HiFlow: Training-free High-Resolution Image Generation with Flow-Aligned Guidance

We are very encouraged to see that you found our work effective and conducted comprehensive experiments. We sincerely thank you for your valuable suggestions, which certainly help improve our work. We have accordingly refined our paper as follows:

Q1: The figure outlining the pipeline is not straightforward to follow and makes it hard to grasp the essence of the method. Arrows eventually pointing to acceleration can be misleading. Illustration can be clarified further.

A1: Thanks for your valuable suggestions, and we sincerely apologize for any misunderstanding that may have been caused. The acceleration depicted in the pipeline figure is merely for visualization purposes, and the flow arrows should not eventually point to acceleration, as this could be misleading. We will comprehensively restructure the pipeline diagram in future versions for better presentation.

Q2: The choice of guidance weight decay function and its impact on parameters and image outputs of different resolutions are not extensively discussed. How sensitive is the method to the weight hyperparameters used in all three alignments?

A2: Thanks for your constructive advice. We have supplemented comprehensive sensitivity analysis experiments regarding guidance weight strategies (direction guidance weight $\alpha$ and acceleration guidance weight $\beta$) and other hyperparameters (noise adding ratio $\tau$ and normalized cutoff frequency $D$) at 2K and 4K resolution, as shown in the following tables.

For 2K generation, linear decay and cosine decay have similar performance, while for 4K generation, linear decay slightly outperforms cosine decay. We speculate that this is because the noise adding ratio is lower in the 4K generation, and the guidance strength of cosine decay may be insufficient at this lower noise level. Overall, both linear and cosine decay strategies enable gradually weakening control, significantly outperforming the constant guidance weight strategy without any decay. In our experiments, we used linear decay for both 2K and 4K.

Furthermore, we have also discussed the choices for noise adding ratio $\tau$ and normalized cutoff frequency $D$. For 2K generation, a relatively wide range of $\tau$ (e.g., $\tau\in[0.5,0.7]$) yields similar results. However, larger $\tau$ entails higher latency. Considering both performance and time cost, $\tau=0.6$ is chosen. For 4K generation, given the unstable synthesis capability of the backbone model, a smaller noise adding ratio ($\tau\in[0.2, 0.3]$) is more suitable. For both 2K and 4K generation, a moderate normalized cutoff frequency (e.g., $D\in[0.4,0.5]$) is recommended, as such a frequency effectively captures the image layout without carrying low-resolution detail information. In our experiments, we used $\tau=0.6$ for 2K, $\tau=0.3$ for 4K, and $D=0.4$ for both 2K and 4K.

Table: Quantitative evaluation on guidance weight strategies $\alpha$ and $\beta$ (2K resolution).

Table: Quantitative evaluation on guidance weight strategies $\alpha$ and $\beta$ (4K resolution).

Table: Quantitative evaluation on hyperparameters $\tau$ and $D$ (2K resolution).

Table: Quantitative evaluation on hyperparameters $\tau$ and $D$ (4K resolution).

Q3: More discussion about achieving fidelity with respect to the reference can be added. For instance in Fig. 5, although the palm tree and owl zoom-ins present more visual details, they are not consistent with the reference.

A3: Thank you for your valuable advice. Previous high-resolution generation works (e.g., DemoFusion and DiffuseHigh) typically enforced alignment of each step on their sampling trajectory with the same low-resolution endpoint. Despite higher similarity with the reference, they usually suffer from a limited amount of new details and risk generating artifacts and low-fidelity details. In contrast, HiFlow leverages the step-wise information of the low-resolution flow for guided generation, without mandating consistency with the low-resolution result. Instead of copying the low-resolution information, HiFlow effectively extends the model's synthesis capability learned at the training resolution to the high-resolution space through the proposed flow-aligned guidance, achieving high-resolution image generation with high fidelity and rich details.

Q4: How robust is the method to low-resolution reference? Would artifacts and lack of details in the reference potentially propagate or constrain the generation of high-res image?

A4: Thanks for your constructive comment. HiFlow is relatively robust to local artifacts in the low-resolution flow but may fail when facing severe structural anomalies.

It is observed that local artifacts in low-resolution images can be corrected in our high-resolution results. For instance, please refer to the "street" case in the lower right corner of Fig.F.5 in the appendix. In its 1K result (will be added in future versions), the items in the store window are blurry artifacts. However, in the 4K result generated by HiFlow, the artifacts are replaced with reasonable product details. This is because HiFlow leverages the low-resolution trajectory for flow-aligned guidance, which is a guided generation process rather than directly copying low-resolution information, allowing for the generation of new, reasonable details to replace artifacts. Additional visual results on artifact correction will be added in future versions.

However, if there exist significant structural anomalies (such as duplicate limbs) in the low-resolution results, the high-resolution results may inherit these errors. This stems from the limited performance of the image generation backbone.

Fortunately, given HiFlow's training-free and model-agnostic nature, such flaws can be effectively mitigated by integrating HiFlow into a stronger backbone model, using ControlNet to introduce external control conditions for controllable generation (see Fig.8 (b) in the main paper), or applying inference-time scaling techniques to search for a better low-resolution trajectory for the subsequent high-resolution generation.

Moreover, the lack of details in the reference typically does not affect the high-resolution generation. Consider the synthesis process from 1K to 4K, where 15 times more new content is generated, far exceeding the original, allowing for the addition of more details. However, the style specified by the prompt can have some impact on the amount of detail. For example, the comic/anime style will have slightly fewer details compared to those in the realistic style.

Thank you for sharing additional results verifying the effects of hyperparameters and weight decay functions across resolutions. The provided tables and discussion help clarify the design choices. Given that the method offers training-free adaption to high-resolution generations through bootstrapping on its low-resolution sample while improving details and being robust to artifacts, I maintain my original rating to recommend acceptance.

We are highly encouraged to see that you found our method effective, reasonable, and easy to understand. We sincerely thank you for your valuable suggestions, which certainly help improve our work. We have accordingly refined our paper as follows:

Q1: The acceleration visualizations are unclear. Could the authors provide more explanation or interpretation regarding what these visualizations represent and how they support the claims about detail fidelity?

A1: Thank you for your valuable advice, and we sincerely apologize for any misunderstanding that may have been caused. As we discussed in Section 3.3 in the main paper, the flow acceleration $a_t$ can eventually be expressed as:

$a_t = -\frac{1}{t_i}\frac{X_{0\leftarrow t_{i-1}}-X_{0\leftarrow t_i}}{t_{i-1}-t_i}=-\frac{1}{t_i}\frac{dX_{0\leftarrow t}}{dt},$

which indicates that the acceleration term $a_t$ essentially depicts the first order derivative of the estimated clean sample $X_{0\leftarrow t}$ with respect to timestep $t$, multiplied by a time-dependent factor $-1/t$. Note that the estimated clean sample $X_{0\leftarrow t}$ stands for the noise-free component of current noisy latent $X_t$, i.e. the expected clean image at timestep $t$. Therefore, $a_t$ can serve as an indicator of the sequence of content synthesized at each timestep, capturing the difference between estimated clean samples. In other words, $a_t$ reflects what content the model is responsible for adding at different timestep $t$. We visualize $a_t$ using the jet map from matplotlib, as shown in Fig.D.1 in the appendix, with the results clearly reflecting the model's synthesis content sequence. Leveraging acceleration alignment, we explicitly guide the model on what content to synthesize at each timestep in high-resolution generation, thereby avoiding the generation of unrealistic contents like repetitive patterns and abnormal textures and facilitating higher detail fidelity.

Q2: The evaluation dataset has not been specified or discussed. Only a single evaluation dataset is used in quantitative experiments, which may not provide a comprehensive view of HiFlow's effectiveness.

A2: Thanks for your valuable suggestions, and we sincerely apologize for any unclear descriptions regarding our evaluation dataset. The dataset we used contains 1K high-quality captions, primarily collected from previous works on high-resolution image generation (e.g., UltraPixel [1], I-Max [2]) and open-source datasets (e.g., LAION-400M [3], Aesthetic-4K [4]). Then, GPT-4o was employed to filter and polish them to improve quality. Eventually, our dataset covers a diverse range of generation scenarios and provides precise descriptions of image details. A brief comparison of the caption quality between our self-collected dataset and the open-sourced LAION-400M dataset is shown below:

Captions sampled from LAION-400M:

"Khoni Makan Urdu Novel by A Hameed"

"geisha+hairstyle+portrait+2"

Captions sampled from our evaluation dataset:

"A blood-red Ferrari SF90 parked on a rain-soaked city street at night, reflecting neon lights from nearby buildings. The wet pavement glistens, and the car’s smooth curves are highlighted by the ambient glow of the urban environment"

"Digital art of a beautiful tiger under an apple tree, cartoon style, matte painting, magic realism, bright colors, hyper quality, high detail, high resolution."

For a more comprehensive assessment, we have randomly sampled 1K captions from the LAION-5B [5] dataset to construct a new benchmark for quantitative evaluation and ablation study. The results are shown in the following tables. Please note that, due to the suboptimal quality of captions in the LAION-5B dataset, the CLIP Score for all tested methods has declined compared to our self-collected benchmark.

Table: Quantitative Evaluation on LAION-5B Benchmark.

Table: Ablation Study on LAION-5B Benchmark.

Q3: Can the three techniques proposed by HiFlow be well applied to high-resolution video generation tasks?

A3: Thank you for your constructive suggestions. We have validated the potential of HiFlow on the state-of-the-art T2V model WAN 2.1 [6], in which HiFlow exhibits remarkable effectiveness in training-free high-resolution video generation with flow-aligned guidance. Specifically, we integrate HiFlow with WAN 2.1-1.3B to generate videos at a resolution of $2080\times1200$ and set the number of frames to $33$ to save GPU memory. As measured by VBench [7] and CLIP [8] Score, HiFlow significantly improves WAN 2.1's generation capability at high resolution, especially in terms of visual quality and text-image similarity. Quantitative results are listed below. Please note that WAN 2.1 usually experiences generation collapse when directly inferring high-resolution videos, resulting in semantically void static videos, which is why its background consistency is slightly higher than HiFlow.

Reference

[1] Ren J, Li W, Chen H, et al. Ultrapixel: Advancing ultra high-resolution image synthesis to new peaks[J]. Advances in Neural Information Processing Systems, 2024, 37: 111131-111171.

[2] Du R, Liu D, Zhuo L, et al. I-max: Maximize the resolution potential of pre-trained rectified flow transformers with projected flow[J]. 2024.

[3] Schuhmann C, Vencu R, Beaumont R, et al. Laion-400m: Open dataset of clip-filtered 400 million image-text pairs[J]. arXiv preprint arXiv:2111.02114, 2021.

[4] Zhang J, Huang Q, Liu J, et al. Diffusion-4k: Ultra-high-resolution image synthesis with latent diffusion models[C]//Proceedings of the Computer Vision and Pattern Recognition Conference. 2025: 23464-23473.

[5] Schuhmann C, Beaumont R, Vencu R, et al. Laion-5b: An open large-scale dataset for training next generation image-text models[J]. Advances in neural information processing systems, 2022, 35: 25278-25294.

[6] Wan T, Wang A, Ai B, et al. Wan: Open and advanced large-scale video generative models[J]. arXiv preprint arXiv:2503.20314, 2025.

[7] Huang Z, He Y, Yu J, et al. Vbench: Comprehensive benchmark suite for video generative models[C]//Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2024: 21807-21818.

[8] Radford A, Kim J W, Hallacy C, et al. Learning transferable visual models from natural language supervision[C]//International conference on machine learning. PmLR, 2021: 8748-8763.

We are very encouraged to see that you found our work innovative, sound and addressing a significant challenge in text-to-image generation. We sincerely thank you for your valuable suggestions, which certainly help improve our work. We have accordingly refined our paper as follows:

Q1: Motivation of acceleration alignment, how does aligning acceleration empirically improve detail fidelity compared to direction alignment alone?

A1: Thanks for your valuable suggestions. Equipped with initialization alignment and direction alignment, we are able to generate high-resolution images with rich details and reasonable structures. However, it is observed that the synthesized details are often low-fidelity and unrealistic (see Fig.3 (d) in the main paper). To address these issues, we analyze the flow velocity $v_t$ at each timestep. It indicates the denoising direction of each step in the sampling trajectory, thereby determining the position of the next state. The emergence of low-fidelity details suggests that the content synthesized by the high-resolution flow deviates from the normal content synthesis distribution. This stems from the flow model's unstable performance in high-resolution generation.

To this end, we consider utilizing the rate of change of velocity (which represents acceleration in physics) to control the amount of change in velocity at each timestep within a reasonable range, thereby avoiding suboptimal denoising directions caused by unreasonable velocity predictions during high-resolution generation. Such a guidance signal is provided by the acceleration of the reference flow at each timestep, as it reflects the detail synthesis distribution learned by the model at its training resolution.

Through further derivation of the acceleration (detailed in the main paper), we uncover that the acceleration term $a_t$ can be expressed as: $a_t = -\frac{1}{t_i}\frac{X_{0\leftarrow t_{i-1}}-X_{0\leftarrow t_i}}{t_{i-1}-t_i}=-\frac{1}{t_i}\frac{dX_{0\leftarrow t}}{dt},$ which indicates that the acceleration term $a_t$ essentially depicts the first order derivative of the estimated clean sample $X_{0\leftarrow t}$ with respect to timestep $t$, multiplied by a time-dependent factor $-1/t$. Therefore, $a_t$ can serve as an indicator of the sequence of content synthesized at each timestep, capturing the difference between estimated clean samples. In other words, $a_t$ reflects what content the model is responsible for adding at different timesteps.

Motivated by the above analysis and derivation, we adopt acceleration alignment in high-resolution generation to guide the model on what content to synthesize at each timestep, thereby avoiding the generation of unrealistic contents and facilitating higher detail fidelity. In contrast, using only direction alignment does not achieve the same effect, as shown in the visual ablation results in Fig.7 in the main paper.

Q2: Sensitivity Analysis of Hyperparameters.

A2: Thanks for your constructive suggestions. We have supplemented comprehensive sensitivity analysis experiments regarding hyperparameters (noise adding ratio $\tau$ and normalized cutoff frequency $D$) at 2K and 4K resolution, as shown in the following tables.

For 2K generation, a relatively wide range of $\tau$ (e.g., $\tau\in[0.5,0.7]$) yields similar results. However, larger $\tau$ entails higher latency. Considering both performance and time cost, $\tau=0.6$ is chosen. For 4K generation, given the unstable synthesis capability of the backbone model, a smaller noise adding ratio ($\tau\in[0.2, 0.3]$) is more suitable. For both 2K and 4K generation, a moderate normalized cutoff frequency (e.g., $D\in[0.4,0.5]$) is recommended, as such a frequency effectively captures the image layout without carrying low-resolution detail information. In our experiments, we adopted $\tau=0.6$ for 2K generation, $\tau=0.3$ for 4K generation, and $D=0.4$ for both 2K and 4K generation.

Table: Quantitative evaluation on hyperparameters (2K resolution).

Table: Quantitative evaluation on hyperparameters (4K resolution).

Q3: Mitigation strategies for structural flaws from low-resolution inputs.

A3: Thank you for your valuable advice. Here, we provide three simple and effective methods to reduce the potential structural error in the low-resolution flow, thereby fundamentally preventing error propagation:

1. Since HiFlow is training-free and model-agnostic, it can be seamlessly adapted to a stronger image generation backbone, thereby reducing the probability of structural anomalies in the low-resolution flow. For example, HiFlow exhibits far fewer structural anomalies on Flux compared to SDXL.

2. HiFlow can be combined with controllable generation techniques such as ControlNet [1] (see Fig.8 (b) in the main paper). Therefore, ControlNet can be utilized to introduce structural control signals to avoid potential structural anomalies.

3. Inference time scaling methods [2] can be adopted to improve the quality of low-resolution results by searching for a better initial noise (to obtain a better low-resolution flow) for the subsequent high-resolution generation. They typically include an auxiliary evaluation model (such as a MLLM or a specific verifier model like ImageReward [3]) to assess the output quality and iteratively search for the next noise in the neighborhood of already searched high-quality noises. Since the evaluation is conducted at low resolution (1K), this approach does not entail a significant time cost.

Reference

[1] Zhang L, Rao A, Agrawala M. Adding conditional control to text-to-image diffusion models[C]//Proceedings of the IEEE/CVF international conference on computer vision. 2023: 3836-3847.

[2] Ma N, Tong S, Jia H, et al. Inference-time scaling for diffusion models beyond scaling denoising steps[J]. arXiv preprint arXiv:2501.09732, 2025.

[3] Xu J, Liu X, Wu Y, et al. Imagereward: Learning and evaluating human preferences for text-to-image generation[J]. Advances in Neural Information Processing Systems, 2023, 36: 15903-15935.

We are very encouraged to see that you found our method reasonable, interpretable and effective. We sincerely thank you for your valuable suggestions, which certainly help improve our work. We have accordingly refined our paper as follows:

Q1: HiFlow depends on low-resolution trajectory quality. The artifact or mistakes in the low-resolution image can have a bad influence on the high-resolution generation.

A1: Thanks for your constructive comment. HiFlow is relatively robust to local artifacts in the low-resolution flow but may fail when facing severe structural anomalies.

It is observed that local artifacts in low-resolution images can be corrected in our high-resolution results. For instance, please refer to the "street" case in the lower right corner of Fig.F.5 in the appendix. In its 1K result (will be added in future versions), the items in the store window are blurry artifacts. However, in the 4K result generated by HiFlow, the artifacts are replaced with reasonable product details. This is because HiFlow leverages the low-resolution trajectory for flow-aligned guidance, which is a guided generation process rather than directly copying low-resolution information, allowing for the generation of new, reasonable details to replace artifacts. Additional visual results on artifact correction will be added in future versions.

However, if there exist significant structural anomalies (such as duplicate limbs) in the low-resolution results, the high-resolution results may inherit these errors. This stems from the limited performance of the image generation backbone.

Fortunately, given HiFlow's training-free and model-agnostic nature, such flaws can be effectively mitigated by integrating HiFlow into a stronger backbone model, using ControlNet [1] to introduce external control conditions for controllable generation (see Fig.8 (b) in the main paper), or applying inference-time scaling techniques [2] to search for a better low-resolution trajectory for the subsequent high-resolution generation.

Q2: How robust the virtual reference flow is to artifacts in the low-resolution generation? Is there any method to reduce the risk of error propagation?

A2: Thank you for your valuable suggestion. As we discussed in the answer to Question 1, HiFlow (which obtains guidance from the virtual reference flow) is relatively robust to local artifacts but is not robust to severe structural anomalies.

Here, we provide three simple and effective methods to reduce the potential structural error in the low-resolution flow, thereby fundamentally preventing error propagation:

1. Since HiFlow is training-free and model-agnostic, it can be seamlessly adapted to a stronger image generation backbone, thereby reducing the probability of structural anomalies in the low-resolution flow. For example, HiFlow exhibits far fewer structural anomalies on Flux compared to SDXL.

2. HiFlow can be combined with controllable generation techniques such as ControlNet [1] (see Fig.8 (b) in the main paper). Therefore, ControlNet can be utilized to introduce structural control signals to avoid potential structural anomalies.

3. Inference time scaling methods [2] can be adopted to improve the quality of low-resolution results by searching for a better initial noise (to obtain a better low-resolution flow) for the subsequent high-resolution generation. They typically include an auxiliary evaluation model (such as a MLLM or a specific verifier model like ImageReward [3]) to assess the output quality and iteratively search for the next noise in the neighborhood of already searched high-quality noises. Since the evaluation is conducted at low resolution (1K), this approach does not entail a significant time cost.

Q3: The method requires high memory and computational cost. There are some acceleration sampling methods for diffusion or flow methods. Can they be used in the proposed method to accelerate the generation?

A3: Thanks for your insightful advice. As a training-free and model-agnostic framework, HiFlow can be seamlessly integrated with various acceleration methods for diffusion models. Here we take TeaCache [4] (an advanced caching-based acceleration technique) as an example. Equipped with TeaCache, HiFlow achieves a notable speedup in generating high-resolution images without significant quality degradation. Quantitative results are listed below:

Q4: Is there any detection method to prevent errors in the alignments?

A4: Thanks for your constructive comment. MLLM or reward models can be employed as detectors for errors in low-resolution results. For instance, inference time scaling techniques [2] typically include an auxiliary evaluation model (such as a MLLM or a specific verifier model like ImageReward [3]) to assess the quality of the diffusion model's outputs and iteratively search for the next noise in the neighborhood of already searched high-quality noises. Therefore, these auxiliary evaluation models can serve as effective detectors for structural anomalies in the low-resolution results, thus preventing errors in the following alignments for high-resolution generation.

Reference

[1] Zhang L, Rao A, Agrawala M. Adding conditional control to text-to-image diffusion models[C]//Proceedings of the IEEE/CVF international conference on computer vision. 2023: 3836-3847.

[2] Ma N, Tong S, Jia H, et al. Inference-time scaling for diffusion models beyond scaling denoising steps[J]. arXiv preprint arXiv:2501.09732, 2025.

[3] Xu J, Liu X, Wu Y, et al. Imagereward: Learning and evaluating human preferences for text-to-image generation[J]. Advances in Neural Information Processing Systems, 2023, 36: 15903-15935.

[4] Liu F, Zhang S, Wang X, et al. Timestep Embedding Tells: It's Time to Cache for Video Diffusion Model[C]//Proceedings of the Computer Vision and Pattern Recognition Conference. 2025: 7353-7363.

We are highly encouraged that you have found our work to have significant improvements over various strong baselines. We sincerely thank you for your valuable suggestions, which certainly help improve our work. We have accordingly refined our paper as follows:

Q1: HiFlow is a cascaded approach, thus all intermediate states have to be synthesized for generating a high-resolution image.

A1: Thanks for your valuable comment. Admittedly, given the cascaded nature of HiFlow, we have to synthesize all intermediate states in the process of generating high-resolution images. However, it can be theoretically and experimentally proven that the cascaded synthesis of high-resolution images is more efficient than direct synthesis in both time and memory.

Assuming the single-step inference time cost for generating a 1K image is $m$, due to the quadratic increase in time cost with the number of image tokens in self-attention, it can be approximated that the single-step inference time cost for generating an $n$K image is $n^2m$. Therefore, the time cost for directly sampling 30 steps to generate a 4K image can be expressed as:

$t_\text{Direct} = 30 \times 4^2\times m = 480m.$

In HiFlow, we perform the full 30-step generation at the 1K resolution, but only a portion of the timesteps at 2K and higher resolutions. According to our parameter settings, the time cost for HiFlow to synthesize a 4K image can be estimated as:

$t_\text{HiFlow} = 30 \times m + 18 \times 2^2 \times m + 9 \times 3^2 \times m + 9 \times 4^2 \times m = 327m,$

which indicates $t_\text{HiFlow} < t_\text{Direct}$, demonstrating that HiFlow is more efficient than directly inferring a 4K image. The latency comparison is provided in the following table:

Actually, HiFlow has achieved state-of-the-art efficiency among training-free methods, as shown in Tab.2 in the main paper.

Moreover, since the intermediate states are stored in the form of latent representations rather than internal model features (such as hidden states), the additional memory overhead is not significant, as shown in the following table:

Q2: What do $X_{0\leftarrow t}$ and $X_{1\leftarrow t}$ represent, respectively? How can we extract $X_{0\leftarrow t}$ given the prediction of the model and how does it look for a sample generation?

A2: Thanks for your constructive suggestion, and we sincerely apologize for any misunderstandings that may have been caused. $X_{0\leftarrow t}$ denotes the predicted/estimated clean component of the current noisy latent $X_t$, while $X_{1\leftarrow t}$ represents its corresponding noise component at timestep $t$.

For rectified flow models, the model output $v_\theta(X_t, t, c)$ stands for the flow vector/velocity (we use $v_t$ to denote $v_\theta(X_t, t, c)$ for simplicity). Given the model output $v_t$ and current noisy latent $X_t$ at timestep $t$, the estimated clean sample $X_{0\leftarrow t}$ and its corresponding estimated noise $X_{1\leftarrow t}$ can be obtained by:

$X_{0\leftarrow t} = X_t - v_tt,$ $X_{1\leftarrow t} = X_t + v_t(1-t).$ We will include visualizations of $X_{0\leftarrow t}$ and $X_{1\leftarrow t}$ in future versions to provide further clarity. At the current stage, a visualization example of $X_{0\leftarrow t}$ can be found in our pipeline figure (e.g., the visualization of $X^\text{low}_{0\leftarrow \tau}$).

Q3: Motivation of acceleration alignment.

A3: Thank you for your constructive comment. Equipped with initialization alignment and direction alignment, we are able to generate high-resolution images with rich details and reasonable structures. However, it is observed that the synthesized details are often low-fidelity and unrealistic (see Fig.3 (d) in the main paper). To address these issues, we analyze the flow velocity $v_t$ at each timestep. It indicates the denoising direction of each step in the sampling trajectory, thereby determining the position of the next state. The emergence of low-fidelity details suggests that the content synthesized by the high-resolution flow deviates from the normal content synthesis distribution. This stems from the flow model's unstable performance in high-resolution generation.

To this end, we consider utilizing the rate of change of velocity (which represents acceleration in physics) to control the amount of change in velocity at each timestep within a reasonable range, thereby avoiding suboptimal denoising directions caused by unreasonable velocity predictions during high-resolution generation. Such a guidance signal is provided by the acceleration of the reference flow at each timestep, as it reflects the detail synthesis distribution learned by the model at its training resolution.

Through further derivation of the acceleration (detailed in the main paper), we uncover that the acceleration term $a_t$ can be expressed as: $a_t = -\frac{1}{t_i}\frac{X_{0\leftarrow t_{i-1}}-X_{0\leftarrow t_i}}{t_{i-1}-t_i}=-\frac{1}{t_i}\frac{dX_{0\leftarrow t}}{dt},$ which indicates that the acceleration term $a_t$ essentially depicts the first order derivative of the estimated clean sample $X_{0\leftarrow t}$ with respect to timestep $t$, multiplied by a time-dependent factor $-1/t$. Therefore, $a_t$ can serve as an indicator of the sequence of content synthesized at each timestep, capturing the difference between estimated clean samples. In other words, $a_t$ reflects what content the model is responsible for adding at different timesteps. Motivated by the above analysis and derivation, we adopt acceleration alignment in high-resolution generation to facilitate higher detail fidelity.