajectories of the current step using those of previous steps, allowing us to skip the calculations for these steps, as shown in Sec. 2. Based on Local Transition Coherence, we propose a new training-free acceleration method called LTC-ACCEL, which improves the efficiency of the sampling process while maintaining the quality of the generated samples. It's important to note that Local Transition Coherence places no restrictions on the network's structure, meaning that LTC-ACCEL can be applied to nearly any diffusion model.
# 3.2. LTC-Accel: Transition Approximation
LTC-Accel reduces unnecessary computations by approximating the update trajectories of the current step using those from adjacent steps. In this section, we first introduce the formula for the approximated step. Next, we explain the conditions for this approximation and present the overall algorithm, followed by a description of the derivation.
Definition 3.3. With $\phi(t)$ denoting the denoising progress at step $t$ , the approximated step $x_{t}^{*}$ of step $t$ is defined as
$$
\mathbf {x} _ {t} ^ {*} = \mathbf {x} _ {t + 1} + w _ {g} \gamma \left(\Delta \mathbf {x} _ {t + 2, t + 1}\right), \tag {3}
$$
where $w_{g} = \frac{(\Delta\mathbf{x}_{t + 1,t})\cdot(\Delta\mathbf{x}_{t + 2,t + 1})}{\gamma\left\|(\Delta\mathbf{x}_{t + 2,t + 1})\right\|^{2}},\gamma = \frac{\phi(t) - \phi(t + 1)}{\phi(t + 1) - \phi(t + 2)}.$
Here, we would like to emphasize that although the calculation of $w_{g}$ relies on the target variable $\mathbf{x}_t$ , $w_{g}$ itself is a convergent quantity that depends solely on the step $t$ . To clearly identify the positions of the approximated steps, we define the acceleration condition:
Definition 3.4. The acceleration condition is defined as follows:
$$
t \bmod r = r - 1, \tag {4}
$$
where $t$ is the step number, and $r$ is a constant, mod stands for the modulo operation.
Based on these definitions, we propose LTC-ACCEL. During inference, following Eq. (2), we identify acceleration intervals. If the current step lies within an acceleration interval and satisfies the acceleration condition, we replace the original transition with the approximated step, as shown in Eq. (3). The detailed algorithm is presented in Algorithm 1.
# 3.2.1. Formalizing $\gamma$ and $w_{g}$
In this section, we explain how to select $\gamma$ and $w_{g}$ , which are crucial for implementing LTC-AccEL. The goal is to find appropriate values for $w_{g}$ and $\gamma$ that minimize the error of the approximated step, described as the difference between the approximated value $\mathbf{x}_t^*$ and the target value $\mathbf{x}_t$ as follows:
Definition 3.5. Parameter $w_{g}$ and $\gamma$ is defined as
$$
w _ {g}, \gamma = \underset {w _ {g}, \gamma} {\operatorname {a r g m i n}} \left(\left\| \Delta \mathbf {x} _ {t + 1, t} - w _ {g} \gamma \Delta \mathbf {x} _ {t + 2, t + 1} \right\| ^ {2}\right). \tag {5}
$$
Figure 4. Variation of PSNR values between original images and those generated by LTC-Accel as a function of bias, following the same experimental setup as Fig. 3.
Empirically determined value of $\gamma$ : $\gamma$ controls the relative weighting of the step intervals, effectively adjusting the influence of denoising progress on the update process. We denote the denoising progress at step $t$ as $\phi(t)$ and define it as $\phi(t) = \sqrt{\mathrm{SNR}_t}$ , where SNR represents the signal-to-noise ratio. This choice is motivated by the observation that as denoising progresses, the signal becomes increasingly dominant over noise, leading to a higher SNR. Taking
the square root of SNR provides a measure that scales more linearly with the improvement in signal quality, offering a practical representation of denoising progress. Consequently, we quantify the progress over the interval $[t,t + 1]$ as $\phi (t) - \phi (t + 1)$ , which serves as the foundation for defining $\gamma$ as follows:
$$
\gamma = \frac {\phi (t) - \phi (t + 1)}{\phi (t + 1) - \phi (t + 2)}. \tag {6}
$$
Optimal of $w_{g}$ : $w_{g}$ scales the magnitude of the transition operator. It is determined by minimizing the discrepancy between the actual transition and the approximated transition step, as given in Eq. (3). Here we provide the values of $w_{g}$ as follows (see supplementary for details):
$$
w _ {g} = \frac {\Delta \mathbf {x} _ {t + 1 , t} \cdot \Delta \mathbf {x} _ {t + 2 , t + 1}}{\gamma \left\| \Delta \mathbf {x} _ {t + 2 , t + 1} \right\| ^ {2}}. \tag {7}
$$
# 3.2.2. Convergence analysis of $w_{g}$
As shown in Eq. (5), the calculation of $w_{g}$ depends on $\mathbf{x}_{t}$ . However, during sampling, the value of $x_{t}$ is the target we aim to approximate, which poses a challenge to the approximation process. Fortunately, we observe that $w_{g}$ consistently exhibits convergence for across varying $\mathbf{x}_{t}$ , allowing us to determine the corresponding $w_{g}$ solely from $t$ . In this section, we first introduce the algorithm for evaluating $w_{g}$ , and then employ it to conduct a rigorous convergence analysis of $w_{g}$ .
Algorithm for Estimating $w_{g}$ : Computing $w_{g}$ is challenging because approximating $\mathbf{x}_t$ introduces cumulative errors that propagate through subsequent steps, affecting the accuracy of the sampling process, as illustrated in Sec. 2. To effectively mitigate this issue, we propose a two-step algorithm: 1) compute the current $w_{g}$ and use it to derive the approximated step $\mathbf{x}_t^*$ , which serves as the input for the next iteration; 2) perform a local search to optimize $w_{g}$ across the entire acceleration interval, minimizing cumulative errors (see Algorithm 2 for details).
Algorithm for Refining the Estimation of $w_{g}$ : Although the $w_{g}$ obtained by Algorithm 2 performs well, we introduce an optional refinement step to further improve the fidelity of accelerated images. Specifically, we use PSNR to evaluate and enhance the quality of accelerated images. This metric quantifies fidelity by measuring the similarity between an accelerated image and its non-accelerated counterpart. Typically, a PSNR above 30 dB signifies high-fidelity generation. The refinement algorithm consists of: 1) introducing a bias to adjust all $w_{g}$ values, and 2) conducting an end-to-end search within a predefined bias interval to determine the optimal adjustment (see Algorithm 3 for details).
Analysis of results: Similar to the convergence behavior observed in Sec. 2, the $w_{g}$ computed by Algorithm 2 consistently converges, ensuring the generality of our method
(see supplementary for more details). Additionally, Fig. 4 demonstrates that introducing a bias further enhances image similarity, increasing the PSNR from 37.5 to 39. The symmetry observed between bias and PSNR allows efficient optimization through binary search.
Algorithm 1 LTC-Accel Acceleration
1: Input: Diffusion model $p_{\theta}$ , acceleration interval $[a, b]$ , acceleration cycle $r$ , mapping $\phi$ , constant sequence $w_{g}$ , initial noise $\mathbf{x}_{N}$ .
2: Output: $x_{0}$ .
3: for $t = N$ to 0 do
4: if $t \in [a, b]$ and $t \mod r = r - 1$ then
5: $\gamma = \frac{\phi(t) - \phi(t + 1)}{\phi(t + 1) - \phi(t + 2)}$
6: $\mathbf{x}_t = \mathbf{x}_{t + 1} + w_g[t] \cdot \gamma \cdot \Delta \mathbf{x}_{t + 2, t + 1}$
7: else
8: $\mathbf{x}_t = p_{\theta}(\mathbf{x}_{t + 1}, t)$
9: end if
10: end for
11: return $\mathbf{x}_0$
Algorithm 2 Calculate $w_{g}$
1: Input: Diffusion model $p_{\theta}$ , acceleration interval $[a, b]$ , acceleration cycle $r$ , mapping $\phi$ , initial noise $\mathbf{x}_N$ .
2: Output: $w_g$ .
3: for $t = N$ to 0 do
4: if $t \in [a, b]$ and $t \mod r = r - 1$ then
5: $\gamma = \frac{\phi(t) - \phi(t + 1)}{\phi(t + 1) - \phi(t + 2)}$
6: $w_g[t] = \frac{\Delta x_{t + 1,t} \cdot \Delta x_{t + 2,t + 1}}{\gamma\|\Delta x_{t + 2,t + 1}\|^2}$
7: $\mathbf{x}_t^* = \mathbf{x}_{t + 1} + w_g\gamma (\Delta \mathbf{x}_{t + 2,t + 1})$
8: $\mathbf{x}_t = \mathbf{x}_t^*$
9: else
10: $\mathbf{x}_t = p_\theta (\mathbf{x}_{t + 1}, t)$
11: end if
12: end for
13: return $w_g$
Algorithm 3 (Optional) Improve $w_{g}$
1: Input: Diffusion model $p_{\theta}$ , free ride $p_{\theta}^{*}$ , bias interval [c,d], noise $x_0$ .
2: Output: Constant bias*.
3: $\mathbf{x}_0 = \prod_{t=N}^0 p_{\theta}(\mathbf{x}_{t+1}, t)$
4: bias* = argmax (PSNR(xN, $\prod_{t=N}^0 p_{\theta}^{*}(\mathbf{x}_{t+1}, t, w_g + bias)$ )
5: return bias*
(a)SD v2 (DDIM, ImageReward↑).
(b)SD v3.5 (DPMSolver++,ImageReward↑).
(c)SD v3.5 (EDM, ImageReward↑).
(d)SD v2 (DDIM,PickScore↑).
(e)SD v3.5 (DPMSolver++,PickScore↑).
(f)SD v3.5 (EDM,PickScore↑).
Figure 5. Quantitative results of text-to-image. We present our results on Stable Diffusion v2 and Stable Diffusion v3.5 by measuring the ImageReward and PickScore using 1000 prompt-image pairs. To demonstrate our compatibility with most schedulers, we use DDIM for sampling on Stable Diffusion v2, DPM-Solver++ and EDM for sampling on Stable Diffusion v3.5. The results demonstrate that our method achieves a $1.67 \times$ acceleration on Stable Diffusion v3.5, as well as a $1.67 \times$ acceleration on Stable Diffusion v2.
# 3.3. Error Analysis of the Approximated Step
In this section, we demonstrate that the error introduced by the approximation is generally negligible. We first provide the upper bound of the error of approximating a single step, followed by a comprehensive evaluation of the actual error incurred throughout the sampling process in practice.
Error of approximating a single step: Using the expressions for $w_{g}$ and $\gamma$ , we can estimate the relative error between the approximated step and the original step. When the angle between $\Delta \mathbf{x}_{t + 1,t}$ and $\Delta \mathbf{x}_{t + 2,t + 1}$ is less than a threshold $\tau$ , the relative error $\epsilon_r$ can be expressed as follows (see appendix for details):
$$
\epsilon_ {r} = \frac {\left\| \mathbf {x} _ {t} - \mathbf {x} _ {t} ^ {*} \right\| ^ {2}}{\left\| \Delta \mathbf {x} _ {t + 1 , t} \right\| ^ {2}} < \tau^ {2}. \tag {8}
$$
This implies that the relative error introduced by the approximate step is smaller than the update term of the original process, scaled by $\tau^2$ . When $\tau$ is typically on the order of magnitude of $[0.1, 0.2]$ , $\epsilon_r$ becomes negligible.
Error in practice: As the approximation of steps extends to $N$ steps during inference, the error accumulates, leading
to the results shown in the figure. The findings indicate that even when $32.5\%$ of the steps are approximated, the resulting error remains only $6.0\%$ , demonstrating that the error is nearly imperceptible. Notably, our method, LTC-AccEL, achieves a PSNR of 36.6, as illustrated in Fig. 4.
# 4. Experiments
In this section, we conduct extensive experiments to validate our method's effectiveness. First, in Sec. 4.1, we provide an overview of the experimental setup. Then, in Sec. 4.2 and Sec. 4.3, we present a comprehensive evaluation of text-to-image and text-to-video synthesis. In Sec. 4.4, we assess the integration of our method with other methods. Finally, we conduct ablation studies and provide detailed experimental settings in the Appendix.
# 4.1. Experimental Settings
In all experiments, unless otherwise specified, we use a classifier-free guidance [5] intensity of 7.5 without additional enhancement techniques. To evaluate acceleration performance, we perform inference in float16 and measure
<table><tr><td rowspan="2">Model</td><td colspan="3">DeepCache</td><td colspan="3">LTC-AccEL</td><td rowspan="2">Acceleration Condition</td><td rowspan="2">Speedup</td></tr><tr><td>Steps</td><td>Time(ms)</td><td>ImageReward↑</td><td>Steps</td><td>Time(ms)</td><td>ImageReward↑</td></tr><tr><td rowspan="4">SD v2</td><td>10</td><td>264</td><td>-0.2246</td><td>8</td><td>208</td><td>-0.2739</td><td>t mod r = r - 3, t > 4</td><td>1.25×</td></tr><tr><td>20</td><td>524</td><td>0.2445</td><td>16</td><td>419</td><td>0.2456</td><td>t mod r = r - 3, t > 8</td><td>1.25×</td></tr><tr><td>50</td><td>1411</td><td>0.4039</td><td>38</td><td>1038</td><td>0.4096</td><td>t mod r = r - 3, t > 12</td><td>1.41×</td></tr><tr><td>100</td><td>3014</td><td>0.4242</td><td>75</td><td>2171</td><td>0.4246</td><td>t mod r = r - 3, 24 < t ≤ 90</td><td>1.38×</td></tr></table>
Table 1. Quantitative evaluation of text-to-image generation via DDIM Sampling with LTC-Accel and DeepCache. In this experiment, the parameter $N$ of DeepCache is set to $N = 2$ , and the period parameter $r$ is set to $r = 3$ . The results are bold if they are better both in speed and quality. The results demonstrate that our method can be combined with DeepCache, achieving an additional $1.41 \times$ acceleration on top of DeepCache's speedup.
<table><tr><td rowspan="2">Model</td><td colspan="2">Ays</td><td colspan="2">LTC-AccEL</td><td rowspan="2">Speedup</td></tr><tr><td>Steps</td><td>ImageReward↑</td><td>Steps</td><td>ImageReward↑</td></tr><tr><td rowspan="3">SD v1.5</td><td>10</td><td>0.1332</td><td>8</td><td>0.1309</td><td>1.25×</td></tr><tr><td>20</td><td>0.1632</td><td>15</td><td>0.1510</td><td>1.33×</td></tr><tr><td>30</td><td>0.1901</td><td>20</td><td>0.2131</td><td>1.50×</td></tr></table>
Table 2. Quantitative evaluation of text-to-image generation via DPM-Solver++ sampling with LTC-Accel and Align Your Steps. The results demonstrate that our method can be integrated with Align Your Steps, achieving a $1.25 \times$ acceleration with minimal impact on the generation quality.
speedup based on the number of inference steps. Additionally, we set $\phi(t)$ , as mentioned in Sec. 3.2, to the $\sqrt{\mathrm{SNR}_t}$ values of the current step. All experiments are conducted without any additional training and we ensure that both the original model and LTC-AccEL start with consistent initial noise. In addition, for each prompt, we sample a unique starting noise to ensure variability.
# 4.2. Text-to-image Synthesis Task
In this section, we evaluate the performance of LTC-AccEL in text-to-image synthesis task.
Settings: We first introduce the configurations used for evaluation in this section: 1) Baselines: DDIM for Stable Diffusion v2 [36], EDM [8] and DPM-Solver++ [22] for Stable Diffusion v3.5-mid [3]. 2) Datasets: We employ the random 1,000 prompts from the MS-COCO 2017 dataset [21] for Stable Diffusion v2 trials, and Stable Diffusion v3.5-mid. 3) Metrics: In our experiments with Stable Diffusion v2 and v3.5-mid, we used the ImageReward metric [50] and PickScore [13]. ImageReward is a model trained on human comparisons to evaluate text-to-image synthesis, considering factors like alignment with text and aesthetic quality. PickScore, based on CLIP and trained on the Pick-a-Pic dataset, predicts user preferences for generated images.
Results: Fig. 5 presents the acceleration results from our experiments. LTC-AccEL demonstrates consistently strong performance across different text-to-image models and sampling methods. In particular, we obtain a $1.67 \times$ speedup on Stable Diffusion v2 and v3.5, which is notably high for a
training-free method.
# 4.3. Text-to-video Synthesis Task
In this section, we evaluate the performance of LTC-Accel on several video models in the text-to-video synthesis task. Settings: The configurations used for evaluation are as follows: 1) Baselines: We use Animated-Diff [4] and CogVideoX [53] 2B as baselines, with epiCRealism [2] as the base model for Animated-Diff. 2) Datasets: We randomly select 100 prompts from the MS-COCO 2017 dataset [21]. 3) Metrics: Following prior work [48], we evaluate video quality using Frame Consistency and Textual Faithfulness. Specifically, for Frame Consistency, we compute CLIP image embeddings for each frame and report the average cosine similarity across all frame pairs. For Textual Faithfulness, we compute the average ImageReward score between each frame and its corresponding text prompt.
Results: As shown in Tab. 3, LTC-AccEL obtains promising results across different video generation models. Notably, it can even achieve a $1.54 \times$ speedup with almost no impact on video generation quality.
# 4.4. Compatibility with Other Methods
Since LTC-AccEL leverages the relationship between the network's output, it introduces a completely new approach to acceleration. This makes it compatible with a wide variety of both training-based and training-free methods. In this section, we combine LTC-AccEL with various existing acceleration methods, both training-free and training-based,
<table><tr><td rowspan="2">Model</td><td colspan="3">Original</td><td colspan="3">LTC-AccEL</td><td rowspan="2">Speedup</td></tr><tr><td>Steps</td><td>Text↑</td><td>Smooth↑</td><td>Steps</td><td>Text↑</td><td>Smooth↑</td></tr><tr><td>Animated-Diff</td><td>10</td><td>0.2439</td><td>0.9713</td><td>7</td><td>0.2426</td><td>0.9700</td><td>1.43×</td></tr><tr><td>Animated-Diff</td><td>20</td><td>0.3050</td><td>0.9729</td><td>13</td><td>0.2939</td><td>0.9732</td><td>1.54×</td></tr><tr><td>Animated-Diff</td><td>30</td><td>0.3662</td><td>0.9676</td><td>19</td><td>0.3465</td><td>0.9681</td><td>1.58×</td></tr><tr><td>CogVideoX 2B</td><td>20</td><td>-0.1441</td><td>0.9442</td><td>14</td><td>-0.1673</td><td>0.9361</td><td>1.43×</td></tr><tr><td>CogVideoX 2B</td><td>30</td><td>0.2302</td><td>0.9464</td><td>19</td><td>0.2320</td><td>0.9435</td><td>1.58×</td></tr><tr><td>CogVideoX 2B</td><td>40</td><td>0.3918</td><td>0.9514</td><td>26</td><td>0.3775</td><td>0.9511</td><td>1.54×</td></tr><tr><td>CogVideoX 2B (int8)</td><td>40</td><td>0.2113</td><td>0.9456</td><td>26</td><td>0.2010</td><td>0.9449</td><td>1.54×</td></tr></table>
Table 3. Quantitative results of text-to-video, comparing Original and LTC-Accel settings. Text and Smooth denote Textual Faithfulness and Frame Consistency, respectively. The results are bold if they are better both in speed and quality. The results demonstrate that our method can be combined with video models well, achieving a $1.58 \times$ acceleration at most.
<table><tr><td rowspan="2">Model</td><td colspan="3">Original</td><td colspan="3">Distillation</td><td colspan="3">LTC-AccEL</td><td rowspan="2">Speedup</td></tr><tr><td>Steps</td><td>Text↑</td><td>Smooth↑</td><td>Steps</td><td>Text↑</td><td>Smooth↑</td><td>Steps</td><td>Text↑</td><td>Smooth↑</td></tr><tr><td>Animated-Diff-Lightning</td><td>4</td><td>0.3662</td><td>0.9685</td><td>3</td><td>0.2913</td><td>0.9673</td><td>3</td><td>0.3550</td><td>0.9645</td><td>1.33×</td></tr><tr><td>Animated-Diff-Lightning</td><td>8</td><td>0.3371</td><td>0.9697</td><td>5</td><td>0.2978</td><td>0.9690</td><td>5</td><td>0.3493</td><td>0.9654</td><td>1.60×</td></tr></table>
Table 4. Quantitative results of text-to-video, comparing Animated-Diff-Lightning (original steps), Animated-Diff-Lightning (same steps as LTC-AccEL), and LTC-AccEL. The results are bold if they are better both in speed and quality. The results demonstrate that our method can be integrated with Animated-Diff-Lightning, achieving an additional $1.60 \times$ acceleration with minimal impact on the generation quality.
for text-to-image and text-to-video tasks.
# 4.4.1. Combined with Training-Free Methods
In this part, our sampler configurations are meticulously set up as follows: 1) Baselines: We select DeepCache, Align Your Steps, and INT8 quantization as representatives of training-free methods and conduct experiments on Stable Diffusion v2. Specifically, DeepCache is a novel training-free method that accelerates diffusion models by leveraging temporal redundancy in the denoising process to cache and reuse features, while Align Your Steps is a principled method for optimizing sampling schedules in diffusion models, particularly efficient in few-step synthesis. INT8 quantization converts high-precision model parameters to 8-bit integers, accelerating video processing and inference while maintaining acceptable quality. 2) Datasets: The random 1,000 prompts from the MS-COCO 2017. 3) Metrics: ImageReward introduced in Sec. 4.2.
Results: Tab. 1 shows combining our method with Deep-Cache yields a $2.3 \times$ speedup and boosts ImageReward. Tab. 2 shows 10 Ays steps achieve 0.1332, while our method reaches 0.1309 with only 8 steps ( $1.25 \times$ faster). At 20 Ays steps ImageReward is 0.1632, our 15-step variant scores 0.1510 ( $1.33 \times$ faster). At 30 Ays steps ImageReward is 0.1901, while our 20-step variant surpasses it with 0.2131 ( $1.50 \times$ speedup). Finally, INT8 quantization on CogVideoX remains effective with our scheduler (Tab. 3).
# 4.4.2. Combined with Training-Based Methods
In particular, considering the setup of the distilled model, we do not use classifier-free guidance in this section. Our sampler configurations are meticulously set up as follows: 1) Baselines: We use Animated-Diff-Lightning as a representative of distilled models. Animated-Diff-Lighting [20] is a distilled version of the Animated-Diff model, designed to retain core functionality while optimizing performance. Specifically, we use the 8-step and 4-step weights of Animated-Diff-Lightning, where the 8-step weights correspond to 8-step inference and the 4-step weights correspond to 4-step inference. 2) Datasets: The random 100 prompts from the MS-COCO 2017 dataset [21]. 3) Metrics: Frame Consistency and Textual Faithfulness introduced in Sec. 4.3.
Results: The results in Tab. 4 show that our model can effectively accelerate distilled models, and even speed up the 4-step model to 3 steps with minimal impact on video generation quality, when compared to the original process with the same computational cost.
# 5. Limitations
Our method has two main limitations. First, its effectiveness relies on the Local Transition Coherence phenomenon, which weakens with very few sampling steps (under three). Second, while training-free, it mainly requires tuning optimal intervals, as other hyperparameters are straightforward.
# 6. Acknowledgement
This work received strong support from all co-authors. Fan Cheng provided overall guidance and supplied the computational resources. Shangwen Zhu was deeply involved throughout the entire project. Han Zhang contributed powerful theoretical insights. Zhantao Yang offered profound advice on manuscript writing and experimental design. Qianyu Peng helped design the experimental coding pipeline. Zhao Pu and Huangji Wang also proposed valuable suggestions for the paper. Also this work was supported in part by the National Key R&D Program of China under Grant 2022YFA1005000, in part by the NSFCunder Grant 61701304.
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