Text-to-Image Rectified Flow as Plug-and-Play Priors

## Abstract

Abstract Large-scale diffusion models have achieved remarkable performance in generative tasks. Beyond their initial training applications, these models have proven their ability to function as versatile plug-and-play priors. For instance, 2D diffusion models can serve as loss functions to optimize 3D implicit models. Rectified Flow, a novel class of generative models, has demonstrated superior performance across various domains. Compared to diffusion-based methods, rectified flow approaches surpass them in terms of generation quality and efficiency. In this work, we present theoretical and experimental evidence demonstrating that rectified flow based methods offer similar functionalities to diffusion models — they can also serve as effective priors. Besides the generative capabilities of diffusion priors, motivated by the unique time-symmetry properties of rectified flow models, a variant of our method can additionally perform image inversion. Experimentally, our rectified flow based priors outperform their diffusion counterparts — the SDS and VSD losses — in text-to-3D generation. Our method also displays competitive performance in image inversion and editing. Code is available at: https://github.com/yangxiaofeng/rectified_flow_prior .

## 1 Introduction

Large-scale diffusion models (Ho et al., ; Song & Ermon, ; ; Rombach et al., ; Karras et al., ) have made significant advances in recent years. Applications in image generation (Rombach et al., ; Dhariwal & Nichol, ; Ho et al., ; Ramesh et al., ; Saharia et al., ), video creation (Guo et al., ; Blattmann et al., ), and music production (Huang et al., ) have demonstrated superior performance compared to traditional Generative Adversarial Networks (GANs) (Goodfellow et al., ; Karras et al., ; Brock, ). Beyond excelling in tasks for which they are specifically trained, various studies (Graikos et al., ; Poole et al., ; Wang et al., ; Yu et al., ) indicate that these models can also serve as plug-and-play priors for related tasks, i.e., using the pretrained diffusion models as loss functions. For instance, Dreamfusion (Poole et al., ) introduces the SDS loss, utilizing a pretrained text-to-image diffusion model to generate 3D objects. DDS (Hertz et al., ) extends the original SDS loss to address image editing challenges. Several subsequent works (Wang et al., ; Yu et al., ; Katzir et al., ; Yang et al., ) have refined the SDS loss to further enhance generation quality and diversity, applying diffusion priors to a variety of downstream applications, including 3D editing, 4D generation, and human avatar creation.

Rectified flow (Liu et al., ; Lipman et al., ; Albergo & Vanden-Eijnden, ) is a special type of flow-based method that connects data and noise on a straight line. Recently, methods based on rectified flow have garnered considerable research interest. Initial work such as InstalFlow (Liu et al., ) has demonstrated the capability to generate high-quality images in just a few inference steps. More recent developments, including SiT (Ma et al., ) and Stable Diffusion 3 (Esser et al., ), have achieved new state-of-the-art performance in image generation. Given this growing research focus, it remains to be seen whether large-scale pretrained rectified flow models can function as effective priors, similar to diffusion-based methods.

In this work, we explore how to distill knowledge from pretrained text-to-image rectified flow models and use them as priors for other tasks. To ensure our approach is generalizable and applicable to a wide range of flow-matching methods, we develop our method based on the generalized Stochastic Interpolants framework (Albergo et al., ) rather than directly deriving it from the rectified flow formulation. We then incorporate specific interpolation factors of rectified flow to adapt our method to this particular model type. We propose three methods. The first, named RFDS (Rectified Flow Distillation Sampling), is intended to serve as a baseline method for rectified flow priors, analogous to the SDS loss in diffusion models. Specifically, we derive the baseline RFDS by calculating the gradients of the input image by reversing the flow-matching training process. We observe a phenomenon similar to that seen in diffusion-based methods: by removing the Jacobian of the rectified flow network, RFDS can generate meaningful images or 3D objects given text conditions.

Moreover, inspired by the straight line trajectories of rectified flow, we notice that the baseline RFDS can be easily extended to optimize randomly sampled input noise by taking the “negative gradient” of the original RFDS. We refer to this method as iRFDS, which represents the inverse of RFDS. Optimizing noise is crucial for tasks like image inversion and editing. Typically, an image editing problem involves identifying the original noise of a given real image and subsequently altering the text prompt to edit the image. Our experiments demonstrate that iRFDS is effective at performing image inversion and editing on real-world images.

Finally, we introduce RFDS-Rev (RFDS Reversal) to enhance the generation quality of the baseline RFDS loss. Our observations reveal that the original RFDS loss exhibits behaviors similar to those of the SDS loss, such as limited detail and diversity in generated content. We attribute these issues to the mode-seeking tendency of the RFDS loss due to random sampling. The baseline RFDS leads to averaged images with diminished detail when random noise sampling is used. To address these challenges, we propose RFDS-Rev, which iteratively applies iRFDS for flow reversal to determine the original noise, and RFDS for knowledge distillation to refine the input. Experimentally, we find that the RFDS-Rev method significantly outperforms both the RFDS baseline and the diffusion-based VSD loss.

Figure: Figure 1: Demonstration of potential use cases of the proposed rectified flow priors. Our methods can be used on 2D inversion and editing and text-to-3D generation.
Refer to caption: x1.png

Additionally, we demonstrate that our method is applicable to score-matching methods, such as diffusion models. The diffusion models, trained with score-matching objectives, can be written in deterministic PF-ODEs, making them compatible with our proposed methods. Notably, when we formulate score-matching models in terms of PF-ODEs, our proposed RFDS baseline becomes identical to the SDS loss. Furthermore, our introduced iRFDS and RFDS-Rev expand upon previous SDS-like, score-matching-based knowledge distillation approaches, broadening their scope and applicability.

Our experiments are conducted on 2D image inversion and editing for iRFDS and text-to-3D generation for RFDS and RFDS-Rev. Notably, the RFDS-Rev method achieves a new state-of-the-art performance in text-to-3D benchmarks among all 2D lifting methods, surpassing a broad spectrum of diffusion priors. Some generation results can be found in Fig. 1.

To summarize our contributions:

- •
We propose the first series of studies that utilize pretrained rectified flow models as priors. Our methods span a wide array of applications, from generative tasks such as text-to-3D generation to the inversion and editing of real images.
- •
Compared to diffusion-based priors, our methods significantly outperform them in text-to-3D generation and achieve highly competitive results in image inversion and editing.

## 2 Preliminaries: Flow-based models and Rectified Flow

The idea of rectified flow is proposed in multiple concurrent works (Liu et al., ; Lipman et al., ; Albergo & Vanden-Eijnden, ). Here, we follow the interpretation of Stochastic Interpolants (Albergo & Vanden-Eijnden, ; Ma et al., ) to briefly introduce the basic concepts.

The Stochastic Interpolants framework starts by defining a general process of interpolating noise and image:

$$ $\displaystyle\bm{x_{t}}=\alpha_{t}\bm{\bm{x_{*}}}+\sigma_{t}\bm{\bm{\epsilon}}.\;$ (1) $$

Here, $\bm{x_{*}}\sim p(\bm{x})$ represents the data sampled from the data distribution, while $\bm{\epsilon}\sim\mathcal{N}(0,\bm{I})$ denotes noise drawn from a standard Gaussian distribution. $\alpha_{t}$ and $\sigma_{t}$ are two pre-defined variables used to control the interpolation trajectory and are only related to $t$. Rectified flow is a special case of the interpolation in Eq. 1 by defining $\alpha_{t}$ and $\sigma_{t}$ to change linearly with time $t$. In conditional flow matching (Lipman et al., ), the parameters are set as $\alpha_{t}=1-t$ and $\sigma_{t}=t$. In rectified flow (Liu et al., ), the settings are reversed, with $\alpha_{t}=t$ and $\sigma_{t}=1-t$.

The process of obtaining $\bm{x_{t}}$ can also be formulated as a probability flow ODE (PF-ODE) with a velocity field:

$$ $\displaystyle\dot{\bm{x_{t}}}=\bm{v}(\bm{x_{t}},t),\;$ (2) $$

$$ $\displaystyle\bm{v}(\bm{x_{t}},t)=\dot{\alpha_{t}}\mathop{\mathbb{E}}[\bm{x_{* }}\mid\bm{x_{t}}=\bm{x}]+\dot{\sigma_{t}}\mathop{\mathbb{E}}[\bm{\epsilon}\mid \bm{x_{t}}=\bm{x}],\;$ (3) $$

where $\dot{\alpha_{t}}$ and $\dot{\sigma_{t}}$ are the gradients of $\alpha_{t}$ and $\sigma_{t}$ with respect to $t$. We refer readers to Stochastic Interpolants (Albergo et al., ) and SiT (Ma et al., ) for detailed proofs of the above two equations.

Practically, flow-based generative models learn the velocity $\bm{v}$ by parameterizing it with neural networks using parameters $\bm{\phi}$ and optimizing a flow-matching objective:

$$ $\displaystyle\underset{\bm{\phi}}{\text{min}}\;\int_{0}^{1}\mathbb{E}\left[ \parallel\bm{v_{\phi}}(\bm{x_{t}},t)-\dot{\alpha_{t}}\bm{x_{*}}-\dot{\sigma_{t }}\bm{\epsilon}\parallel^{2}\right]\text{d}t.\;$ (4) $$

However, it is important to note that the primary objective of this work is not to sample $\bm{x_{t}}$ (e.g., generating images using rectified flow networks). Instead, our aim is to distill knowledge from such pretrained networks—specifically by employing the pretrained network as a loss function—to enhance the functionality of image generation networks across a wider array of applications, including image editing and text-to-3D generation.

Our proposed method is also related to widely studied diffusion-based priors. We discuss these related works in Appendix Sec C.

## 3 Methods

In this section, we discuss the three proposed distillation methods: the RFDS (Rectified Flow Distillation Sampling) baseline method, the iRFDS (inverse RFDS) method for image inversion and finally the RFDS-Rev (RFDS-Reversal) method to improve the generation quality of baseline RFDS.

Formulation. The problem of optimization using pretrained rectified flow models $\bm{v_{\phi}}$ as loss functions can be formatted as follows: we would like to optimize $\bm{x}=g(\bm{\theta})$ by $\bm{\theta^{\ast}}=\text{argmin}_{\bm{\theta}}\mathcal{L}(\bm{\phi},\bm{x}=g(
\bm{\theta}))$. The form of $\bm{x}$ can be Neural Radiance Field or 3D Gaussian Splatting (Kerbl et al., ) in the 3D generation problem, where the parameter $\bm{\theta}$ denotes the parameters of the 3D models. In the 2D case, $\bm{x}$ is directly $\bm{\theta}$. In the remainder of this section, we prove how to define the loss $\mathcal{L}$ and find its gradients with respect to $\bm{\theta}$.

### 3.1 RFDS

Consider the training loss function of flow-based generative models in Eq. 4. Using the pretrained network as a loss function can be seen as optimizing the input rather than the model parameters. Specifically, when we place the optimization variable $\bm{x}$ in the aforementioned equation, it transforms as follows:

$$ $\displaystyle\int_{0}^{1}\mathbb{E}\left[\parallel\bm{v_{\phi}}(\bm{x_{t}},t)- \dot{\alpha_{t}}\bm{x}-\dot{\sigma_{t}}\bm{\epsilon}\parallel^{2}\right]\text{ d}t,\;\text{with}\;\bm{x}=g(\bm{\theta})\;\text{and}\;\bm{x_{t}}=\alpha_{t}\bm {x}+\sigma_{t}\bm{\epsilon}.$ (5) $$

Here, the network parameter $\bm{\phi}$ is fixed and $\bm{\epsilon}$ is a randomly sampled noise.

To find $\bm{\theta}$, the gradients of the above equation with respect to $\bm{\theta}$ can be written as:

$$ $\displaystyle\nabla_{\bm{\theta}}\mathcal{L}_{\text{rfds}}(\bm{\phi},\bm{x}, \bm{\epsilon},t)=2\times\mathbb{E}\left[\underbrace{(\bm{v_{\phi}}(\bm{x_{t}}, t)-\dot{\alpha_{t}}\bm{x}-\dot{\sigma_{t}}\bm{\epsilon})}_{\text{Flow Residual }}(\frac{\partial(\bm{v_{\phi}}(\bm{x_{t}},t)-\dot{\alpha_{t}}\bm{x}-\dot{ \sigma_{t}}\bm{\epsilon})}{\partial\bm{x}})\underbrace{\frac{\partial\bm{x}}{ \partial\bm{\theta}}}_{\text{Generator Jacobian}}\right].$ (6) $$

It can be further simplified as:

$$ $\displaystyle\nabla_{\bm{\theta}}\mathcal{L}_{\text{rfds}}(\bm{\phi},\bm{x}, \bm{\epsilon},t)=2\times\mathbb{E}\left[\underbrace{(\bm{v_{\phi}}(\bm{x_{t}}, t)-\dot{\alpha_{t}}\bm{x}-\dot{\sigma_{t}}\bm{\epsilon})}_{\text{Flow Residual }}(\underbrace{\frac{\partial(-\dot{\alpha_{t}}\bm{x}-\dot{\sigma_{t}}\bm{ \epsilon})}{\partial\bm{x}}}_{-\dot{\alpha_{t}}}+\underbrace{\frac{\partial\bm {v_{\phi}}(\bm{x_{t}},t)}{\partial\bm{x_{t}}}}_{\text{Network Jacobian}} \underbrace{\frac{\partial\bm{x_{t}}}{\partial\bm{x}}}_{\alpha_{t}}) \underbrace{\frac{\partial\bm{x}}{\partial\bm{\theta}}}_{\text{Generator Jacobian}}\right].$ (7) $$

As highlighted in diffusion-based methods (Poole et al., ), calculating the network Jacobian is computationally expensive and reacts inadequately to low levels of noise. We observe similar behaviors in models based on flow-matching. Consequently, we also choose to disregard the rectified flow network Jacobian by setting it to the identity matrix, akin to the approach taken with diffusion priors. This modification leads to the final RFDS loss:

$$ $\displaystyle\nabla_{\bm{\theta}}\mathcal{L}_{\text{rfds}}(\bm{\phi},\bm{x}, \bm{\epsilon},t)\simeq\mathbb{E}\left[w(t)\underbrace{(\bm{v_{\phi}}(\bm{x_{t} },t)-\dot{\alpha_{t}}\bm{x}-\dot{\sigma_{t}}\bm{\epsilon})}_{\text{Flow Residual}}\underbrace{\frac{\partial\bm{x}}{\partial\bm{\theta}}}_{\text{ Generator Jacobian}}\right].$ (8) $$

Here we use $w(t)$ to represent a value related to timestep $t$, and it absorbs all constant values in Eq. 7. The RFDS loss is able to use the pretrained rectified flow model as a loss function to optimize a given image $\bm{x}$. Given a rectified flow based model, we can easily obtain its corresponding RFDS loss by setting $\dot{\alpha_{t}}$ and $\dot{\sigma_{t}}$ to $-1$ and $1$ or vice versa, depending on the way it formulates Eq. 1. We include a detailed algorithm for optimization using RFDS is in Appendix Sec D.

### 3.2 iRFDS

A particularly interesting characteristic of the velocity prediction objective is its time-symmetry property (Liu et al., ). This allows the models to flow from noise to image and also from image back to noise. Motivated by this property, we observe that our method can be easily extended to optimize the noise. If our optimization objective changes from the input image $\bm{x}=g(\bm{\theta})$ to the noise $\bm{\epsilon}$, Eq. 7 now becomes:

$$ $\displaystyle\nabla_{\bm{\epsilon}}\mathcal{L}_{\text{irfds}}(\bm{\phi},\bm{x} ,\bm{\epsilon},t)=2\times\mathbb{E}\left[\underbrace{(\bm{v_{\phi}}(\bm{x_{t}} ,t)-\dot{\alpha_{t}}\bm{x}-\dot{\sigma_{t}}\bm{\epsilon})}_{\text{Flow Residual}}(\underbrace{\frac{\partial(-\dot{\alpha_{t}}\bm{x}-\dot{\sigma_{t}} \bm{\epsilon})}{\partial\bm{\epsilon}}}_{-\dot{\sigma_{t}}}+\underbrace{\frac{ \partial\bm{v_{\phi}}(\bm{x_{t}},t)}{\partial\bm{x_{t}}}}_{\text{Network Jacobian}}\underbrace{\frac{\partial\bm{x_{t}}}{\partial\bm{\epsilon}}}_{ \sigma_{t}})\right].$ (9) $$

Therefore, the final form of iRFDS can be represented as:

$$ $\displaystyle\nabla_{\bm{\epsilon}}\mathcal{L}_{\text{irfds}}(\bm{\phi},\bm{x} ,\bm{\epsilon},t)\simeq\mathbb{E}\left[w^{\prime}(t)\underbrace{(\bm{v_{\phi}} (\bm{x_{t}},t)-\dot{\alpha_{t}}\bm{x}-\dot{\sigma_{t}}\bm{\epsilon})}_{\text{ Flow Residual}}\right],$ (10) $$

where the value $w^{\prime}(t)$ should have opposite signs to $w(t)$ due to the relations between $\sigma_{t}$ and $\alpha_{t}$ as stated in Sec. 2.

Optimizing and recovering the original noise from an image is crucial for image inversion and editing problems. By first retrieving the original noise and subsequently modifying the caption, we demonstrate in the experiment section that our method can effectively edit real-world images. A detailed algorithm of iRFDS is included in Appendix Sec D.

### 3.3 RFDS-Rev

RFDS-Reversal (RFDS-Rev) is designed to enhance the baseline RFDS in terms of generation quality. We observe that the RFDS method encounters issues similar to those found with the SDS loss, such as a lack of object details. While several approaches, like the VSD loss, have been proposed to improve the SDS loss and some are applicable to rectified flows, none shows effective results with rectified flow models based on our experiments.

Figure: Algorithm 1 The RFDS-Rev Algorithm.

To enhance the baseline RFDS, we draw inspiration from the learning mechanisms of Reflow (Liu et al., ; ). Recall that Reflow straightens the trajectory from noise to image, leading to one-to-one matching of the image and noise. In contrast, the mode-seeking nature of the original RFDS, which optimizes the image based on random noises, leads to an averaged velocity and consequently blurred images. As shown on the left side of Fig. 2, when two noise points are sampled, although both give gradients towards the high-density areas in the image domain, the averaged gradient does not necessarily point in the correct direction. To address this issue, we first introduce a critical assumption:

Assumption 1: For a model finetuned with Reflow, given a sample $\bm{x_{*}}$ from data distribution $p(\bm{x})$, there is at most one corresponding $\bm{\epsilon}$ from noise distribution $\mathcal{N}(0,\bm{I})$ that corresponds to $\bm{x_{*}}$.

This assumption is straightforward, as the training process for Reflow enforces a linear, non-crossing flow (Liu et al., ). Based on this assumption, we propose RFDS-Reversal (RFDS-Rev), a two-stage method to improve the baseline RFDS. Specifically, as depicted on the right in Fig. 2, the first stage performs noise reversal. In this stage, we use iRFDS to perform image inversion and optimize each randomly sampled noise such that their reversal occupies a relatively static position within the noise distribution. Once the reversal is determined, in the second stage, we apply RFDS to the reversed noise. The algorithm of RFDS-Rev is summarized in Algorithm 1. In experiments, we observe that running iRFDS for just one step yields very satisfactory results. Unless specified otherwise, the experiments involving RFDS-Rev employ $n=1$ as the default configuration. Although RFDS-Rev was initially designed with the assumption of models fine-tuned using Reflow, our experimental results reveal that it enhances the performance of the baseline RFDS on models both with and without Reflow training.

Figure: Figure 2: Illustration of our proposed methods.
Refer to caption: x2.png

### 3.4 Applying iRFDS and RFDS-Rev to Diffusion Models

As discussed in previous works (Song et al., ; Albergo et al., ), diffusion models trained with score-matching objectives have a deterministic PF-ODE form and can be expressed in the form of Eq. 2. We observe that by converting the score function to a velocity field, all three of our proposed methods become applicable to diffusion models. Additionally, we prove that our proposed RFDS baseline is identical to the vanilla SDS loss when applied to diffusion models. We include a detailed proof in Appendix Sec A.

### 3.5 Classifier Free Guidance (CFG)

The above equations are derived using the rectified flow network $\bm{v_{\phi}}$. In practice, since the base rectified flow models (Liu et al., ; Esser et al., ) are usually trained with classifier free guidance (Ho & Salimans, ), we observe that using a classifier free guidance version of the network $\bm{\hat{v}_{\phi}}$ helps to improve the performance. Ablation experiments on this problem are included in Appendix Sec E.

## 4 Experiments

In this section, we conduct extensive experiments to compare our proposed methods with diffusion-based approaches. We perform experiments on two types of rectified flow-based methods: Stable Diffusion v3 (SD3), trained with flow-matching but without Reflow finetuning, and InstaFlow, finetuned with Reflow. In terms of 2D performance, Stable Diffusion v3 is one of the state-of-the-art text-to-image models, trained with more data and using larger backbones. InstaFlow achieves results similar to those of Stable Diffusion v2.1 (SD2.1) (Rombach et al., ). First, we focus on evaluating RFDS and RFDS-Rev in both 2D and 3D text-guided generation scenarios. Subsequently, we explore the performance of iRFDS in image inversion tasks. The diffusion-based methods are implemented using SD2.1 and the Threestudio codebase (Guo et al., ). We include the implementation details in the Appendix for further reference.

Figure: Figure 3: 2D Comparison. Text Prompts: “A castle next to a mountain”, “An astronaut is riding a horse” and “A monster truck”.
Refer to caption: x3.png

Figure: Figure 4: 3D Comparison. Text Prompts: “An antique wooden rocking horse”, “A bear holding a sign that says Hello world” and “Hot popcorn jump out from the red striped popcorn maker”.
Refer to caption: x4.png

### 4.1 RFDS vs. RFDS-Rev vs. Diffusion Priors vs. Diffusion RFDS-Rev

Toy Experiments on Optimization of 2D Case. We begin by conducting an intuitive experiment in a 2D setting, where we set $\bm{x}=\bm{\theta}$. This simplified setup removes the complexities of the 3D model, allowing us to demonstrate the potential upper limit of 3D generation quality. Results are shown in Fig. 3. Results reveal that our RFDS baseline, when integrated with InstaFlow, performs comparably to the diffusion-based SDS loss. Moreover, when combined with Stable Diffusion v3, the RFDS baseline significantly enhances generation quality.

We also apply our proposed method, RFDS-Rev, to two rectified flow-based models and the diffusion model Stable Diffusion v2.1, as discussed in Sec 3.4. To better approximate the real use cases, we use only one step of iRFDS to improve efficiency for all experiments. Our results indicate that RFDS-Rev significantly enhances generation performance on InstaFlow, moderately improves performance on SD3, and slightly improves performance on the diffusion model. These findings are consistent with the assumptions made when proposing the RFDS-Rev method. The Reflow process straightens the noise-to-data trajectory, making our assumptions particularly applicable to models finetuned with Reflow. Although SD3 is not finetuned with Reflow, our method still improves generation quality. However, in score-matching models like diffusion, noise is applied stochastically to corrupt the data, making it challenging to trace the original noise with just one step of iRFDS. For this reason, in the 3D experiments, we apply our methods only to flow-matching based approaches, and compare them with SDS-like diffusion-based approaches.

**Table 1: Results of Text-to-3D on T^3Bench dataset. Our proposed methods achieve state-of-the-art performance among 2D lifting methods, beating the diffusion based SDS and VSD priors.**
| Method | Dreamfusion (SDS) | ProlificDreamer (VSD) | RFDS | RFDS-Rev | RFDS | RFDS-Rev |
| --- | --- | --- | --- | --- | --- | --- |
| Base Model | Diffusion | Diffusion | InstaFlow | InstaFlow | SD3 | SD3 |
| Single Object | 24.9 | 51.1 | 46.9 | 57.6 | 49.4 | 59.8 |
| Surroundings | 19.3 | 42.5 | 34.5 | 44.6 | 39.3 | 54.5 |
| Multiple Objects | 17.3 | 45.7 | 28.3 | 44.6 | 42.9 | 55.2 |
| Average | 20.5 | 46.4 | 36.5 | 48.9 | 43.9 | 56.5 |

Figure: Figure 5: Comparison of 2D editing. Our iRFDS method is able to perform prompt-faithful editing.
Refer to caption: x5.png

Text-to-3D Generation by Lifting 2D Models. An important application of rectified flow or diffusion priors is lifting models from 2D to 3D. We present both quantitative and qualitative results for text-to-3D generation. The qualitative results are displayed in Fig. 4. We observe that both of our proposed methods are capable of generating high-quality 3D objects, with the RFDS-Rev method enhancing the baseline RFDS in terms of object detail and color accuracy. Qualitatively, when applied to similar quality base models
(InstaFlow and SD2.1), the RFDS baseline shows competitive performance compared to the SDS loss used in diffusion-based methods. Compared to VSD, RFDS-Rev achieves a comparable level of detail in generated objects. Notably, VSD experiences issues with “exploding” artifacts. In contrast, the RFDS-Rev loss does not exhibit this problem. When we apply our method to the more powerful SD3 base model, we observe that it outperforms diffusion priors. Moreover, RFDS-Rev further enhances the generation quality compared to the RFDS baseline on SD3. Additional qualitative results of RFDS-Rev are included in Appendix I.

We also conduct quantitative experiments on the text-to-3D benchmark T^3Bench (He et al., ). The dataset contains 300 text prompts for text-to-3D generation, making it the largest text-to-3D benchmark available. Results are demonstrated in Table 1. We report the quality score, derived by rendering multi-view images and calculating the CLIP (Radford et al., ) and ImageReward (Xu et al., ) scores between the rendered images and the corresponding text prompt. We observe that our proposed methods significantly outperform diffusion-based methods. Furthermore, the RFDS-Rev method sets a new state-of-the-art performance among all 2D lifting methods in this benchmark.

### 4.2 iRFDS vs. Diffusion Methods

In this section, we study the performance of iRFDS in 2D image inversion and subsequent text-guided editing. Image inversion is also a widely explored topic in diffusion-based methods, known for its capability to edit real-world images. We compare iRFDS against a popular method – null inversion – on real-world images. Additionally, we evaluate our method against the diffusion prior based optimization method, the DDS loss (Hertz et al., ), which directly optimizes the original images.

The results of the inversion and editing experiments are summarized in Fig. 5. Compared to the diffusion-based null inversion, our proposed iRFDS method delivers highly competitive performance. Additionally, the diffusion prior DDS loss tends to generate images with overly saturated colors. Among the different variants of our iRFDS methods, we find that the model finetuned with Reflow produces the best results. Further visualizations can be found in Appendix Sec. H.

To further validate the performance improvements, we conducted quantitative experiments to calculate the CLIP score between the target caption and the image after editing. Additionally, we carry out a user study to evaluate the editing performance from the users’ perspective. The experiments are performed on 15 real images randomly collected from the internet, with each image being edited three times using different captions. The results are summarized in Table. 2. We observe that our proposed method iRFDS + InstaFlow achieves the best performance in terms of CLIP scores and user preference.

**Table 2: Quantitative comparison of 2D editing.**
| Method | DDS | Null Inversion | iRFDS (InstaFlow) | iRFDS (SD3) | iRFDS (Diffusion) |
| --- | --- | --- | --- | --- | --- |
| CLIP Score | 0.294 | 0.298 | 0.306 | 0.297 | 0.296 |
| User Preference | 6.8% | 18.6% | 45.3% | 17.1% | 12.2% |

### 4.3 Ablation Experiments

iRFDS optimization steps in RFDS-Rev (Algorithm 1). Fig. 6 shows results from both the 2D and 3D cases. We observe that performing the iRFDS for 1 step achieves the best efficiency and performance trade-off.

Figure: Figure 6: Experiments of the noise optimization step in RFDS-Rev. Top: 2D case. Bottom: 3D case. Optimizing the iRFDS for one step offers the optimal balance between efficiency and performance.
Refer to caption: x6.png

w/ Network Jacobian vs. w/o Network Jacobian. As illustrated in Fig. 7, we observe that keeping the network Jacobian can hardly generate meaningful images even in the 2D case. This observation is consistent for both SD3 and InstaFlow.

Figure: Figure 7: Ablation experiments of ignoring the rectified flow network Jacobian. We observe that it is difficult to generate images by keeping the Jacobian of the rectified flow network.
Refer to caption: x7.png

Additional Ablation Results. We also include additional ablation results in Appendix Sec E. The experiments include: ablation on the effect of CFG, RFDS-Rev vs. directly applying the same idea of VSD to rectified flow and a comparison of computational cost between our methods and diffusion-based methods.

## 5 Summary of observations and Discussion

Summary of observations. 1), RFDS and RFDS-Rev are effective on flow-matching models, regardless of whether Reflow fine-tuning is applied (Fig. 3, 4, Table. 1). 2), Reflow fine-tuning enhances iRFDS performance on image inversion and editing tasks (Fig. 5, Table 2). 3). When applied to score-matching-based methods like diffusion models, RFDS is equivalent to the SDS loss. RFDS-Rev offers slight improvements over the SDS baseline. While iRFDS may not produce the best editing results with diffusion models, it presents a simple alternative to other inversion methods.

Additional advantages over diffusion based priors. Besides the performance improvements, we observe that methods based on rectified flow achieve faster convergence during the optimization of 3D models. Intuitively, if we rearrange Eq. 8, $x$ can be regarded as learning toward a direct objective $v_{\phi}+\epsilon$. In contrast, diffusion models rely on the difference in predicted noises to guide the optimization process. A detailed visual comparison is included in Appendix Sec F.

## 6 Conclusion, Limitations and Broader Impacts

In this work, we introduce the SDS and VSD counterparts in rectified flow based methods. We propose three methods that utilize rectified flow as plug-and-play priors. Our two generative methods, RFDS and RFDS-Rev, outperform SDS and VSD in terms of text-to-3D generation. Additionally, the iRFDS method demonstrates robust capabilities in image inversion and text-guided editing.

Limitations. Since the 2D model lacks training with camera pose information, our proposed methods encounter similar issues to the SDS and VSD losses in 3D generation, such as the multi-face issue. These limitations can be addressed in future studies by training pose-aware models using multi-view data, similar to current diffusion based approaches (Ye et al., ; Shi et al., ; Li et al., ; Shi et al., ; Long et al., ). Moreover, currently our proposed iRFDS method does not taken the CFG mismatch issue into considerations. A promising future direction will be combining the iRFDS method with null-inversion (Mokady et al., ) to address the CFG issue.

Broader Impacts. Our approach significantly expands the potential applications of pretrained rectified flow models. We demonstrate that a text-to-image model can be adapted for both image editing and text-to-3D generation tasks. However, since we utilize pretrained text-to-image rectified flow models as our foundational network, our methods might also inherit the biases present in these base networks.

## Appendix

## A Proof: RFDS, iRFDS, RFDS-Rev with Diffusion models

RFDS is Identical to SDS When Expressed in Terms of Score Function

As proven in Stochastic Interpolants (Albergo et al., ), the velocity $\bm{v}(\bm{x_{t}})$ can be expressed in terms of a score function $\bm{s}$ learned with score-matching objective

$$ $\displaystyle\bm{v}(\bm{x_{t}})=\frac{\sigma_{t}\bm{s}(\bm{x_{t}})(\dot{\alpha _{t}}\sigma_{t}-\alpha_{t}\dot{\sigma_{t}})+\alpha_{t}\bm{x_{t}}}{\alpha_{t}}.\;$ (11) $$

For the detailed proof of this relation, we refer the readers to Albergo et al. ().

By substituting this relation into RFDS (Eq. 8) and considering the relation $\bm{s}=\frac{-\bm{\epsilon_{\phi}}}{\sigma_{t}}$, we directly obtain the same equation as the SDS loss

$$ $\displaystyle\nabla_{\bm{\theta}}\mathcal{L}_{\text{rfds}}(\bm{\phi},\bm{x}, \bm{\epsilon},t)\simeq\mathbb{E}\left[w(t)\underbrace{(\bm{\epsilon_{\phi}}( \bm{x_{t}})-\bm{\epsilon})}_{\text{Score Residual}}\underbrace{\frac{\partial \bm{x}}{\partial\bm{\theta}}}_{\text{Generator Jacobian}}\right].$ (12) $$

iRFDS Expressed in Terms of Score Function

Similarly, we can derive the iRFDS in terms of score function

$$ $\displaystyle\nabla_{\bm{\epsilon}}\mathcal{L}_{\text{irfds}}(\bm{\phi},\bm{x} ,\bm{\epsilon},t)\simeq\mathbb{E}\left[w^{\prime}(t)\underbrace{(\bm{\epsilon_ {\phi}}(\bm{x_{t}})-\bm{\epsilon})}_{\text{Score Residual}}\right].$ (13) $$

After the two formulas are derived, we can naturally arrive at RFDS-Rev.

## B Implementation Details

RFDS and RFDS-Rev for 3D generation. We use the 3D model implicit model Instant-NGP (Müller et al., ) as the 3D backbone. Each 3D model is optimized for 15000 steps. We use a CFG of 50 for all 3D experiments and 2D toy experiments. The model is optimized with a resolution of 256 for the first 5000 steps and then 500 for the final 10000 steps. The experiments are carried out on NVIDIA A6000 GPUs. On InstaFlow, generating one 3D scene using RFDS-Rev takes around 30 mins wall-clock time. On SD3, generating one 3D scene using RFDS-Rev takes around 1 hour. We use $w(t)=1$ on SD3 and $w(t)=-1$ on InstaFlow. Choosing iRFDS step size is important to achieve high quality generation with RFDS-Rev. For InstaFlow, we use a stepsize 1. For SD3, we observe that a stepsize of $1-\sigma_{t}$ produce reasonable results.

iRFDS for image inversion and editing. The inversion starts from a randomly sampled Gaussian noise. We optimize the noise for 1000 steps using iRFDS and CFG 1 with a learning rate of 3*10-3. To facilitate effective noise optimization, we add one additional loss to enforce the noise follows a Gaussian distribution. Specifically, we add a loss to enforce the mean and variance of the current noise to be zero and one respectively. After the noise is optimized, we change the caption to the target caption and run the forward flow for 5 steps using CFG 1.5. We use $w^{\prime}(t)=-1$ on SD3 and $w^{\prime}(t)=1$ on InstaFlow.

## C Additional Related Works

Diffusion as plug-and-play priors. Our work is greatly motivated by the development of diffusion-based priors. The earliest work of diffusion prior (Graikos et al., ) requires to backpropagate through the diffusion U-Net. Dreamfusion (Poole et al., ) recognizes that such a backpropagate process greatly hurts the performance of diffusion priors. By ignoring the U-Net Jacobian, the SDS loss proposed in Dreamfusion can be used for 3D generation and image editing. However, the initial version of the SDS loss suffers greatly from the lack of details and diversity. DDS loss (Hertz et al., ) proposes an improved version of the SDS to improve image editing by taking the difference between the current SDS and the source image SDS. VSD loss (Wang et al., ) improves the SDS loss for 3D generation problems. Specifically, it first trains a LoRA of the current 3D model and then takes the difference between the diffusion SDS and LoRA SDS. Although lots of methods have been proposed for diffusion models, this is the first work that studies how to effectively use rectified flow as priors.

## D Algorithm for RFDS and iRFDS

We list the detailed algorithm for RFDS and iRFDS in Algorithm 2 and Algorithm 3.

Figure: Algorithm 2 The RFDS Algorithm.

## E Additional Ablation Experiments

Ablation Results on CFG. The scale of classifier-free guidance (CFG) (Ho & Salimans, ) plays a crucial role in diffusion-based methods, such as SDS and VSD. We observe a very similar phenomenon with the rectified flow priors. As demonstrated in Fig. 8, both of the proposed methods require a CFG greater than 10 to learn reasonable shapes. However, when the CFG becomes excessively large, the 3D objects generated by RFDS exhibit over-saturated colors. In contrast, RFDS-Rev remains robust to large CFG values, even when the CFG exceeds 2000.

Figure: Figure 8: Ablation experiments of classifer free guidance scale on text-to-3D generation. Prompt: A DSLR image of a hamburger.
Refer to caption: x8.png

RFDS-Rev vs. RFDS-VSD. As mentioned in the main text, some of the existing methods aimed at improving the diffusion models can be used directly on rectified flow based methods. We explore to combine VSD with the baseline RFDS, denoted as RFDS-VSD. Specifically, we train a rectified flow LoRA model based on the current rendered images and then calculate the gradients by taking the difference between RFDS and RFDS-LoRA following the VSD setting. Results are shown in Fig. 9. Our experiments, conducted using the InstaFlow backbone, demonstrate that RFDS-Rev produces significantly better results compared to RFDS-VSD, despite RFDS-VSD requiring more computational resources. Notably, implementing VSD on the SD3 model presents significant challenges for most currently available commercial GPUs due to its requirement for fine-tuning the base model, which demands excessive GPU memory.

Figure: Figure 9: Ablation experiments of RFDS-Rev vs. RFDS-VSD. Top: 2D case. Bottom: 3D case.
Refer to caption: x9.png

## F Comparison of Convergence Speed.

As listed in Fig. 10, we observe that our rectified flow based methods lead to much faster convergence speed when doing text-to-3D generation.

Figure: Figure 10: Comparison of convergence speed in 3D generation. Caption: A DSLR image of a hamburger. The 3D model is trained with the same learning rate. We observe that the rectified flow based methods converge much faster compared with diffusion-based methods.
Refer to caption: x10.png

## G Comparison of the Computational Cost.

We evaluate the computational costs by examining the number of forward and backward passes of the diffusion or rectified flow network required in 1 optimization iteration. Results are list in Table. 3. The RFDS baseline has the same computational demands as the SDS loss. Due to the calculation of CFG (Ho & Salimans, ), they both require two forward passes. RFDS-Rev requires only one additional forward pass, whereas VSD needs two additional forward passes and one additional costly backward pass.

**Table 3: Computational cost of one iteration based on the number of forward and backward passes of the network.**
| Method |  | SDS Poole et al. () | VSD Wang et al. () | DDS Hertz et al. () | RFDS | iRFDS | RFDS-Rev |
| --- | --- | --- | --- | --- | --- | --- | --- |
| Category | - | Diffusion | Diffusion | Diffusion | Rectified Flow | Rectified Flow | Rectified Flow |
| Computation | Forward | 2 | 4 | 2 | 2 | 1 | 3 |
| Backward | 0 | 1 | 0 | 0 | 0 | 0 |  |

## H More results of image inversion and editing using iRFDS.

We show more results of 2D editing in Fig. 11.

Figure: Figure 11: More results on 2D editing.
Refer to caption: x11.png

## I More results of text-to-3D generation

We show more qualitative results of text-to-3D generation in Fig. 12,Fig. 13, Fig. 14 and Fig. 15.

Figure: Figure 12: More results on text-to-3D generation. Model:SD3
Refer to caption: x12.png

Figure: Figure 13: More results on text-to-3D generation. Model:SD3
Refer to caption: x13.png

Figure: Figure 14: More results on text-to-3D generation. Model:InstaFlow
Refer to caption: x14.png

Figure: Figure 15: More results on text-to-3D generation. Model:InstaFlow
Refer to caption: x15.png

## J iRFDS user study details

The user study is carried out with google doc. The users are ask to select the best editing results from the 4 methods. A screenshot of the user study is shown in Fig 16.

Figure: Figure 16: User study page
Refer to caption: x16.png

## Peer Reviews

confidence: 4
contribution: 3
initial_rating: 6
presentation: 3
questions: - The authors are strongly encouraged to discuss more on the quality degradation issues mentioned in weaknesses. If this is an effect of the proposed algorithm, it should be discussed throughly. 
- Authors should consider  extending the quantitative results on the reconstruction properties of the iRFDS. Despite the fact that the current evaluation assesses the edit in terms of success in reflecting the semantics, the qualitative results seems that the algorithm fails in preserving edit independent details.
soundness: 4
strengths: - The paper proposed the first algorithm that utilizes rectified flow models as priors, to both enable implicit information encoded in the rectified flow model and inversion based image editing with such models.
- In addition to the baseline method provided, authors also propose an extension named RFDS-Rev, that improves over the baseline objective RFDS, that combines the algorithms proposed together and promises improved generation quality.
- Proposed method showcases satisfactory results on Text-to-3D generation, which shows the effectiveness of the proposed method over providing a prior on multiple views.
- Authors introduce a simplifying assumption enabling to efficiently using rectified flow models as priors, by simplifying the generator Jacobian. This serves as a modification for improving the efficiency of the proposed method.
- The paper provides sufficient amount of experiments demonstrating the effect of the design decisions made on the algorithms, which also serve as insightful observations (number of steps, effect of the Jacobian).
summary: The submitted work propose a way of utilizing rectified flow models a prior, that implies the internal knowledge of the model as in the form of an objective. Throughout the manuscript, the authors propose three different algorithms in this regard, where they are named as RFDS (Rectified Flow Distillation Sampling), iRFDS (inverse RFDS) and RFDS-Rev (RFDS Reversal). While discussing the analogy between the SDS (Score Distillation Sampling), which serves as a prior for models trained with score-matching objective (e.g. diffusion models), they demonstrate how these algorithms can be utilized as a loss objective reflecting the knowledge of the rectified flow model and the image inversion & editing task. Furthermore, the authors propose RFDS-Rev algorithm as the improved version of the baseline algorithm (RFDS).

To demonstrate the effectiveness of the set of the proposed algorithms, authors show the effectiveness of them on a variety of tasks. Initially, the authors demonstrate how does the proposed method improve over SDS in diffusion models in terms of generation quality. Following, they illustrate the applications of the proposed algorithms in inversion based tasks (e.g. image editing) and text-to-3D generation with a 2D prior from rectified flow models. For all of the demonstrated algorithms, authors provide qualitative and quantitative results that shows the effectiveness of the proposed framework.
weaknesses: - In the examples provided, there is a significant saturation effect on the provided results (see Fig. 5, row 2 and Fig. 6, examples from SD3). It is unclear if that effect is a result of the proposed method or a property of the rectified flow models. 
- While the image editing results seem semantically correct, there seems to be significant changes in the provided images (See Fig. 5) compared to methods such as Null-text Inversion. Despite the fact that the authors provide a user study and CLIP score based comparisons, the faithful reconstruction property is not discussed and it is unclear that how successful the provided approach is.
- In generation results provided in Fig. 7 (fox example), the generation results seem degraded in terms of quality and provides artifacts. It also seems that RFDS in general produces these artifacts. If the alternative method RFDS-Rev recovers those, authors need to provide related discussions and examples on its performance on the performed tasks (such as inversion based editing). If this algorithm is not applicable for such a scenario, it should be mentioned as a limitation of the method.

---

confidence: 5
contribution: 3
initial_rating: 6
presentation: 3
questions: 1. Why do the bottles change across n=1 and n‎ = 2 while boots stay the same in Figure 6? The only difference I catch between boots and bottles is 2D and 3D.
2. Why does the network Jacobian harm the results?
soundness: 3
strengths: 1. This paper tackles a long-standing problem: SDS. SDS with rectified flow is not good enough and the proposed method generates sharp results.
2. The proposed method is easy to understand and mostly sound.
3. The proposed method is generalizable to a wide range of flow-based methods.
4. Preliminary is thorough enough to provide the knowledge base.
5. Figure 2 greatly helps understanding the intuition of RFDS-Rev.
6. Experiments are well-organized from 2D to 3D.
summary: This paper proposes to use rectified flow for SDS instead of diffusion models.

The propose method has three components:
* Rectified flow distillation sampling (RFDS) = typical SDS but with rectified flow
    * Equations are the same with SDS except having *flow residual* instead of denoising loss
    * It uses random noises to compute the *flow residual*.
* Optimizing the *noise* (iRFDS) with the same flow residual
* Full algorithm (RFDS-Rev) with RFDS and iRFDS
    * iRFDS starting from a random noise
    * RFDS with the optimized noise

iRFDS and RFDS-Rev are applicable to diffusion models, especially with classifier-free guidance.
weaknesses: (Ordered by importance. Resolving them will raise my rating.)

1. Subsection 3.2 should provide the theoretical justification for the reason why optimizing the noise helps RFDS.
2. Choice of the competitors for text-based image editing is not sound because it covers only inversion variants. Answering following questions may improve soundness: Why should we compare only with inversion variants? Why prompt-to-prompt variants (e.g., DDPM inversion + P2P) should be ignored?
3. The text-to-3D results still suffer from Janus problem. Discussion in this direction would enrich the paper.
4. Question of the user study is ambiguous: Given the source image, "a boat in a river", which method is better by changing boat -> rock? There are different aspects of being "better", e.g., consistency except the boat, and they should be separately evaluated.
5. Results of generated 3D assets (Figure 4) should be rendered in multiple views to be evaluated. Supp. materials have viewpoint-varying videos. Mentioning a Supp. would suffice.
6. Introduction is verbose. It would be clearer if non-essential sentences are removed.

Misc.

L169 using pretrained rectified flow models v_phi -> using a pre-trained rectified flow model v_phi

---

confidence: 3
contribution: 2
initial_rating: 3
presentation: 2
questions: See weaknesses
soundness: 3
strengths: 1. The paper analyzes the refined process of the rectified flow.

2. Using the rectified flow as the priors is interesting.

3. The experiments are sufficient.
summary: This paper uses the SOTA rectified-flow-based model as plug-and-play priors to lift the text-to-2D model into a text-to-3D model, with RFDS and RFDS-Rev. By removing the Jacobian of the rectified flow network, RFDS can generate meaningful images or 3D objects given text conditions. RFDS-Rev iteratively applies iRFDS for flow reversal to determine the original noise, and RFDS for knowledge distillation to refine the input.
weaknesses: * Writing needed to be improved, especially, from Lines 100-107, which is important but the logic is somewhat unclear.

* The focus of the paper is a little confusing, including Image inversion, editing, and text-to-3D generation. In my view, text-to-3d must be the key contribution as it use the 2D model as the priors.

* What is the difference between RFDS Loss and SDS loss. It seems that RFDS is the version of the flow-based model.

* What is the speed impact of the iterative application of iRED in REDS-rev?

---

confidence: 3
contribution: 3
initial_rating: 6
presentation: 3
questions: Please see the weakness section.
soundness: 2
strengths: 1. The proposed RFDS, which poses similarity to SDS, presents an effective way to adapt pre-trained Rectified Flow models to tasks such as text-to-3D. This contribution is fundamental since there is a growing trend toward Rectified Flow models in the community.

2. The authors conducted extensive experiments with various Rectified Flow/Diffusion baselines, which proves the versatility and efficacy of the proposed RFDS framework.

3. The proposed method shows solid performance and faster convergence speed compared to baselines, which is noticeable.

4. This paper is easy to follow and comprehend.
summary: This paper presents a framework that distills knowledge from the pre-trained text-to-image rectified flow models, which serve as a strong prior and apply to various downstream tasks such as image editing and text-to-3D. Similar to ‘Score Distillation Sampling’ (SDS) loss, authors propose a novel loss termed ‘Rectified Flow Distillation Sampling’ (RFDS) that is fully compatible with Rectified Flow models and partially with Diffusion models. Furthermore, they suggest iRFDS and RFDS-Reversal, the variant of their proposed loss, that can be applied to the image inversion and RFDS-based enhancement mechanism, respectively. The authors conducted extensive experiments to validate the efficiency and efficacy of their method.
weaknesses: 1. As far as my understanding is correct, RFDS-Rev redirects the gradients (velocities) of the rendered image to points close to the same data distribution mode given different noisy samples to handle common issues such as blurriness that could arise from averaging different-mode directing gradients. For this reviewer, it is unclear how iRFDS can enhance the performance of models without Reflow since these models would not have perfect straight-line paths. Approximated starting points (initial noise) would not guarantee a ‘static position’ within the noise distribution, and I think the more detailed explanation or empirical evidence would further make this work concrete. 

2. The results in image editing (Fig.5) do not seem convincing since semantics that are supposed to remain still are also being changed, such as the global contrast of the image, textures, and object shapes. This makes me doubtful if the proposed iRFDS can indeed optimize the valid initial noise given data. Maybe a simple reconstruction test (from optimized noise to the original data) would further provide a concrete evaluation.

3. I think the explanation of faster convergence speed compared to SDS/VSD is weak since it is an important property in the field of 3D generation methods using diffusion priors. Further elaboration or evidence of this feature would help readers fully comprehend their work (e.g., comparing convergence curves with respect to the number of iterations or wall-clock time).

4. Weak baseline methods. While I appreciate the paper's contribution (the first attempt to use Rectified Flow as priors) and the results are quite promising, baseline methods are rather weak (DreamFusion and VSD are quite outdated at the moment). It would be great if the authors compared against state-of-the-art text-to-3D methods, e.g., LucidDreamer [1], DreamCraft3D [2] or even GaussianDreamer [3] using different 3D representations.

[1] LucidDreamer: Towards High-Fidelity Text-to-3D Generation via Interval Score Matching, Liang et al., CVPR 2024

[2] DreamCraft3D: Hierarchical 3D Generation with Bootstrapped Diffusion Prior, Sun et al., ICLR 2024

[3] Fast Generation from Text to 3D Gaussians by Bridging 2D and 3D Diffusion Models, Yi et al., CVPR 2024

Meta-review: This work proposes to distill knowledge from the pretrained rectified flow models, which serve as a powerful prior and can be plugged and played into various downstream tasks. The contribution is recognized as fundamental and the experiments are extensive, as commonly appreciated by reviewers. It receives three borderline accept and one borderline reject, but generally being consistently positive especially after the rebuttal. Several concerns raised by reviewers include more clarifications about figures/introduction, weak baselines, analysis about speed, etc. Authors provided detailed feedback via rebuttal and discussions, and reviewers mostly acknowledge that concerns are addressed well. AC agrees that it tackles a long-standing problem with a more fundamental solution that could impact and benefit many following works in this direction. After checking all the reviews and discussions, a decision of acceptance is made and authors are encouraged to include all revisions and newly added results/explanations in the final version.

Decision: Accept (Poster)