IV-mixed Sampler: Leveraging Image Diffusion Models for Enhanced Video Synthesis

## Abstract

Abstract The multi-step sampling mechanism, a key feature of visual diffusion models, has significant potential to replicate the success of OpenAI’s Strawberry in enhancing performance by increasing the inference computational cost. Sufficient prior studies have demonstrated that correctly scaling up computation in the sampling process can successfully lead to improved generation quality, enhanced image editing, and compositional generalization. While there have been rapid advancements in developing inference-heavy algorithms for improved image generation, relatively little work has explored inference scaling laws in video diffusion models (VDMs). Furthermore, existing research shows only minimal performance gains that are perceptible to the naked eye. To address this, we design a novel training-free algorithm IV-Mixed Sampler that leverages the strengths of image diffusion models (IDMs) to assist VDMs surpass their current capabilities. The core of IV-Mixed Sampler is to use IDMs to significantly enhance the quality of each video frame and VDMs ensure the temporal coherence of the video during the sampling process. Our experiments have demonstrated that IV-Mixed Sampler achieves state-of-the-art performance on 4 benchmarks including UCF-101-FVD, MSR-VTT-FVD, Chronomagic-Bench-150, and Chronomagic-Bench-1649. For example, the open-source Animatediff with IV-Mixed Sampler reduces the UMT-FVD score from 275.2 to 228.6, closing to 223.1 from the closed-source Pika-2.0.

## 1 Introduction

In the large foundation models era, maximizing the inference potential of foundation models [, ] that require high pre-training costs has become a research staple for academics [, ]. Efficient plug-and-play algorithms [, ] can significantly drive large-scale models to reach their full potential and outperform the original counterparts due to low trial-and-error costs. In contrast to popular inference-heavy algorithms (e.g., chain-of-thought (CoT) [] and OpenAI’s Strawberry []), which consistently emerge in the large language model (LLM) field, text-to-video (T2V) synthesis still faces the prevalent challenge of low-quality synthesized videos that lack semantic faithfulness [, ]. This limitation severely hampers the deployment and application of video diffusion models (VDMs). Motivated by the success of inference scaling laws in LLMs, we inevitably wonder whether a Markovian chain exists within VDMs similar to that of the autoregressive models [, ], allowing us to utilize its properties to enhance VDMs’ inference performance? The answer is obvious because the diffusion model is established on differential equations that incorporate both a forward and a reverse process [], allowing it to be fully considered a Markov chain during inference.

Figure: Figure 2: UMTScore (↑) vs. UMT-FVD (↓) with Animatediff [] on Chronomagic-Bench-150 []. In the legend, “R”, “I”, and “V” represent the score function estimation using random Gaussian noise, IDM, and VDM, respectively. Moreover, the front of the horizontal line “-” refers to the additive noise form, while the back of “-” represents the denoising paradigm. For instance, “RR-II” stands for a two-step of adding noise with Guassian noise followed by two-step of denoising performed using IDM.
Refer to caption: x2.png

#### Motivation.

VDM-based training-free algorithms typically face a significant challenge: their performance ceiling is constrained by the VDM itself. To be specific, the videos synthesized from most open-source VDMs [, ] exhibit several inherent problems, such as weak semantic consistency between the videos and the prompts, as well as low quality. A widely accepted perspective [, ] on this phenomenon is that underperforming VDMs cannot overcome their intrinsic limitations because they are trained on low-quality, small-scale T2V datasets. In contrast, image diffusion models (IDMs) can now reliably serve commercial application scenarios [], thanks to the well-established dataset ecosystem created by the AIGC community. This discrepancy naturally prompts us to consider whether we can view IDMs as tools to enhance VDMs and how to make IDMs effective assistants for VDMs.

Since diffusion models employ a multi-step sampling mechanism and the quality of synthesized samples from IDMs is significantly higher than that from VDMs, it is reasonable to use IDMs and VDMs alternately for score function estimation throughout the reverse sampling process. However, this straightforward paradigm leads to a loss of temporal coherence in the synthesized videos during our initial empirical explorations. Inspired by SDEdit [], we enhance the quality of each frame at every denoising step by performing the following additional operation: 1) first adding Gaussian noise and 2) then denoising using IDMs. Unfortunately, as illustrated in Fig. 2, the approach “R-$[\cdot]$”, which use Gaussian noise to perform the forward diffusion process, result in significantly lower quality of the synthesized video compared to the standard DDIM process (i.e., Origin in Fig. 2). This phenomenon arises because “R-$[\cdot]$” over-introduces invalid information (i.e., Gaussian noise) into the synthesized video during denoising. Given this, we consider the more robust deterministic sampling method to integrate the video denoising process with the image denoising process, as this paradigm is stable and effectively reduces truncation errors in practical discrete sampling.

In this paper, we consider the widely used deterministic function DDIM-Inversion [] to inject perturbations into the video. The experimental results of labeled “I-$[\cdot]$” and “V-$[\cdot]$” in Fig. 2 demonstrate that first performing DDIM-Inversion and then executing DDIM before each denoising step significantly improves video quality. Additionally, the observation that “I-$[\cdot]$” significantly surpasses “V-$[\cdot]$” further substantiates that IDMs trained on high-quality datasets can play a positive role in the video sampling process. Motivated by this, we further explore the upper bound of the performance gain that IDM provides for video synthesis. We primarily extend the paradigm of the single-step diffusion process and the single-step reverse process to multiple steps. Then, to ensure inference efficiency, we investigate all possible combinations in the two-step diffusion process and the two-step inverse process, collectively naming this series of algorithms IV-mixed Sampler.

#### Contribution.

Specifically, 1) we construct IV-mixed Sampler under a rigorous mathematical framework and demonstrate, through theoretical analysis, that it can be elegantly transformed into a standard inverse ordinary differential equation (ODE) process. For the sake of intuition, we present IV-mixed Sampler (w.r.t., “IV-IV”) on Fig. 3 and its pseudo code in Appendix B. 2) The empirically optimal IV-mixed Sampler further reduces the UMT-FVD by approximately 10 points compared to the best “I-I” in Fig. 2 and by 39.72 points over FreeInit []. Furthermore, 3) we conduct sufficient ablation studies to determine which classifier-free guidance (CFG) [] scale and which sampling paradigm yield the best performance for various metrics at what sampling intervals. In addition to this, 4) qualitative and quantitative comparison experiments have amply demonstrated that our algorithm achieves state-of-the-art (SOTA) performance on four popular benchmarks: UCF-101-FVD [], MSR-VTT-FVD [], Chronomagic-Bench-150 [], and Chronomagic-1649 []. These competitive outcomes demonstrate that our proposed IV-mixed Sampler dramatically improves the visual quality and semantic faithfulness of the synthesized video.

## 2 Preliminary

We review VDMs, SDEdit, DDIM & DDIM-Inversion in this section and further bootstrap how past work has designed VDM-based plug-and-play algorithms in Appendix A.3.

Figure: Figure 3: Overview of our IV-mixed Sampler, Video-based Sampler and Image-based Sampler. IV-mixed Sampler utilizes IDM and VDM to ensure synthesized video quality and temporal coherence, respectively.
Refer to caption: x3.png

#### Diffusion Models.

Diffusion models [, , ] including IDMs and VDMs consist of a forward process and a reverse process. Given $\mathbf{x}_{0}$ represent a D-dimensional random variable sampled from the real data distribution $q_{0}(\mathbf{x}_{0})$. The forward process injects Guassian noise $\epsilon_{t}\sim\mathcal{N}(0,\mathbf{I})$ to the clean data as follows:

$$ $\begin{split}&\mathbf{x}_{t}=\alpha_{t}\mathbf{x}_{0}+\sigma_{t}\epsilon_{t}, \\ \end{split}$ (1) $$

where $t\sim\mathcal{U}[\eta,1]$ ($\eta$ is a very small quantity defaulting to 1e-5) and $\alpha_{t}$ and $\sigma_{t}$ are components of a predefined noise schedule. $\sigma_{t}$ is monotonically increasing from 0 0 to $1$ in all diffusion models, while $\alpha_{t}$ can either remain constant (e.g., EDM []) or decrease monotonically (e.g., VP-SDE [] and Rectified Flow []) from 0 0 to $1$. The forward process in Eq. 1 can be rewritten as the following stochastic differential equation (SDE):

$$ $\begin{split}d\mathbf{x}_{t}=f(t)\mathbf{x}_{t}dt+g(t)\overline{\bm{\omega}}_{ t},\end{split}$ (2) $$

where $f(t)$ and $g(t)$ denote the drift coefficient of $\mathbf{x}_{t}$ and the diffusion coefficient of $\mathbf{x}_{t}$, respectively. $\overline{\bm{\omega}}_{t}$ refers to a standard Wiener process. Eq. 2 has a corresponding ODE-based reverse process defined as:

$$ $\begin{split}d\mathbf{x}_{t}=f(t)\mathbf{x}_{t}-\frac{1}{2}g^{2}(t)\nabla_{ \mathbf{x}}\log q_{t}(\mathbf{x}),\end{split}$ (3) $$

where $\nabla_{\mathbf{x}}\log q_{t}(\mathbf{x})$ denotes the score function $\nabla_{\mathbf{x}_{t}}\log p_{t}(\mathbf{x}_{t})$. Since $\nabla_{\mathbf{x}}\log q_{t}(\mathbf{x})$ cannot be accessed during the reverse process, it must be replaced by a linear transformation $\frac{\bm{\epsilon}_{\theta}(\mathbf{x}_{t},t)}{-\sigma_{t}}$ using the noise estimation model $\bm{\epsilon}_{\theta}(\cdot,\cdot)$ or the score function estimation model $\mathbf{s}_{\theta}(\cdot,\cdot)$.

#### Video Diffusion Model vs. Image Diffusion Model.

The most critical differences between IDM and VDM lie in their training sets and model architectures. Regarding training sets, IDM typically utilizes large-scale, high-quality datasets, enabled by the increasing availability of both real and synthetic image datasets []. Conversely, the performance of VDMs is significantly constrained by the limited number of publicly available video datasets, such as Webvid-10M [] and Pandas-70M [], which contain low-quality real data. In terms of model architectures, several VDMs differ from their IDM counterparts because video data $\mathbf{x}_{0}\in\mathbb{R}^{b\times\mathrm{c}\times\mathrm{t}\times\mathrm{h}
\times\mathrm{w}}$ includes an additional time dimension $\mathrm{t}$, unlike image data $\mathbf{x}_{0}\in\mathbb{R}^{b\times\mathrm{c}\times\mathrm{h}\times\mathrm{w}}$, where $\mathrm{b}$, $\mathrm{c}$, $\mathrm{h}$, and $\mathrm{w}$ refer to batch size, number of channels, height, and width, respectively. Therefore, most VDMs incorporate both spatial and temporal blocks, where the spatial block aligns with the module used in the mainstream IDMs, while the temporal block employs 3D convolutions [] or tokens in the time dimension [] to capture temporal information.

#### SDEdit.

SDEdit [] is an image editing method that produces a latent variable capable of reconstructing the input $\mathbf{x}_{0}$. It first injects Gaussian noise into $\mathbf{x}_{0}$, then performs editing in the latent space, and finally obtains pure samples through a standard reverse process. This approach provides a scheme for editing the latent variable using IDM at each step of sampling. Since SDEdit is nontrivial to invert, we employ DDIM-Inversion [] to map the latent $\mathbf{x}_{t}$ back to its previous counterpart $\mathbf{x}_{t+\Delta t}$, where $1-t\geq\Delta t>0$.

#### DDIM & DDIM-Inversion.

DDIM [] serves as an efficient ODE-based sampler that iteratively refines the initial Gaussian noise $\mathbf{x}_{T}$, ultimately generating a “clean” video $\mathbf{x}_{0}$ that conforms to the data distribution $p_{0}(\mathbf{x}_{0})$. A notable characteristic of DDIM is its adherence to deterministic sampling. The synthesized data produced by DDIM can be expressed as follows:

$$ $\begin{split}&\mathbf{x}_{t}=\pounds(\mathbf{x}_{s})=\alpha_{t}\left(\frac{ \mathbf{x}_{s}-\sigma_{s}\bm{\epsilon}_{\theta}(\mathbf{x}_{s},s)}{\alpha_{s}} \right)+\sigma_{t}\bm{\epsilon}_{\theta}(\mathbf{x}_{s},s).\ \end{split}$ (4) $$

In this equation, $s$ and $t$ denote timesteps $\in\mathcal{U}[0,1]$, with the condition that $t\leq s$. When under the constraint $t\geq s$, the standard DDIM in Eq. 4 is referred to as DDIM-Inversion $\mathbf{x}_{t}=\pounds^{-\!1}(\mathbf{x}_{s})$. In practical, DDIM is often incorporated into classifier-free guidance for more precise control as well as higher quality data synthesis. Thus, Eq. 4 can be transferred into

$$ $\begin{split}&\mathbf{x}_{t}=\pounds(\mathbf{x}_{s},\omega)=\Big{[}\alpha_{t} \mathbf{x}_{s}+(\alpha_{s}\sigma_{t}-\alpha_{t}\sigma_{s})\\ &[(\omega+1)\bm{\epsilon}_{\theta}(\mathbf{x}_{s},s,\mathbf{c})-\omega\bm{ \epsilon}_{\theta}(\mathbf{x}_{s},s,\varnothing)]\Big{]}/\alpha_{s},\\ \end{split}$ (5) $$

where $\mathbf{c}$, $\varnothing$ and $\omega$ stand for the text prompt, the null prompt and the CFG scale, respectively.

## 3 Approach

Observing that IDMs produce high-quality samples without ensuring temporal coherence, while VDMs ensure temporal continuity but generate low-quality video, we propose IV-mixed Sampler to combine the strengths of both IDMs and VDMs (see Fig. 3). In this section, we first describe how to sample from $\mathbf{x}_{t}$ to $\mathbf{x}_{t+\Delta t}$ and from $\mathbf{x}_{t+\Delta t}$ to $\mathbf{x}_{t}$ using IDM and VDM. We then introduce IV-mixed Sampler and outline its design space of hyperparameters, followed by a theoretical analysis. Finally, we discuss the effect of sampling in the latent space on IV-mixed Sampler.

### 3.1 Forward (Go!!) and Reverse (Back!!)

A crucial step in overcoming the bottleneck of VDM $\epsilon_{\theta}^{\tiny\mathbf{\mathrm{V}}}(\cdot,\cdot)$ with IDM $\epsilon_{\theta}^{\tiny\mathbf{\mathrm{I}}}(\cdot,\cdot)$ is to address the domain gap between IDM and VDM caused by differences in training data. Therefore, a specialized rescheduling paradigm is required to achieve the mapping $\mathbf{x}_{t}\rightarrow\pounds^{-\!1}(\mathbf{x}_{t})\rightarrow\pounds(
\pounds^{-\!1}(\mathbf{x}_{t}))=\mathbf{x}_{t}$, where $\pounds(\cdot)$ is a deterministic function with an inverse $\pounds^{-\!1}(\cdot)$. Given this, we can modify $\mathbf{x}_{x+\Delta t}\approx\pounds^{-\!1}(\mathbf{x}_{t})$ without disrupting the standard sampling process. We utilize DDIM-Inversion and DDIM to implement $\pounds^{-\!1}(\cdot,\cdot)$ and $\pounds(\cdot,\cdot)$, respectively. By introducing CFG, we can define a new paradigm to implement IDMs’ information injection via the operator $\mathtt{G}$, i.e. semantic information injection:

$$ $\begin{split}\mathbf{x}^{\prime}_{t}&=\mathcal{I}(\mathbf{x}_{t},\omega_{ \textrm{go}},\omega_{\textrm{back}},\mathtt{G},\epsilon^{\textrm{go}}_{\theta} ,\epsilon^{\textrm{back}}_{\theta})=\pounds(\mathbf{u}+\mathtt{G}(\mathbf{u}), \omega_{\textrm{back}}),\\ &\text{ where }\mathbf{u}=\pounds^{-\!1}(\mathbf{x}_{t},\omega_{\textrm{go}}). \\ \end{split}$ (6) $$

**Table 1: Quantitative comparison with popular heavy-inference algorithms on Chronomagic-Bench-150. ($+\Delta$ $[\cdot]$) stands for the improvement of IV-mixed Sampler compared to the “Standard DDIM”. I4VGen is not compared across other architectures because its official implementation is limited to Animatediff.**
| Model | Method | Extra Model | UMT-FVD (↓) | UMTScore (↑) | GPT4o-MTScore (↑) |
| --- | --- | --- | --- | --- | --- |
| VideoCrafterV2 | Standard DPM-Solver++ | ✗ | 214.06 | 2.76 | 2.87 |
| IV-mixed Sampler (ours) | ✓ | 210.57 ($+\Delta$ 3.49) | 3.29 ($+\Delta$ 0.53) | 3.30 ($+\Delta$ 0.43) |  |
| ModelScope-T2V | Standard DDIM | ✗ | 241.61 | 2.66 | 2.96 |
| FreeInit | ✗ | 220.96 | 3.01 | 3.09 |  |
| IV-mixed Sampler (ours) | ✓ | 234.90 ($+\Delta$ 6.71) | 3.02 ($+\Delta$ 0.36) | 3.14 ($+\Delta$ 0.18) |  |
| Animatediff<br>(SD V1.5,<br>Motion Adapter V3) | Standard DDIM | ✗ | 275.18 | 2.82 | 2.83 |
| FreeInit | ✗ | 268.31 | 2.82 | 2.59 |  |
| I4VGen | ✓ | 227.21 | 2.66 | 3.02 |  |
| IV-mixed Sampler (ours) | ✓ | 228.59 ($+\Delta$ 46.59) | 3.30 ($+\Delta$ 0.48) | 3.55 ($+\Delta$ 0.72) |  |

**Table 2: Quantitative comparison with popular heavy-inference algorithms, including FreeInit and I4VGen, on Chronomagic-Bench-1649 []. Yellow cells stands for the winner.**
| Model | Method | Extra Model | UMT-FVD (↓) | UMTScore (↑) | GPT4o-MTScore (↑) |
| --- | --- | --- | --- | --- | --- |
| VideoCrafterV2 | Standard DPM-Solver++ | ✗ | 178.45 | 2.75 | 2.68 |
| IV-mixed Sampler (ours) | ✓ | 172.02 ($+\Delta$ 6.43) | 3.35 ($+\Delta$ 0.60) | 3.04 ($+\Delta$ 0.36) |  |
| ModelScope-T2V | Standard DDIM | ✗ | 199.52 | 2.99 | 3.17 |
| IV-mixed Sampler (ours) | ✓ | 197.44 ($+\Delta$ 2.08) | 3.06 ($+\Delta$ 0.07) | 3.25 ($+\Delta$ 0.08) |  |
| Animatediff<br>(SD V1.5,<br>Motion Adapter V3) | Standard DDIM | ✗ | 219.29 | 3.08 | 2.62 |
| FreeInit | ✗ | 209.62 | 3.08 | 2.73 |  |
| I4VGen | ✓ | 206.21 | 3.21 | 3.07 |  |
| IV-mixed Sampler (ours) | ✓ | 192.72 ($+\Delta$ 26.57) | 3.40 ($+\Delta$ 0.32) | 3.34 ($+\Delta$ 0.72) |  |

In Eq. 6, $\omega_{\textrm{go}}$ and $\omega_{\textrm{back}}$ stand for the CFG scales for the DDIM-Inversion and DDIM, respectively. $\epsilon^{\textrm{go}}_{\theta}(\cdot,\cdot)$ and $\epsilon^{\textrm{back}}_{\theta}(\cdot,\cdot)$ are the noise estimation models used to perform $\pounds^{-\!1}(\cdot,\cdot)$ and $\pounds(\cdot,\cdot)$, respectively. $\mathtt{G}$ is any function whose mission is to make modifications to $\mathbf{u}$. It is worth noting that for IDMs, we first reshape $\mathbf{x}_{t}$ from the shape $b\!\times\!c\!\times\!t\!\times\!h\!\times\!w$ to $(b\!\times\!t)\!\times\!c\!\times\!h\!\times\!w$, and then pass it through the noise estimation model to perform the operation $\mathcal{I}$ in the practical implementation. If $\omega_{\textrm{go}}\equiv\omega_{\textrm{back}}$, $\epsilon^{\textrm{go}}_{\theta}(\cdot,\cdot)\equiv\epsilon^{\textrm{back}}_{
\theta}(\cdot,\cdot)$ and $\mathtt{G}(\cdot)$ is an identity operator, then $\mathbf{x}^{\prime}_{t}\equiv\mathbf{x}_{t}$. To understand how $\mathcal{I}$ injects semantic information, we rewrite Eq. 7 using a first-order Taylor expansion as

$$ $\begin{split}&\mathcal{I}(\mathbf{x}_{t},\omega_{\textrm{go}},\omega_{\textrm{ back}},\mathtt{G},\epsilon^{\textrm{go}}_{\theta},\epsilon^{\textrm{back}}_{ \theta})=\pounds(\pounds^{-\!1}(\mathbf{x}_{t},\omega_{\textrm{go}})+\mathtt{G }(\pounds^{-\!1}(\mathbf{x}_{t},\omega_{\textrm{go}})),\omega_{\textrm{back}}) \\ &=\pounds(\pounds^{-\!1}(\mathbf{x}_{t},\omega_{\textrm{go}}),\omega_{\textrm{ go}})+(\omega_{\textrm{back}}-\omega_{\textrm{go}})\frac{\partial\pounds( \pounds^{-\!1}(\mathbf{x}_{t},\omega_{\textrm{go}}),\omega_{\textrm{go}})}{ \partial\omega_{\textrm{go}}}\\ &+\mathtt{G}(\pounds^{-\!1}(\mathbf{x}_{t},\omega_{\textrm{go}}))\frac{ \partial\pounds(\pounds^{-\!1}(\mathbf{x}_{t},\omega_{\textrm{go}}),\omega_{ \textrm{go}})}{\partial\pounds^{-\!1}(\mathbf{x}_{t},\omega_{\textrm{go}})}+ \mathcal{O}((\omega_{\textrm{back}}-\omega_{\textrm{go}})^{2})\\ &+\mathcal{O}(\mathtt{G}(\pounds^{-\!1}(\mathbf{x}_{t},\omega_{\textrm{go}}))^ {2})=\mathbf{x}_{t}\text{{\color[rgb]{0.172549,0.627451,0.172549}\definecolor[ named]{pgfstrokecolor}{rgb}{0.172549,0.627451,0.172549}\quad\# define }}{ \color[rgb]{0.172549,0.627451,0.172549}\definecolor[named]{pgfstrokecolor}{rgb }{0.172549,0.627451,0.172549}J=\alpha_{t+\Delta t}\sigma_{t}-\alpha_{t}\sigma_ {t+\Delta t}}\\ &+{\color[rgb]{0.580392,0.403922,0.741176}\definecolor[named]{pgfstrokecolor}{ rgb}{0.580392,0.403922,0.741176}(\omega_{\textrm{back}}-\omega_{\textrm{go}}) \Big{[}\partial\Big{(}\mathbf{x}_{t}+[J[(\omega_{\textrm{back}}+1)\epsilon^{ \textrm{back}}_{\theta}(\mathbf{x}_{t+\Delta t},t+\Delta t,\mathbf{c})}\\ &{\color[rgb]{0.580392,0.403922,0.741176}\definecolor[named]{pgfstrokecolor}{ rgb}{0.580392,0.403922,0.741176}-\omega_{\textrm{back}}\epsilon^{\textrm{back} }_{\theta}(\mathbf{x}_{t+\Delta t},t+\Delta t,\varnothing)]/\alpha_{t+\Delta t }]\Big{)}\Big{]}/\partial\omega_{\textrm{go}}}\\ &+(\omega_{\textrm{back}}-\omega_{\textrm{go}})\Big{[}\partial\Big{(}(\alpha_{ t}\sigma_{t+\Delta t}-\alpha_{t+\Delta t}\sigma_{t})[(\omega_{\textrm{go}}+1) \epsilon^{\textrm{go}}_{\theta}(\mathbf{x}_{t},t,\mathbf{c})\\ &-\omega_{\textrm{go}}\epsilon^{\textrm{go}}_{\theta}(\mathbf{x}_{t},t, \varnothing)]/\alpha_{t+\Delta t}\Big{)}\Big{]}/\partial\omega_{\textrm{go}}\\ &+\mathtt{G}(\pounds^{-\!1}(\mathbf{x}_{t},\omega_{\textrm{go}}))\frac{ \partial\pounds(\pounds^{-\!1}(\mathbf{x}_{t},\omega_{\textrm{go}}),\omega_{ \textrm{go}})}{\partial\pounds^{-\!1}(\mathbf{x}_{t},\omega_{\textrm{go}})}\\ &=\mathbf{x}_{t}+{\color[rgb]{0.890196,0.466667,0.760784}\definecolor[named]{ pgfstrokecolor}{rgb}{0.890196,0.466667,0.760784}(\omega_{\textrm{back}}-\omega _{\textrm{go}})\frac{(\alpha_{t}\sigma_{t+\Delta t}-\alpha_{t+\Delta t}\sigma_ {t})[\epsilon^{\textrm{go}}_{\theta}(\mathbf{x}_{t},t,\mathbf{c})-\epsilon^{ \textrm{go}}_{\theta}(\mathbf{x}_{t},t,\varnothing)]}{\alpha_{t+\Delta t}}}\\ &+\mathtt{G}(\pounds^{-\!1}(\mathbf{x}_{t},\omega_{\textrm{go}}))\frac{ \partial\pounds(\pounds^{-\!1}(\mathbf{x}_{t},\omega_{\textrm{go}}),\omega_{ \textrm{go}})}{\partial\pounds^{-\!1}(\mathbf{x}_{t},\omega_{\textrm{go}})}. \text{{\color[rgb]{0.580392,0.403922,0.741176}\definecolor[named]{ pgfstrokecolor}{rgb}{0.580392,0.403922,0.741176}\quad\# Ignore second-order and higher terms.}}\end{split}$ (7) $$

Observing the pink term in Eq. 7, we can inject semantic information from both $\epsilon^{\textrm{go}}_{\theta}(\cdot,\cdot)$ and $\epsilon^{\textrm{back}}_{\theta}(\cdot,\cdot)$ into $\mathbf{x}_{t}$ by setting $\omega_{\textrm{back}}-\omega_{\textrm{go}}>0$. In particular, we set $\omega_{\textrm{back}}=-\omega_{\textrm{go}}$ and $\omega_{\textrm{back}}>0$ by default. Given this, we only need to replace $\epsilon^{\textrm{go}}_{\theta}$ with $\epsilon_{\theta}^{\tiny\mathbf{\mathrm{I}}}(\cdot,\cdot)$ or $\epsilon_{\theta}^{\tiny\mathbf{\mathrm{V}}}(\cdot,\cdot)$ to inject specific semantic information, thereby enhancing the visual quality or temporal coherence of the synthesized video.

### 3.2 IV-mixed Sampler

**Table 3: Quantitative comparison on UCF-101 datasets using Animatediff and ModelScope-T2V. ($+\Delta$ $[\cdot]$) indicates the improvement of IV-mixed Sampler compared to the “Standard DDIM”.**
| Model | Method | Extra Model | FVD (↓)<br>(StyleGAN) | FVD (↓)<br>(VideoGPT) |
| --- | --- | --- | --- | --- |
| Animatediff<br>(SD V1.5,<br>Motion Adapter V3) | Standard DDIM | ✗ | 815.08 | 819.93 |
| FreeInit | ✗ | 805.33 | 807.04 |  |
| Unictrl | ✗ | 1859.13 | 1863.35 |  |
| I4VGen | ✓ | 803.25 | 805.77 |  |
| IV-mixed Sampler (ours) | ✓ | 800.45 ($+\Delta$ 14.63) | 804.88 ($+\Delta$ 15.05) |  |
| ModelScope-T2V | Standard DDIM | ✗ | 1492.17 | 1484.97 |
| IV-mixed Sampler (ours) | ✓ | 841.64 ($+\Delta$ 650.53) | 838.05 ($+\Delta$ 646.92) |  |

**Table 4: Quantitative comparison on MSR-VTT using Animatediff and ModelScope-T2V. ($+\Delta$ $[\cdot]$) indicates the improvement of IV-mixed Sampler compared to the “Standard DDIM”.**
| Model | Method | Extra Model | FVD (↓)<br>(StyleGAN) | FVD (↓)<br>(VideoGPT) |
| --- | --- | --- | --- | --- |
| Animatediff<br>(SD V1.5,<br>Motion Adapter V3) | Standard DDIM | ✗ | 762.23 | 761.01 |
| FreeInit | ✗ | 732.57 | 731.04 |  |
| I4VGen | ✓ | 741.56 | 740.13 |  |
| IV-mixed Sampler (ours) | ✓ | 721.32 ($+\Delta$ 40.91) | 719.9 ($+\Delta$ 41.11) |  |
| ModelScope-T2V | Standard DDIM | ✗ | 739.12 | 737.24 |
| IV-mixed Sampler (ours) | ✓ | 603.31 ($+\Delta$ 135.81) | 601.89 ($+\Delta$ 135.35) |  |

The paradigm defined in Eq. 6 enables us to easily describe all the algorithms shown in Fig. 2 that do not use Gaussian noise for score function estimation. For instance, “I-I” and “V-V” can represent $\mathcal{I}(\mathbf{x}_{t},-h,h,\mathtt{G},\bm{\epsilon}_{\theta}^{\mathrm{I}}
,\bm{\epsilon}_{\theta}^{\mathrm{I}})$ and $\mathcal{I}(\mathbf{x}_{t},-h,h,\mathtt{G},\bm{\epsilon}_{\theta}^{\mathrm{V}}
,\bm{\epsilon}_{\theta}^{\mathrm{V}})$, respectively, under the condition $h\!>\!0$ and $\mathtt{G}$ is an identity operator. Clearly, this represents only a single-step injection of semantic information. We can construct IV-mixed Sampler to allow multi-step injections of semantic information using $\mathtt{G}$ and the recursive definition:

$$ $\begin{split}\mathbf{x}^{\prime}_{t}=\ &\mathtt{G}^{1}(\mathbf{x}_{t})= \mathcal{I}(\mathbf{x}_{t},-h,h,\mathtt{G}^{2},\bm{\epsilon}_{\theta}^{1, \textrm{go}},\bm{\epsilon}_{\theta}^{1,\textrm{back}}),\\ &\mathtt{G}^{2}(\mathbf{y})=\mathcal{I}(\mathbf{y},-h,h,\mathtt{G}^{3},\bm{ \epsilon}_{\theta}^{2,\textrm{go}},\bm{\epsilon}_{\theta}^{2,\textrm{back}}), \\ &\mathbf{\small\vdots}\\ &\mathtt{G}^{N}(\mathbf{y})=\mathcal{I}(\mathbf{y},-h,h,\mathtt{G}^{N+1},\bm{ \epsilon}_{\theta}^{N,\textrm{go}},\bm{\epsilon}_{\theta}^{N,\textrm{back}}), \\ &\text{\quad s.t.\quad}N\geq 1,\\ \end{split}$ (8) $$

where $N$ and $\mathtt{G}^{N+1}$ refer to the number of semantic information injection and the identity operator, respectively. Through Eq. 8, we can easily represent IV-mixed Sampler with different $N$. For instance, following the definition in Fig. 2, “IV-VI” can be described as $\mathbf{x}^{\prime}_{t}=\mathtt{G}^{1}(\mathbf{x}_{t})=\mathcal{I}(\mathbf{x}_
{t},-h,h,\mathtt{G}^{2},\bm{\epsilon}_{\theta}^{\mathrm{I}},\bm{\epsilon}_{
\theta}^{\mathrm{I}})$, $\mathtt{G}^{2}(\mathbf{y})=\mathcal{I}(\mathbf{y},-h,h,\mathtt{G}^{3},\bm{
\epsilon}_{\theta}^{\mathrm{V}},\bm{\epsilon}_{\theta}^{\mathrm{V}})$ and $\mathtt{G}^{3}$ is an identity operator. Considering the computational overhead and performance trade-offs, this paper focuses only on the scenario where $N=2$. In Sec. 4’s ablation study, we further restrict $\bm{\epsilon}_{\theta}^{1,\textrm{go}}$, $\bm{\epsilon}_{\theta}^{1,\textrm{back}}$, $\bm{\epsilon}_{\theta}^{2,\textrm{go}}$, and $\bm{\epsilon}_{\theta}^{2,\textrm{back}}$ to two models each, occupied by $\epsilon_{\theta}^{\tiny\mathbf{\mathrm{I}}}(\cdot,\cdot)$ and $\epsilon_{\theta}^{\tiny\mathbf{\mathrm{V}}}(\cdot,\cdot)$ (w.r.t., $C_{2}^{4}$ combinations), and find that “IV-IV” performs best. The visualization in Fig. 1 demonstrates that “IV-IV” significantly improves both the visual quality of the synthesized video and the consistency between the video and the text prompt.

### 3.3 Discussion

#### Hyperparameter Design Space.

In this paper, we elucidate three design choices: the $C_{2}^{4}$ combinations mentioned in Sec. 3.2, the intervals at which IV-mixed Sampler is performed during standard DDIM sampling, and the dynamic CFG scale. All three forms are expected to find the empirically optimal solution, with the first two being natural explorations and the last addressing the domain gap between IDMs and VDMs, which is expected to be mitigated by adjusting the CFG scale. For the last one, to be specific, we re-express $-h$ and $h$ in Eq. 8 as $-h^{\textrm{go}}(t)$ and $h^{\textrm{back}}(t)$. Inspired by the Karras’s noise schedule [], we define $h^{\textrm{go}}(t)$ and $h^{\textrm{back}}(t)$ as

$$ $\begin{split}&h^{\textrm{go}}(t)=({\left[\gamma^{\textrm{begin}}_{\textrm{go}} \right]}^{\frac{1}{\rho}}+t({\left[\gamma^{\textrm{end}}_{\textrm{go}}\right]} ^{\frac{1}{\rho}}-{\left[\gamma^{\textrm{begin}}_{\textrm{go}}\right]}^{\frac{ 1}{\rho}}))^{\rho},\\ &h^{\textrm{back}}(t)=({\left[\gamma^{\textrm{begin}}_{\textrm{back}}\right]}^ {\frac{1}{\rho}}+t({\left[\gamma^{\textrm{end}}_{\textrm{back}}\right]}^{\frac {1}{\rho}}-{\left[\gamma^{\textrm{begin}}_{\textrm{back}}\right]}^{\frac{1}{ \rho}}))^{\rho},\\ \end{split}$ (9) $$

where $\gamma^{\textrm{end}}_{\textrm{go}}$ and $\gamma^{\textrm{end}}_{\textrm{back}}$ represent the CFG scales when $t=1$, while $\gamma^{\textrm{begin}}_{\textrm{go}}$ and $\gamma^{\textrm{begin}}_{\textrm{back}}$ denote the CFG scales when $t=0$. The parameter $\rho$ controls the concave and convex properties of the CFG scale curve with respect to $t$. The experiments in Sec. 4 demonstrate that the dynamic CFG scale can be adjusted to achieve performance improvements for specific aspects (e.g., semantic faithfulness).

#### Theoretical Analysis.

As shown in Theorem 3.1, IV-mixed Sampler can be elegantly transformed into an ODE, taking the same form as Eq. 3. Consequently, IV-mixed Sampler preserves the standard sampling process (e.g., DDIM or Euler–Maruyama), enabling a trade-off between temporal coherence and visual quality by adjusting the parameters $\omega^{\textrm{IDM}}_{\textrm{go-back}}$, $\omega^{\textrm{VDM}}_{\textrm{go-back}}$, and $\omega$.

###### Theorem 3.1 .

(the proof in Appendix C) IV-mixed Sampler can be transferred to an ODE. For example, the ODE corresponding to “IV-IV” is

$$ $\begin{split}&d\mathbf{x}_{t}=f(t)\mathbf{x}_{t}-\frac{1}{2}g^{2}(t)\Big{[} \omega^{\textrm{IDM}}_{\textrm{go-back}}\frac{g^{2}(t)}{2}\nabla_{\mathbf{x}} \log q^{\textrm{IDM}}_{t}(\mathbf{c}|\mathbf{x})\\ &+(\omega^{\textrm{VDM}}_{\textrm{go-back}}+\omega)\frac{g^{2}(t)}{2}\nabla_{ \mathbf{x}}\log q^{\textrm{VDM}}_{t}(\mathbf{c}|\mathbf{x})\Big{]},\\ \end{split}$ (10) $$

Here, $\omega$ refers to the vanilla CFG scale, while both $\omega^{\textrm{IDM}}_{\textrm{go-back}}$ and $\omega^{\textrm{IDM}}_{\textrm{go-back}}$ are CFG scales that are greater than 0. Let $\nabla_{\mathbf{x}}\log q^{\textrm{IDM}}_{t}(\mathbf{c}|\mathbf{x})$ and $\nabla_{\mathbf{x}}\log q^{\textrm{VDM}}_{t}(\mathbf{c}|\mathbf{x})$ represent the score function estimated for $p_{t}(\mathbf{x}_{t})$ using IDM and VDM under classifier-free guidance.

Figure: Figure 4: Ablation studies on sampling intervals of IV-mixed Sampler (“IV-IV”) with Animatediff (SD V1.5, Motion Adapter V3). The Begin%-End% in the legend indicates the portion of the entire sampling process performed by IV-mixed Sampler. For example, in a 50-step sampling scenario, 0%-50% corresponds to IV-mixed Sampler being applied during steps 1-25. More details of “IV-VI” can be found in Appendix D.
Refer to caption: x4.png

Figure: Figure 5: Ablation studies on different $C_{4}^{2}$ species combinations with Animatediff (SD V1.5, Motion Adapter V3). We can clearly observe that IV-mixed Sampler (“IV-IV”) is the winner across all metrics.
Refer to caption: x5.png

Figure: Figure 6: Ablation studies on dynamic CFG scale with Animatediff (SD V1.5, Motion Adapter V3). We ensure that $h^{\textrm{go}}(t)\equiv h^{\textrm{back}}(t)$. Consequently, the IDM dynamic CFG scale corresponds to IDM’s $\gamma_{\textrm{go}}^{\textrm{end}}-\gamma_{\textrm{go}}^{\textrm{begin}}$. Similarly, the VDM dynamic CFG scale corresponds to VDM’s $\gamma_{\textrm{go}}^{\textrm{end}}-\gamma_{\textrm{go}}^{\textrm{begin}}$. $\log_{7}(\rho)$ is 1, 0, and -1 indicates whether the change from $\gamma_{\textrm{go}}^{\textrm{end}}$ to $\gamma_{\textrm{go}}^{\textrm{begin}}$ is convex, linear, or concave, respectively.
Refer to caption: x6.png

###### Theorem 3.1 .

#### The Influence of Latent Space.

Most current high-resolution IDMs and VDMs follow the latent diffusion model (LDM) paradigm []. As a result, leveraging IV-mixed Sampler requires IDM and VDM to share the same latent space, meaning they must use the same VAE []. Fortunately, for most VDMs, we always can find the corresponding IDM that share the same latent space with the VDM. For cases where this condition is not met, we can convert the video from shape b$\times$c$\times$t$\times$h$\times$w to (b$\times$t)$\times$c$\times$1$\times$h$\times$w and then pass it through VDM, which is referred to as using “IDM”. This paradigm is also applied in I4VGen [].

## 4 Experiment

In this section, we present experiments to demonstrate the effectiveness of IV-mixed Sampler. Specifically, we perform qualitative and quantitative comparisons across various benchmarks on multiple T2V diffusion models, including ModelScope-T2V [], Animatediff [], and VideoCrafterV2 []. Additionally, we compare IV-mixed Sampler with three heavy-inference algorithms, FreeInit [], Unictrl [] and I4VGen [], on VDM. Note that I4VGen is also an algorithm designed to enhance VDM performance using IDM. However, its IDM is configured to be consistent with VDM, achieving image synthesis by reshaping from b$\times$c$\times$t$\times$h$\times$w to (b$\times$t)$\times$c$\times$1$\times$h$\times$w before passing it through VDM. For further details, please refer to Appendix A.3. Finally, we conduct extensive ablation studies and present visualization to validate the optimal solution of various design choices. More implementation details can be found in Appendix A.

### 4.1 Main Results

#### Chronomagic-Bench 150 & 1649.

We evaluate the effectiveness of IV-mixed Sampler on three different VDMs: VideoCrafterV2, ModelScope-T2V, and Animatediff (SD V1.5, Motion Adapter V3). The comparison results on Chronomagic-Bench-150 (w.r.t, 150 prompts) are presented in Table 1. We employ three metrics in this benchmark: UMT-FVD (for visual quality), UMTScore (for semantic faithfulness), and GPT4o-MTScore (for temporal coherence and metamorphic amplitude) to assess our proposed method. The experimental results in Table 1 show that IV-mixed Sampler significantly outperforms both the standard sampling method and other computationally intensive algorithms. This indicates that rational integration of IDM and VDM has great potential to improve the performance of video synthesis tasks. Although IV-mixed Sampler does not outperform all comparative methods on Animatediff and ModelScope-T2V in terms of UMT-FVD, it still shows a significant improvement over standard sampling algorithms. It is worth noting that ModelScope-T2V was unable to locate a high-quality IDM due to its low resolution (i.e., 224$\times$224) synthesized video. In contrast, IV-mixed Sampler do not perform best on Animatediff because I4VGen is an algorithm that integrates both IDM and VDM. Moreover, on the more comprehensive Chronomagic-Bench-1649 (w.r.t, 1649 prompts), IV-mixed Sampler outperforms all comparative methods across all metrics and models. As illustrated in Table 2, IV-mixed Sampler achieves the best performance on all metrics, even when compared to the latest SOTA method, I4VGen. These experimental results underscore the strong generalization capabilities of IV-mixed Sampler, highlighting its effectiveness as a plug-and-play solution that can be seamlessly integrated across various VDMs.

#### UCF-101-FVD & MSR-VTT-FVD.

Additionally, to complement our experimental results, we conduct experiments on several traditional benchmarks, including UCF-101-FVD and MSR-VTT-FVD. The FVD results for UCF-101 and MSR-VTT are presented in Table 3 and Table 4, respectively. These quantitative results significantly substantiate the superiority of IV-mixed Sampler, highlighting its effectiveness in outperforming existing heavy-inference approaches on VDMs. Through these results and visualized in Fig. 1, IV-mixed Sampler has strong generalization ability across different VDMs, which possesses significant practical application value in real-world scenarios.

### 4.2 Ablation Studies

As described in Sec. 3.3, we elucidate three design choices, namely the sampling interval of IV-mixed Sampler, the $C_{4}^{2}$ species combinations, and the dynamic CFG scale. For 1) the sampling interval of IV-mixed Sampler, the results in Fig. 4 clearly illustrate that performing IV-mixed Sampler across all sampling steps is optimal. Another evident conclusion is that the closer the sampling interval of IV-mixed Sampler is to $t\!=\!1$, the more significant the performance gain. This suggests that to save computational overhead, IV-mixed Sampler can be applied within the 0%-50% sampling interval or even restricted to the 0%-25% interval. For 2) the $C_{4}^{2}$ species combinations, we present its ablation results in Fig. 5. It is evident that “IV-IV” outperforms all metrics and significantly surpasses both FreeInit and standard DDIM. This suggests that there is an empirically optimal combination of results within IV-mixed Sampler. Accordingly, we use “IV-IV” for all comparison experiments. For 3) the dynamic CFG scale, the conclusions are not as intuitive as the first two design choices. Specifically, we considered a total of 15 combinations of dynamic CFG scales, where the CFG scale varies from $\gamma_{\textrm{go}}^{\textrm{end}}$ to $\gamma_{\textrm{go}}^{\textrm{begin}}$ across five convex, five straight, and five concave functions. In Fig. 6, we set $\rho$ to 7, 1, and ${1/7}$(^1^11$\rho=7$ is the default implementation of Karras’s noise schedule [].) to model changes in the CFG scale as convex, straight, and concave functions, respectively. For each specified $\rho$, we consider five combinations of the IDM’s CFG scale $\omega_{\textrm{go-back}}^{\textrm{IDM}}$ and VDM’s CFG scale $\omega_{\textrm{go-back}}^{\textrm{VDM}}$: (1) both remaining constant, (2) $\omega_{\textrm{go-back}}^{\textrm{IDM}}$ increasing and $\omega_{\textrm{go-back}}^{\textrm{VDM}}$ increasing, (3) $\omega_{\textrm{go-back}}^{\textrm{IDM}}$ decreasing and $\omega_{\textrm{go-back}}^{\textrm{VDM}}$ decreasing, (4) $\omega_{\textrm{go-back}}^{\textrm{IDM}}$ increasing and $\omega_{\textrm{go-back}}^{\textrm{VDM}}$ decreasing, and (5) $\omega_{\textrm{go-back}}^{\textrm{IDM}}$ decreasing and $\omega_{\textrm{go-back}}^{\textrm{VDM}}$ increasing. For the “constant” case we make $\gamma_{\textrm{go}}^{\textrm{end}}=\gamma_{\textrm{go}}^{\textrm{begin}}=4$, for the “decreasing” case we make $\gamma_{\textrm{go}}^{\textrm{end}}=6,\ \gamma_{\textrm{go}}^{\textrm{begin}}=2$, and for the “increasing” we make $\gamma_{\textrm{go}}^{\textrm{end}}=2,\ \gamma_{\textrm{go}}^{\textrm{begin}}=6$. As illustrated in Fig. 6, we find that for visual quality (w.r.t., UMT-FVD), keeping both $\omega_{\textrm{go-back}}^{\textrm{IDM}}$ and $\omega_{\textrm{go-back}}^{\textrm{VDM}}$ constant is the best choice. For semantic faithfulness (w.r.t., UMTScore), the optimal strategy is to have both $\omega_{\textrm{go-back}}^{\textrm{IDM}}$ and $\omega_{\textrm{go-back}}^{\textrm{VDM}}$ increasing. For temporal coherence (w.r.t., GPT4o-MTScore), it is optimal for $\omega_{\textrm{go-back}}^{\textrm{IDM}}$ to decrease while $\omega_{\textrm{go-back}}^{\textrm{VDM}}$ increases. Therefore, to enhance the performance of a specific aspect of synthesized video, we can adjust the dynamic CFG scale to achieve the empirically optimal trade-off.

#### Visualization.

We visualize the standard sampling and IV-mixed Sampler of the synthesized video in Fig. 1. It can be observed that IV-mixed Sampler significantly improves both visual quality and semantic faithfulness. In addition to this, we empirically invited a number of other AIGC-related researchers to judge the video quality and agreed that IV-mixed Sampler’s enhancement could be observed by the naked eye.

## 5 Limitation

Althrough IV-mixed Sampler significantly improves the performance of VDM, it introduces additional computational costs. For ”IV-IV” on Animatediff, it increases the number of function evaluation (NFE) from 50 to 250. In the practical implementation, the computational overhead went up from 21s to 92s at a single RTX 4090 GPU. This problem could potentially be addressed in the future by distillation algorithms similar to accelerated sampling [, , ]. This exploration of Inference Scaling Laws first, and then distilling the performance gains it achieves back to the foundation model may be a viable path for the future.

## 6 Conclusion

In this paper, we propose IV-mixed Sampler to enhance the visual quality of synthesized videos by leveraging an IDM while ensuring temporal coherence through a VDM. The algorithm utilizes DDIM and DDIM-Inversion to correct latent representations $\mathbf{x}_{t}$ at any time point $t$, enabling seamless integration into any VDM and sampling interval. IV-mixed Sampler can be formulated as an ODE, achieving a trade-off between visual quality and temporal coherence by adjusting the CFG scales of both the IDM and VDM. In the future, we plan to fine-tune several stronger IDMs, such as FLUX, to better adapt the latent space of target VDMs, thereby further enhancing the performance of VDMs. We anticipate IV-mixed Sampler will be widely applicable in vision generation tasks.

#### Ethics Statement.

We present IV-mixed Sampler, a method designed to enhance the semantic accuracy and visual quality of video produced by Video Diffusion Models. Although our approach does not directly engage with real-world datasets, we are dedicated to ensuring the ethical use of prompts, while respecting user autonomy and striving for positive outcomes. Acknowledging the commercial potential of IV-mixed Sampler, we emphasize a responsible and ethical deployment of the technology, aiming to maximize societal benefits while carefully mitigating any potential risks.

## Appendix A Additional Implementation Details

### A.1 Benchmarks

We present the relevant metrics and benchmarks used for comparison in the main paper..

#### UCF-101-related FVD.

The UCF-101 dataset is an action recognition dataset comprising 101 categories, with all videos sourced from Youtube. Each video has a fixed frame rate of 25 frames per second (FPS) and a resolution of 320×240. Several previous works [, , ] have validated the generation performance of VDMs on the UCF-101 dataset using Fréchet Video Distance (FVD) []. However, a comprehensive evaluation benchmark for UCF-101 is still lacking. To address this, we follow the methodology of FreeInit, utilizing the prompts listed in [] to synthesize videos and assess inference performance with FVD. Specifically, we synthesize 5 videos for each of the 101 prompts provided by [], resulting in a total of 505 synthesized videos. We then compute the FVD between these 505 synthesized videos and 505 randomly sampled videos from the UCF-101 dataset (5 per class), using the built-in FVD evaluation code from Open-Sora-Plan(^2^22[https://github.com/PKU-YuanGroup/Open-Sora-Plan](https://github.com/PKU-YuanGroup/Open-Sora-Plan)).

#### MSR-VTT-related FVD.

The MSR-VTT dataset [] is a large-scale dataset for open-domain video captioning, featuring 10,000 video clips categorized into 20 classes. The standard split of the MSR-VTT dataset includes 6,513 clips for training, 497 clips for validation, and 2,990 clips for testing. For our evaluation, we utilize all 497 validation videos. To ensure evaluation stability, we synthesize a total of 1,491 videos based on prompts from these validation videos, with each prompt producing 3 different videos. We assess the results using the built-in FVD evaluation code from Open-Sora-Plan.

#### Chronomagic-Bench-150.

Chronomagic-Bench-150, introduced in [] and recently accepted by NeurIPS 2024’s dataset and benchmark track, serves as a comprehensive benchmark for metamorphic evaluation of timelapse T2V synthesis. This benchmark includes 4 main categories of time-lapse videos: biological, human-created, meteorological, and physical, further divided into 75 subcategories. Each subcategory contains two challenging prompts, leading to in a total of 150 prompts. We consider three distinct metrics in Chronomagic-Bench-150: UMT-FVD (↓), UMTScore (↑), and GPT4o-MTScore (↑), each addressing different evaluation aspects. Specifically, UMT-FVD (↓) [] leverages the UMT [] feature space to compute FVD, assessing the visual quality of the synthesized video. UMTScore (↑) utilizes the UMT [] feature space to compute CLIPScore [], evaluating the text relevance of the synthesized video. Lastly, GPT4o-MTScore (↑) is a fine-grained metric that employs GPT-4o [] as an evaluator, aligning with human perception to accurately reflect the metamorphic amplitude and temporal coherence of T2V models.

#### Chronomagic-Bench-1649.

Chronomagic-Bench-1649, introduced in [] and recently accepted by NeurIPS 2024’s dataset and benchmark track, is a comprehensive benchmark designed for the metamorphic evaluation of timelapse T2V synthesis. While it shares 75 subcategories with Chronomagic-Bench-150, it offers a more extensive evaluation framework with 1649 prompts, making it significantly more comprehensive than its lightweight counterpart Chronomagic-Bench-150. Chronomagic-Bench-1649 includes 4 key metrics: UMT-FVD (↓), MTScore (↑), UMTScore (↑), and GPT4o-MTScore (↑), each serving to evaluate different aspects of video synthesis. Specifically, UMT-FVD (↓) [] utilizes the UMT [] feature space to compute FVD, assessing the visual quality of the synthesized videos. MTScore (↑) measures metamorphic amplitude, indicating the degree of change between frames. UMTScore (↑) leverages the UMT [] feature space to compute CLIPScore [], evaluating the text relevance of the synthesized videos. Finally, GPT4o-MTScore (↑) is a fine-grained metric that employs GPT-4o [] as an evaluator, aligning with human perception to accurately reflect the metamorphic amplitude and temporal coherence of T2V models. As with to Chronomagic-Bench-150, we choose to ignore the MTScore (↑) metric in our experiments due to its limitations.

### A.2 Video Diffusion Models

We describe the VDMs utilized in this work. Specifically, we employ 3 VDMs with distinct architectures: ModelScope-T2V [], Animatediff [], VideoCrafterV2 [].

#### ModelScope-T2V.

ModelScope-T2V incorporates spatio-temporal blocks to ensure consistent frame generation and smooth motion transitions. Its key features include the utilization of 3D convolution andtraining from scratch. The input video size is structured as ${3\!\times\!16\!\times\!256\!\times\!256}$, where $3$ represents the number of channels, $16$ is the number of frames, and $256\!\times\!256$ indicates the resolution of each frame. This configuration allows the model to effectively capture both spatial adn temporal features, facilitating high-quality video synthesis.

#### Animatediff.

Animatediff does not require training from scratch; instead, it only needs fine-tuning on existing image diffusion models. Its motion adapter serves as a plug-and-play module, allowing most community text-to-image models to be transformed into animation generators. In this paper, we consider the latest version Animatediff (SD V1.5, Motion Adapter V3), which is fine-tuned from SD V1.5. The input video size of Animatediff (SD V1.5, Motion Adapter V3) is ${3\!\times\!16\!\times\!512\!\times\!512}$, where $3$ indicates the number of channels, $16$ represents the number of frames, and $512\!\times\!512$ specifies the resolution. Note that there are differences in the performance of this VDM because we used a different resolution than the one used in the Chronomagic-Bench paper [].

#### VideoCrafterV2.

VideoCrafterV2 focuses on T2V synthesis, aiming to synthesize high-quality videos from prompts. This work investigates a training scheme for video models based on Stable Diffusion [], exploring how to leverage low-quality videos and synthesized high-quality images to develop a superior video model. The input video size of VideoCrafterV2 is ${3\!\times\!16\!\times\!512\!\times\!320}$, where $3$ indicates the number of channels, $16$ represents the number of frames, and $512\!\times\!320$ specifies the resolution.

### A.3 Heavy-inference Algorithm on VDM

Here we discuss two popular VDM-based heavy-inference algorithms FreeInit [] and I4VGen [].

#### I4VGen.

I4VGen [] is a training-free and plug-and-play video diffusion inference framework that enhances text-to-video synthesis by leveraging robust image techniques. To be specific, I4VGen decomposes the process into two stages: anchor image synthesis and anchor image-guided video synthesis. A well-designed generation-selection pipeline is used to create visually realistic and semantically faithful anchor images, while score distillation sampling (SDS) [] is employed to animate the images into dynamic videos, followed by a video regeneration process to refine the output. In its official implementation, both phases are realized by VDM, where the anchor image synthesis is performed by merging the time dimension into the batch size dimension through VDM. In essence, I4VGen does not introduce true IDMs to improve the quality of synthesized video obtained from VDMs.

#### FreeInit.

FreeInit [] is a novel inference-time strategy designed to enhance temporal consistency in video generation using diffusion models. This approach addresses a key issue: the difference in the spatial-temporal frequency distribution of noise between training and inference, which leads to poor video quality. FreeInit iteratively refines the low-frequency components of the initial noise during inference, bridging this gap without requiring additional training.

### A.4 Hyperparameter Settings

**Table 5: Ablation studies with Modelscope-T2V on Chronomagic-Bench-150.**
| Model | Method | Extra Model | UMT-FVD (↓) | UMTScore (↑) | GPT4o-MTScore (↑) |
| --- | --- | --- | --- | --- | --- |
| ModelScope-T2V | Standard DDIM | ✗ | 241.61 | 2.66 | 2.96 |
| IV-mixed Sampler (Mini SD) | ✓ | 247.99 | 2.63 | 3.00 |  |
| IV-mixed Sampler (SD V1.5) | ✓ | 234.90 ($+\Delta$ 6.71) | 3.02 ($+\Delta$ 0.36) | 3.14 ($+\Delta$ 0.18) |  |

**Table 6: Performance comparison of VideoCrafterV2 across different $z\%$ settings.**
| Model | $z\%$ | UMT-FVD (↓) | UMTScore (↑) | GPT4o-MTScore (↑) |
| --- | --- | --- | --- | --- |
| VideoCrafterV2 | Standard DDIM | 214.06 | 2.76 | 2.87 |
| 33.3% | 212.74 | 3.08 | 3.02 |  |
| 50.0% | 208.67 ($+\Delta$ 5.39) | 3.23 | 3.18 |  |
| 66.7% | 210.57 | 3.29 ($+\Delta$ 0.53) | 3.30 ($+\Delta$ 0.43) |  |
| 75.0% | 211.87 | 3.28 | 3.28 |  |

Figure: Figure 7: Ablation studies on sampling intervals of IV-mixed Sampler (“VI-IV”). The Begin%-End% in the legend indicates the portion of the entire sampling process performed by IV-mixed Sampler.
Refer to caption: x7.png

Figure: Figure 8: The visualization of Karras’s noise schedule.
Refer to caption: x8.png

For all comparison experiments, we used the form “IV-IV” and perform IV-mixed Sampler at all time steps of the standard DDIM sampling. In addition, $\gamma^{\textrm{end}}_{\textrm{go}}$, $\gamma^{\textrm{end}}_{\textrm{back}}$, $\gamma^{\textrm{begin}}_{\textrm{go}}$ and $\gamma^{\textrm{begin}}_{\textrm{back}}$ all are set as 4. For both Animatediff and ModelScope-T2V, we use stable diffusion (SD) V1.5 as the IDM. Note that we experimented with using Mini SD as the IDM for ModelScope-T2V to maintain a consistent resolution of 256×256. However, as illustrated in Table 5, we found that its performance was inferior to using SD V1.5 with upsampling and downsampling. For VideoCrafterV2, we use Realistic Vision V6.0 B1 [] as the IDM to accommodate a resolution of 512$\!\times\!$320. For the remaining configurations, we follow the sampling form recommended by the corresponding VDMs. Furthermore, we find that applying “IV-IV” at every step on VideoCrafterV2 destroys temporal coherence. Therefore, we replace “IV-IV” with “VV-VV” for z%. The results of the ablation experiments are shown in Table 6. We finally chose z%=66.7% as the final solution.

## Appendix B Python-style Pseudo Code

We present the python-style pseudo-code in Fig. 1 to make it easier to understand IV-mixed Sampler.

Figure: Algorithm 1 Pseudo code of IV-mixed Sampler (w.r.t., “IV-IV”) ( ) in a PyTorch-like style.
[Uncaptioned image]: x9.png

## Appendix C Theoretical Proof

Here we give the proof of Theorem 3.1 in the main paper. We use “IV-IV” for an example, and the derivation of other forms of IV-mixed Sampler is similar to “IV-IV” and is not described additionally. First, IV-mixed Sampler (w.r.t., “IV-IV”) can be rewritten as

$$ $\begin{split}&\mathbf{x}^{\prime}_{t}=\mathbf{x}_{t}+\omega_{\textrm{go}}^{1} \frac{g^{2}(t)}{2}\nabla_{\mathbf{x}}\log q^{\textrm{IDM}}_{t}(\mathbf{c}| \mathbf{x})+\omega_{\textrm{go}}^{2}\frac{g^{2}(t+\eta)}{2}\nabla_{\mathbf{x}} \log q^{\textrm{VDM}}_{t+\eta}(\mathbf{c}|\mathbf{x})\\ &-\omega_{\textrm{back}}^{2}\frac{g^{2}(t+\eta)}{2}\nabla_{\mathbf{x}}\log q^{ \textrm{IDM}}_{t+\eta}(\mathbf{c}|\mathbf{x})-\omega_{\textrm{back}}^{1}\frac{ g^{2}(t)}{2}\nabla_{\mathbf{x}}\log q^{\textrm{VDM}}_{t}(\mathbf{c}|\mathbf{x} ),\\ \end{split}$ (11) $$

where $\eta$ represents the sampling step, which is usually extremely small. $\nabla_{\mathbf{x}}\log q^{\textrm{IDM}}_{t}(\mathbf{c}|\mathbf{x})$ and $\nabla_{\mathbf{x}}\log q^{\textrm{VDM}}_{t}(\mathbf{c}|\mathbf{x})$ represent the score function estimated for $p_{t}(\mathbf{x}_{t})$ using IDM and VDM under classifier-free guidance. Since $\eta$ is very small, and assume that $\omega^{2}_{\textrm{back}}$ is larger than $\omega^{1}_{\textrm{go}}$ and $\omega^{1}_{\textrm{back}}$ is larger than $\omega^{2}_{\textrm{go}}$, Eq. 11 can be rewritten as

$$ $\begin{split}&\mathbf{x}^{\prime}_{t}=\mathbf{x}_{t}-\omega^{\textrm{IDM}}_{ \textrm{go-back}}\frac{g^{2}(t)}{2}\nabla_{\mathbf{x}}\log q^{\textrm{IDM}}_{t }(\mathbf{c}|\mathbf{x})-\omega^{\textrm{VDM}}_{\textrm{go-back}}\frac{g^{2}(t )}{2}\nabla_{\mathbf{x}}\log q^{\textrm{VDM}}_{t}(\mathbf{c}|\mathbf{x}),\\ \end{split}$ (12) $$

where $\omega^{\textrm{IDM}}_{\textrm{go-back}}$ and $\omega^{\textrm{VDM}}_{\textrm{go-back}}$ are large than 0 0. Given this, IV-mixed Sampler can be written as an ordinary differential equation:

$$ $\begin{split}d\mathbf{x}_{t}=f(t)\mathbf{x}_{t}-\frac{1}{2}g^{2}(t)\left[ \omega^{\textrm{IDM}}_{\textrm{go-back}}\frac{g^{2}(t)}{2}\nabla_{\mathbf{x}} \log q^{\textrm{IDM}}_{t}(\mathbf{c}|\mathbf{x})+(\omega^{\textrm{VDM}}_{ \textrm{go-back}}+\omega)\frac{g^{2}(t)}{2}\nabla_{\mathbf{x}}\log q^{\textrm{ VDM}}_{t}(\mathbf{c}|\mathbf{x}),\right],\end{split}$ (13) $$

where $\omega$ refers to the vanilla CFG scale.

## Appendix D Additional Ablation Study

We present Fig. 7 here as a supplement to Fig 4 (w.r.t., the sampling interval of IV-mixed Sampler) in the main paper. As illuatrated in Fig. 4 and Fig. 7, it can be noticed that “IV-IV” performs significantly better than “VI-IV” under almost all settings. Furthermore, we visualize Karras’s noise schedule of our proposed dynamic CFG scale in Fig. 8 for clear understanding.

## Appendix E Visualization

In order to avoid the size of the paper being too large for the reader, we downsample the video frames and present them here. We present the synthesized video visualization of Animatediff (SD V1.5, Motion Adapter V3) in Fig. 9-10, the synthesized video visualization of ModelScope-T2V in Fig. 11 and the synthesized video visualization of VideoCrafterV2 in Fig. 12.

Figure: Figure 9: The synthesized video visualization of Animatediff (SD V1.5, Motion Adapter V3).
Refer to caption: x10.jpg

Figure: Figure 10: The synthesized video visualization of Animatediff (SD V1.5, Motion Adapter V3).
Refer to caption: x11.jpg

Figure: Figure 11: The synthesized video visualization of ModelScope-T2V.
Refer to caption: x12.jpg

Figure: Figure 12: The synthesized video visualization of VideoCrafterV2.
Refer to caption: x13.jpg

## Peer Reviews

confidence: 4
contribution: 3
initial_rating: 6
presentation: 3
questions: * What is the variance of the quantitative metrics (e.g. FVD in Tables 1 and 2)? The values are pretty close and it’s unclear  if the results are statistically significant
* It would be nice to have more video samples to look at (e.g. on an anonymous website). There is only one set of videos in the supplementary, and it is hard to see motion for ones in the paper appendix.
* Does this method still work in scenarios using distilled models? E.g. 1 step or 2 step generation
soundness: 3
strengths: * The paper is generally clear, and well written
* The proposed method is novel and interesting
* Results seem to show good improvement in generation quality of the videos, while retaining consistent motion
* Main experiments and ablations are thorough and show the benefits and tradeoffs of different instantiations of the proposed method
summary: The paper presents a novel sampling scheme for video diffusion models that leverages pre-train image diffusion models, as they generally have higher visual fidelity compared to current open source video models. The sampling method takes steps forward / backward (DDIM inversion / DDIM) in the diffusion model, alternating between the score functions of the image and video models. Results show high fidelity visual quality while retaining consistent motion in generated video.
weaknesses: * The sampling process requires both I/V models to be in the same underlying latent space, which may be restrictive. How would this method also be used in cases where there is temporal downsampling in the video latent space (as this this is a very common video generation architecture)?
* It is unclear how useful / relevant this method may be ~6+ months from now, as the main motivation of the paper is leveraging the lack of good open source video models, and public video datasets will get better (e.g. OpenVid10M [1]), and better video generation models will be released (e.g. Mochi-1 [2] as of recently).

[1] https://huggingface.co/datasets/nkp37/OpenVid-1M
[2] https://huggingface.co/genmo/mochi-1-preview

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confidence: 3
contribution: 2
initial_rating: 5
presentation: 1
questions: See weakness
soundness: 3
strengths: + The paper combines theoretical proof with practical implementations, and is relatively well-rounded
+ The proposed method seems to make intuitive sense
summary: The paper proposes IV-Mixed Sampler, which is to combine image diffusion models (IDMs) with video diffusion models (VDMs) to get the benefit of higher image quality of IDM and good temporal consistency of VDM. This is achieved by sampling from x_t to x_{t+∆t} and from x_{t+∆t} to x_t using IDM and VDM
weaknesses: The writing of the paper can be improved. Here are several comments but not just limited to these points. Overall the presentation is a bit confusing.
- Why do the paper keep mentioning OpenAI's strawberry in Abstract and Intro, which is closed-sourced and no paper or technical detais was released? How is this important or even related to motivating the paper?
- Figure 2 is confusing and should not be put in the intro. This is more like ablation studies, and it is made rather confusing, especially authors also start to talk about "R-" in the intro out of nowhere (line 94), and the starts to discussion "I-" and "V-" in line 107 without any explanation
- The use of "go", "back", "begin", "end" etc in the equations are also confusing
- Plots like Fig 6 are also hard to read

The results of the model is decent but not very strong. For example, FreeInit is significantly better than ours for UMT-FVD on ModelScope-T2V

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confidence: 3
contribution: 2
initial_rating: 5
presentation: 3
questions: 1. What are the detailed reasons that we can't use different VAEs for IDM and VDM when adapting the proposed method? Do you have experiment results about this?
2. How does the IV-Mixed Sampler perform as the length and complexity of the video sequences increase? Are there any scalability issues that the authors have identified?
3. Potential Limitations: Are there any specific scenarios or types of video content where the IV-Mixed Sampler might underperform? If so, how might these limitations be addressed?
soundness: 2
strengths: Originality: The concept of combining IDMs and VDMs to enhance video synthesis is innovative. The paper addresses a significant gap in the field by improving the visual quality of synthesized videos while preserving temporal coherence.

Quality: The paper is well-structured, with a clear problem statement, methodology, experimental validation, and conclusion. The theoretical analysis provides a solid foundation for the proposed algorithm.

Clarity: The authors have done an excellent job of explaining complex concepts in a clear and concise manner. The figures and tables are well-designed and aid in understanding the content.
summary: The paper introduces IV-Mixed Sampler, a novel algorithm designed to enhance video synthesis by leveraging the strengths of both Image Diffusion Models (IDMs) and Video Diffusion Models (VDMs). The core innovation is the use of IDMs to improve the quality of individual video frames while maintaining temporal coherence through VDMs during the sampling process. The authors claim state-of-the-art performance on four benchmarks, including UCF-101-FVD, MSR-VTT-FVD, Chronomagic-Bench-150, and Chronomagic-Bench-1649. The paper also provides a theoretical analysis of the IV-Mixed Sampler and its transformation into a standard inverse ODE process, as well as an exploration of the design space for hyperparameters.
weaknesses: Evaluation Metrics: The paper employs benchmarks like UCF-FVD and MSR-VTT-FVD, which can not accurately assess text-to-video generation models. More suitable benchmarks like EvalCrafter or Vbench are needed for a comprehensive evaluation.

Demonstration Insufficiency: The provided demos do not clearly demonstrate the proposed method's superiority over baselines, requiring more compelling examples to showcase improvements.

Illustration Clarity: Figure 3's illustrations are not clear. The images presented do not effectively convey the differences in quality and temporal coherence, making it difficult for readers to grasp the paper's points regarding the performance of various samplers. High-quality, clear visualizations are crucial for helping readers understand the nuances of video synthesis methods, and the paper would benefit from improved clarity in its visual aids.

Limited Applicability: The method's compatibility with state-of-the-art video generation models, which often use distinct VAEs from image models, is limited. This restricts its potential applications and prospects in the field.

Meta-review: The paper proposes IV-mixed Sampler, a method for improving the quality and capabilities of video diffusion models by integrating an image diffusion model in the sampling process (since image models are known to have higher visual quality)---effectively mixing the spatial/visual fidelity of an image model with the temporal coherence of a video model. Strengths include the practical value of improving video synthesis without requiring training and comprehensive experimental validation showing improvements over existing methods (state-of-the-art performance across multiple benchmarks). Reviewers questioned whether the improvements were significant enough compared to existing approaches, and raised concerns about limited applicability (since the method requires two models that have been trained on the same latent space). Additional weaknesses include insufficient real-world testing and unclear explanations of some technical components.

Reviews were mixed, but tend positive. Given the reasonable method and compelling results, I am inclined to recommend acceptance.

Decision: Accept (Poster)