MotionCraft: Physics-Based Zero-Shot Video Generation
Authors: Antonio Montanaro
Luca Savant Aira
Emanuele Aiello
Diego Valsesia
Enrico Magli
Venue: NeurIPS 2024 poster (2024)
Keywords: Zero-shot video generation
diffusion model
physics-based video generation
Primary area: generative_models

Abstract: Generating videos with realistic and physically plausible motion is one of the main recent challenges in computer vision. 
While diffusion models are achieving compelling results in image generation, video diffusion models are limited by heavy training and huge models, resulting in videos that are still biased to the training dataset. In this work we propose MotionCraft, a new zero-shot video generator to craft physics-based and realistic videos. MotionCraft is able to warp the noise latent space of an image diffusion model, such as Stable Diffusion, by applying an optical flow derived from a physics simulation. We show that warping the noise latent space results in coherent application of the desired motion while allowing the model to generate missing elements consistent with the scene evolution, which would otherwise result in artefacts or missing content if the flow was applied in the pixel space.
We compare our method with the state-of-the-art Text2Video-Zero reporting qualitative and quantitative improvements, demonstrating the effectiveness of our approach to generate videos with finely-prescribed complex motion dynamics.

MOTIONCRAFT:
Physics-based Zero-Shot Video Generation
Antonio Montanaro'
Luca Savant Aira"
Emanuele Aiello,
Diego Valsesia
Enrico Magli
Politecnico di Torino (name. surname aurname)@polltoo ip
Abstract
Generating videos with realistic and physically plausible motion is one of the main recent challenges in computer vision. While diffusion models are achieving compelling results in image generation, video diffusion models limited by heavy training and huge models, resulting in videos that are still biased to the training dataset. In this work we propose MotionCraft, a new zero-shot video generator craft physics based and realistic videos. MotionCraft is able to warp the noise latent space of an image diffusion model, such as Stable Diffusion, by applying an optical flow derived from physics simulation. We show that warping the noise latent space results coherent application of the desired motion while allowing the model generate missing elements consistent with the scene evolution, which would otherwise result artefacts or missing content the flow was applied the pixel space. We compare method with the state-of-the-aus Text2Video -ideo-Zrro reporting qualitative and quantitative improvements, demonstrating the effectiveness our approach to generate videos with finely-prescribed complex motion dynamics.
Introduction
As human beings, we have always exploited our creativity to generate art, in different forms such as visual art, music or poetry. In vision, we are often inspired by the natural world since our visual system continuously acquire images perceived as a video sequence. Indeed, videos movies are one of the best visual stimuli since they contain images, motion and audio.
Recent generative models for still images based on diffusion models [25 results with quality almost indistinguishable from real images. It is therefore clear that the next big goal is video generation. However, it seems that including the dimension of time remains challenging. Some works such Sora [5] achieve astonishing temporal consistency and photorealism at the expense of enormous computational and data requirements. Moreover, we argue that fine-grained control over the motion dynamics is impossible with simple text prompt. one wants to synthesize video according to some precise physical dynamics, they would not be able to do it with current models. Interestingly, explicitly controlling the motion dynamics also allows to decouple temporal evolution from content generation. Indeed, explicitly injecting the physics of the real world motion dynamics allows to develop more parsimonious models, that not need to brute-force learn them from data.
28 29 achieved remarkable
indicates equal contribution.
Project page: http::://aezeeeeoo..ttttbbbbbbbl
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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Figure I: Melting man simulation. Top: MOTIONCRAFT; Bottom: T2V0 (0) MOTIONCRAFT uses fluid dynamics simulation to warp noise latents and synthetize video frames. T2V0 is unable to simulate the evolution of the melting statue and simply moves the object towards the bottom of the frame.
For this reason, in this paper, investigate the possibility to create zero-shot video generation model that only requires a pretrained still image generator and knowledge of physical laws regarding motion. Indeed, since videos are temporal sequences of images correlated by physical laws, we only need to devise a way to include physical laws in the diffusion prior to animate starting image. We thus advocate for physics simulators appropriate sources of motion, output sequence of optical flows, while also being completely user-controllable, plausible, and explainable.
We propose MOTIONCRAFT, extracted from a physical simulation to warp the noise latent space pretrained image diffusion model to generate videos with complex dynamics without the need to train anything. While using projection motion onto the camera plane as a pixelwise displacement field (optical flow) may seem limiting due to the fact that, if applied in the pixel space, it would not be able to synthesise novel coherent content but only displace pixels, the trick lies in its application in the noise latent domain. Backed by evidence that motion vectors correlate between pixel and noise space, warping of the latter by means that MOTIONCRAPE allows to simultaneously apply the desired motion and exploit the powerful image prior of the generative model. This is capable of adapting the scene the prescribed motion without significant artefacts, generate novel content and shows impressive global consistency (reflections, illumination, etc., consistent with the desired evolution).
bassccs-based zero-shot video generator that uses optical flow
We present quantitative and qualitative experimental results where we show that our zero-shot MOTIONCRAFT is capable of synthesising realistic videos with finely controlled temporal evolution governed by fluid-dynamics equations, rigid body physics, and multi-agent interaction models, while zero-shot state-of-art techniques cannot.
2 Related work
Diffusion Based Video Generation Video Generation 2 is longstanding problem in computer vision aiming learn the distribution of and synthesise realistic videos. Recently, text-based Denoising Diffusion Probabilistic Models (DDPM) 28
31 have been studied to tackle this challenge delivering impressive results. These approaches include Sora (5), Video Diffusion models [17] Imagen-video video [16] and Align your Latents (3. They require sophisticated spatio-temporal denoising architectures at the expense of huge computational requirements and large amounts of paired text- video data for training. To reduce the data requirements, different approaches investigate few-shot and unsupervised learning techniques. Make-a- Video [27] proposes an unsupervised training with only videos, coupled with retrieval strategy to sample using text. On the other hand, Ni et al. [22] optical flow generator that outputs a flow conditioned on a reference image
train a diffusion-basee and textual prompt, that reduces the computational burden of generating videos by training the diffusion process on small flow fields. Differently from them, our approach is zero-shot and we do train anything.
To the best of our knowledge, Text-to-video--Zer 20 and Generative Rendering 6 are the only zero-shot video generators. However, Generative Rendering (concurrent work, with code available)

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qualitative example of the image and latent flows correlation. This figure shows, from left to right, (a) the first RGB frame, (b) the second RGB frame superimposed with the estimated flow in the RGB domain, (c) the first latent frame, (d) the second latent frame superimposed with the estimated flow in the latent domain and (c) the correlation map of the two non-zero flows.
Figure 2:
has significant extra requirements beyond Stable Diffusion (SD) as image generator, in the form of depth-condittoned ControlNet (36), and 3D mesh manually animated, leveraging UV maps to render the scene. Moreover, Generative Rendering cannot render fluids, since they are difficult to represent 3D meshes.
In this paper, we compare our method to Text-to-video-Ze Zero (T2VO), as zero-shot video generator baseline. T2V0 applies constant shift (with a fixed direction) the initial latent noise of SD, sampling each frame sequentially by means of DDPM. As shown in our work, since the motion the noise latent space directly translates into the motion of the pixel space, the generated videos result in a overall shift in the same fixed direction. The largest part of the motion is caused by the stochastic fluctuations of the DDPM sampling strategy leading to unnatural motion and inconsistency of the objects in the different frames. On the contrary, in this work, we avoid the use of a constant warping operation derived from physics simulation flows in the latent space in order incorporate complex motion dynamics.
Diffusion Based Video and Image Editing Recently, different methods exploit the prior of text-to- image diffusion models for video editing. In particular, Tune-A- Aine-A-Vided (35) finetunes a text-to-image diffusion model edit video. They start from the inverted frames in the latent space and use the text prompt as an editing tool. Pix2Video (77 employs self-attention injection mechanism to edit videos using a pretrained image diffusion model.
Other methods use the optical flow to edit reference images or videos. Motion Guidance [T] leverages user defined optical flow that allow zero-shot image editing. It works by guiding the diffusion sampling process with the gradient from a pretrained optical flow network via a guidance loss. LatentWarp 1 and TokenFlow [1]]
optical flow estimated from reference video to warp the latent space of the diffusion model to achieve consistent editing. These methods leverage both diffusion models priors and other components such ControlNet for structural control, and trained flow estimators such as RAFT (32]. Alternatively, we propose a zero-shot video generation method, using only vanilla SD. This means that MOTIONCRAFT does require a reference video but it can animate an image, generated by the SD model or obtained by inverting real one. Moreover, the physics simulations allow generate different videos from the same starting image.
3 Method
This section describes MOTIONCRAFT, zero-shot video generation method, where the meaning of "zero-shot" is twofold: we do not train or finetune any component of the text-to-image diffusion model, nor do not use reference video optical flow estimators starting point. In the following, we used used Stable Diffusion as pretrained text-to-image model.
3.1 Optical Flow preserved in the Latent Space of Stable Diffusion
Our proposed method stems from a key observation: the optical flow estimated between two frames in the pixel space correlated with the flow estimated between the corresponding noise latent representations of SD. We conjecture that this is related to the specific design of the SD variational auto-encoder and denoiser architectures. fact, by largely using convolution operations, they enforce locality prior which preserves spatial information to some extent.

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Y STEPS OF REVERSE DIFFUSION
LATENT ITIMESTEP
FRAME
DOIM INVERSION
O 6
LATENT (TIMESTEP
FRAME 1-1
9
PHYSICS SIMULATION
INVERSION
T
M- OPTICAL FLOW
E
WARP
O
OPTICAL
N
FLOWS
LATENT
FRAME
(TIMESTE 3)
MOTIONCRAFT overview. A video is generated from starting image using pretrained still image generative model by warping noise latents according to an optical flow description of the motion be synthesised.
Figure 3:
In order empirically investigate this phenomenon, we conducted quantitative experiment using the MSU Video Frame Interpolation Benchmark dataset (12), considering only real videos. For each pair of consecutive video frames, the following steps have been taken. We first estimate the optical flow in the RGB space by using well-established method, based on the Gunnar Farneback's 's algorithm, provided by OpenCV [19]. Then, we compute the noise latent representations of the two frames, first encoding the image in the variational autoencoder (VAE) of SD at timestep T = 0, followed by DDIM inversion (29] up to timestep т 400 (same value for all experiments in this work, empirically determined). Finally, correlation coefficient based on cosine similarity is computed between the optical flows estimated the RGB and noise latent spaces. The resulting correlations are then averaged across all pairs of consecutive frames in the dataset, obtaining an average value of 0. 0.727, which indicates a strong correlation between the optical field the RGB and noise latent domains. An example of this experiment is presented in Fig. showcasing the two estimated flows in the image and latent space and their correlation.
3.2 Physics-based zero shot video generation
Based the analysis presented in the previous section, we propose novel zero-shot video generation method, named MOTIONCRAFT, where an image (real or generated), serving as starting frame 1 animated according to a physical simulation, by means of a (possibly (are-varynng) optical-flow generator W in the noise latent space. The outcome is a video made of N frames 1 N that follows the motion prescribed by the physical simulation and evolves the content of the first frame coherently. Inspired by the previous observation, this animation is obtained by warping the noisy latent representation of image in the latent diffusion space. Regarding the physies simulation for the optical flow generation, we use different libraries to simulate different physics, as explained in the experimental section, such as fluid dynamics, rigid motion and multi-agent systems. is also possible, albeit not shown in this paper, to use animation software to generate the required optical flows.
Fig. Billustrates an overview of MOTIONCRAFT highlighting the autoregressive generation of the video. At each iteration 1, the frame 1 is generated using only the information contained in the first frame 1 and the previous frame - Given this Markovian structure. MOTIONCRAFT is characterized by O (1) space complexity and O (N) time complexity with respect to the total number N of frames to be generated. More in detail, first, the two RGB frames 70, 7 encoded into the latent space and they are independently inverted with the reversed DDIM sampling scheme up to fixed diffusion timestep т, obtaining = and 2/-1, respectively. Then, the optical flow warping operator - prescribed by the physical simulation is applied to zf-1, obtaining çf Finally, the next RGB frame // is generated by performing steps of reverse diffusion using the DDIM sampling scheme with novel cross-frame attention mechanism and novel spatial noise map np weighting technique, explained below. Furthermore, exploit the classifier-free guidance (CFG)

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Algorithm 1: Pseudocode of MOTIONCRAFT
Input : P. P.P
Output:
for f f= to do
2
=0 -E(1-11);
// Encode the frame
to = 0
do
// Inversion 1oop
ē < 1 { 1):
// Self-Attention, No MCFA
*111 t DDDDMMnversion (111 ,6,0);
f-1
(6,0)
// -= DDIM
end
Çf -
// Warp the latent
fort = 1 to do
// Generation loop
? - (64442) P: (2f 21 1):
// MCFA with 1 and I
f-1 & - (G(4+1 Poi : at }]
// MCFA with 1 and _
10
11
ê c + t66p E0)
// Classifier-fres guidance
12
cf +
// Perform Spatial-7)
13
end
14
1 + D
// Decode the latent
15 end
16 return 70, ,.... NN-1
technique for generation proposed in [14, with P and Py being the positive and negative prompt. respectively, and 1 being the strength of the CFG. More details be found in the Appendix A
include the DDIM inversion up to timestep r. Starting current frame /f-1 that was previously generated, in line 2 we embed it with the VAE encoder &, obtaining = Then we apply DDIM inversion on =ff11 for timesteps (line 3 - 6). This involves the UNet with the standard self-attention (note the repetition of the noisy latent of (-1)) and the positive prompt P. As briefly reported in (2I), we have also experienced that DDIM inversion is not compatible with CFG; hence, during the inversion, we do not use the negative prompt Pg. The resulting estimated noise is used in line 5 for applying the DDIM inversion step (note that the 7 = O, so pure DDIM performed). Upon completion of the DDIM inversion process, we obtain 2f the noisy latent corresponding to the frame _ -1
Algorithm D reports the pseudocode of MOTIONCRAFT. Lines
In line 7, the optical flow warping operator //-1+1 is applied to the noisy latent of the current frame 2/ to obtain new noisy latent Çf that will generate the successive frame. Finally, in lines 8 - 14, the frame is generated. During this generation phase we use CFG to increase the quality of the generated images, hence also the negative prompt Po is used. To create new content while preserving the original image, we propose two direct generalization of two known techniques: the multiple cross-frame attention (MCFA) mechanism and spatial noise map weighting (Spatial-n).
The MCFA technique generalizes the Cross Frame Attention (CFA) 20 as enables the to-be- generated frame to attend to an arbitrary number of frames. We choose to attend to the first frame and the previous frame (as shown in lines 10 of Alg. and Fig. 33) to ensure long-range and short-range temporal consistency, respectively. MCFA intervenes in all the self-attention blocks of the SD UNet, by replacing the keys and values, that are originally computed from projections of the generating frame features, with the ones computed from the attended frames.
We also propose Spatial-n (line 12), that is novel technique that enables to choose, on pixel-by- pixel basis, whether to use DDIM or DDPM as sampling scheme. This enables the usage of DDPM in regions of the images where novel content should be created (for example, when a new part of an object is entering the scene), while using DDIM in the other regions to ensure consistency and determinism where the already-present content is just moving. Note that this spatial map 1// can be obtained in multiple ways from the physical simulation. For example, // can be set to 1 in regions of the image where the flow is not dell-defined (pointing outside of the image boundaries) or in regions where the optical flow field has discontinuities.
5

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Table 1: Quantitative results.
Frame Consistency
Motion Consistency
T2V0 [20]
MOTIONCRAFT
T2V0 20 MOTIONCRAFT
Fluid
Dragons 0.9664
0.9991
0.6846
0.9637
Melting Man
0.9463
0.9566
0.7817
0.8252
Satellite Scan
0.9588
0.9875
0,2852
0,9219
Rigid Body
Revolving Earth
0.9812
0.9696
0.7213
0.6783
Agents
Birds
0.9765
0.9968
0.8973
0.9385
Average
0.9658 + 0.01
0.9819 + 0.02
0.6740 + 0.23
0.8655 + 0.12
Figure 4: Rigid motion simulation: satellite orbit. Top: MOTIONCRAFT; Bottom: T2V0 20
4 Experimental results
4.1 Experimental setting
In this section, we show examples of video generation based on different physics simulations: rigid body motion, fluid dynamics and multi-agent systems. Given an optical flow, we apply on the SD latent space using MOTIONCRAFT (code is available at https: //t:://meene //mezzelfo github. io/ MotionCraft/). Then, we compare our method to Text2Video- knowledge, is the only diffusion-biii based zero-shot method for video generation.
(20] that, to the best of our
We show qualitative results in Figs. sections. Table I reports two metrics to evaluate the quality of the generated videos. As done in previous works, we use the Frame Consistency metric, defined as the average cosine similarity the CLIP embeddings of consecutive frames. However, this metric presents some limitations, as CLIP focuses on high-level semantic features and on low-level details, resulting in high correlations even if the content changes but its semantics do not (as an example, see the video generated by T2V0 of the dragon Fig. which has Frame Consistency of 0.97 even if the dragons are not the same dragons in each frame). To overcome some of these limitations, we propose novel metric, named Motion Consistency, that measures how similar two frames are while accounting for the motion between them. We start from the observation that, if an object moves through the scene, its textures should remain almost the same, and, if we know its flow, we can bring back that object to overlap with its starting position. Then
which we separately describe in the following
apply similarity distance between the initial image and the next frame brought back by the reversed flow. Given two consecutive frames, we use a high-quality flow estimator (RAFT (32) estimate the optical flow between them and apply it on the second frame to reverse the motion. Then we compute the SSIM metric (4 on the first frame and the registered one.
4.2 Rigid Body flows
Fig. 4 shows pivotal example where MOTIONCRAFT can be directly compared to the state-of-the-art T2V0. in this case we use an optical flow equivalent to a their proposed shift along the vertical axis. This example shows a video generated starting from satellite view of city, and, by simulating the

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Figure 5: Rigid motion simulation: revolving Earth. Top: MOTIONCRAFT; Bottom: T2V0 20
Figure 6: Fluid simulation: dragon fire. Top: MOTIONCRAFT: Bottom: T2V0 20
rectilinear motion of the satellite, new portions of the city appear from the top of the image. While T2V0 struggles with keeping temporal consistency, even with large structural elements (e.g., the river), MOTIONCRAFT is able to coherently scroll down the already present part of the city, while also generating new plausible content in the top part of the frames.
similar case study the Earth rotation in Fig. 5 Here, the optical flow is obtained by simulating rotating sphere that was fitted to the first frame while keeping track of the starting and ending position of each point. As the Earth rotates, a slice disappears from one side and a new one needs to be generated the opposite side. Thanks to the powerful natural image prior of SD, MOTIONCRAFT is able to autonomously generate other continents in the correct position, even if the text prompt contains no reference about them (see Appendix for all the text prompts used in this paper). On the contrary, T2V0 is not able to rotate the Earth consistently while creating new content, as visible in the same Fig.
4.3 Fluids dynamics
In this set of experiments, we use the f-flow (18) library to simulate fluid dynamics (by numerically solving Navier-Stoken equations) with the shape and position provided by the first frame 7 Moreover, we can set up the simulation in different ways, depending on the numerical solvers, i.c. Eulerian (particle-based) Lagrangian (grid-based) initial velocity and force fields. All these different options result in videos that can have the same starting frame but differ in their evolution according the simulation constraints. We extract the velocity field of the simulation as a proxy for the optical flow. Examples the velocity field can be seen in Appendix
add rigid obstacles to the fluid or
define
Fig- 6 shows a fluid simulation of two dragons breathing fire. We can approximate the two initial fire breaths with two centered smoke balls, obtaining binary mask that will be fed to the simulation. At this point, we run the simulation, solving the Navier-Stokes, equations by sequentially evaluating advection, diffusion and pressure. The vorticity and the expansion of the smoke is due to the buoyancy
7

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Figure 7: Multi-agent system simulation: bird flock. Top: MOTIONCRAFT; Bottom: T2V0 20
force set in the desired direction, that in this case such that the two balls cross near the middle of the image.
The figure shows that MOTIONCRAFT produces consistent scene with realistic animation of the fire breaths. Moreover, the global scene illumination seems to change accordingly, and realistic occlusion of dragon due smoke gradually appears. This is mainly due to the MCFA mechanism, as we ablate in Sec. 4.5) T2V0, the scene is not temporally consistent and shows increasingly more artefacts, such color shifts or the fact that the right dragon changes with time, while the left one even disappears.
A similar analysis can be conducted for Fig. T where simulation of melting statue is shown. We can see that the generated video includes bouncing of parts on the ground before the fluid settles.
4.4 Multi-agent systems
Multi-agent systems are another interesting family of simulated dynamics. simple agents model the Boids model (24), consisting of set of point-like agents (named boids) that move according to three steering behaviour rules: separation, as boids avoid collisions with nearby agents by steering away from them, alignment, as boids align their direction with that of nearby agents, and cohesion, as boids move towards the average position of nearby agents to stay together as a group. To simulate this system used the agentpy [9] library, in which the number of agents, the simulation time-steps and different physical parameters related to the steering rules can be chosen.
An example is shown in Fig. 7 generating the temporal evolution of a flock of birds. As SD is not able to generate images with controllable number of agents in specified positions, we start from an image where there is a single agent (a bird in the example). Then, we extract the corresponding latent vector patch with the attention map (8] related to the CLIP token containing the word "bird", and clone it to the simulated positions of the other agents. At this point, evolve the frames according to the optical flow derived from the simulation velocity field.
While MOTIONCRAFT produces realistic flock motion, T2V0 motion is not consistent and the number of birds changes in each frame.
4.5 Ablations
In this section, we ablate the contribution of the most important componentshhypepprrameet in the proposed pipeline. First, we start from investigating the impact of the cross-attention mechanism by comparing four different variants: i) each frame attends itself (no MCFA); ii) each frame attends to the previous frame; iii) each frame attends to the first frame; iv) each frame attends to both the previous frame and the first frame (proposed MCFA). Visual results are shown in Fig. g As can be seen, the MCFA mechanism is necessary to generate plausible frames; moreover, attending only to the first frame reduces the overall motion, (e.g., always showing Africa as in the first frame), while only attending to the previous frame reduces color consistency. Overall, we demonstrate that the proposed MCFA, attending to both the first and the previous frame, represents the optimal solution to keep global consistency with the initial image and local consistency with the preceding frame.

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Figure 8: Ablation Cross-Frams attention. First row: cross frame attention; Second Row: Attend only to the initial frame; Third Row: Attend only to the previous frame; Fourth Row: Attend to the initial and preceding frame (ours).
Figure 9: Ablation Spatial-n) First Row: 7 0; Second Row:
Spatial-1 on.
Fig. shoows the ablation of the Spatial-1 weighting technique. As shown, being able to sample with DDPM in some parts of the image is crucial in order to generate novel plausible content. Indeed, DDPM adds, during each reverse diffusion step, random white noise to the latent. We suppose that this allows to better sample from the real distribution, avoiding artefacts other components of the method, such as the warping operator or the MCFA, would otherwise introduce.
Finally, ablated the partial inversion process, i.e., lines 2-6 in Alg. [ Without the DDIM inversion, textures and details generated by SD cannot be brought into the next frame, resulting in corrupted videos. Visual results can be found in the Appendix B.3

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Figure 10: Additional videos from MOTIONCRAFT. The last row is obtained by applying MOTION-
CRAFT to SDXL 23
4.6
Additional Qualitative Results
Fig. I0 shows some additional results of MOTIONCRAFT. The first row shows a tree growing. This video was obtained using a simple constant nutward-facing radial optical flow applied only on foliage. Note that while the tree grows, its shadow evolution is coherent. As the input flow is zero in this part of the image, the shadow consistency recovered only by Stable Diffusion. The last row show a video obtained by applying MOTIONCRAFT to SDXL. This shows the generalizability of MOTIONCRAFT to different diffusion models, with also different resolutions. Hence, MOTIONCRAFT able to produce high-resolution videos with a high level of detail.
5 Conclusions
In this work, we have presented MOTIONCRAFT, novel zero-shot approach for video generation. Our method allows to generate realistic videos with the image prior of Stable Diffusion and physically-derived optical flow, without any additional training. MOTIONCRAFT warps the noise latent space according the prescribed flow, and with a modified sampling process exploiting multi- frame cross-attention and the spatial-1) variable sampling scheme generates novel plausible contents following the prescribed motion and tempoirally consistent. For the evaluations of the results, we relied on a standard metric and a proposed one, showing that our method is not only qualitatively but also quantitatively superior the ooite--f-thheaat of zero-shot video generation.
10

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Acknowledgements
This publication is part of the project PNRR-NGEU which has received funding from the MUR DM 352/2022. This work was partially supported by the European Union under the Italian National Recovery and Resilience Plan (NRRP) of NexIGenerationEUU partnership on "Telecommunications of the Future" (PE00000001 program "RESTART").
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A Background
DDMs (Denoising Diffusion Models) L5
represents generative modeling approach that leverage a noise diffusion process to model a data distribution starting from random noise. These models are based on a predefined Markovian forward noising chain that progressively adds Gaussian noise to the data in an iterative procedure of T steps. The reverse diffusion process traverses back the Markov Chain and can be written as:
28
Po (x p(xT) II Po(x,-1 1 x.)
Po(2,-1 xx)) (( Mo( t), of
(I)
The training phase optimizes the parameters of the reverse process Pe maximising an evidence lower bound (ELBO) over the target data. The work of (29] shows that is possible to construct non-Markovian process defining a faster sampler (DDIM) that is compatible with the pretrained
model. So starting from po (xFoT)) ). is possible to sample - using:
Ft-1 v
Tt
+ V 04-1 -)()) (.)])]]... & ox(1))+
(2)
and rj E (0, 1) is a parameter controlling the forward process, when 1) 0, the sampling becomes deterministic, when 1) 1, the process result in DDPM sampling. & is the estimated noise present in v,, typically estimated with a UNet architecture [26]: e-(.). Finally, is independent normal stochastic variable. In this work we employ a Latent Diffusion Model [25] that perform the diffusion process over compressed latent space, reducing the computational burden of training in pixel space, while keeping high perceptual quality. Before the diffusion process, VQ-VAE VAE (33) is trained; the input image is then encoded by the VQ-VAE Encoder & that reduces the spatial dimension. The generated features are decoded back to the image space when generating images by means of th VQ-VAE Decoder D. The UNet architecture is tipically composed by convolutional layers followed by spatial self attentttnnton layers and cross-attention conditioning layers. Recent works 44 13 20 propose to reprogram this mechanism to enhance consistency between frames by letting the currently generated frame attend the first frame by swapping the original attention keys (K) and values (V) with the keys and values of the first frame, leading to the Cross-Frame Attention (CFA) mechanism:
where (1)) = "/
1-a--1
Q1- K2 Vdle (Q
Cros-FrrameAAtt((...V) Softmax
V
where V and K' represent the keys and values of the first frame, while Q represents the queries of the current frame, and d2 the channel dimension of the keys. In this work we will use the notation (z(z, P; (a, b, c......, }). where is a latent, P is the prompt, and {a, b, c.... is a list of latents to attend to, as MCFA enables to attends to a list of latents and not only to a single one.
Classifier-Free Guidance (CFG) 14] is widely used technique to guide conditional generation process using linear combination of conditional and unconditonal estimated scores:
= (122, Pa. {... [e, P, {... }) - ce(2, Pa. {...)).
(4)
where y is the scaling factor, Pe represents the null condition and P is the target text prompt.
B Extendend Ablation Study
In this section we show the remaining ablations for the scene Earth, and additional ablations on two new scenes: Dragons and Satellite Scan. The ablations for cross frame attention mechanism can be found in Figures [1 and 12 The ablations the Spatial-7 are shown in Figures 13 and 14 Moreover, we also show the contribution of the inversion mechanism in Figures 15
16 and
14

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B.1 Multiple Cross-Frame Attention Mechanism Ablation
Figure 11: Ablation Cross-Frame attention. First row: cross frame attention; Second Row: Attend only to the initial frame; Third Row: Attend only to the previous frame; Fourth Row: Attend to the initial and preceding frame (ours).
Figure 12: Ablation Cross-Frame attention. First row: no cross frame attention; Second Row: Attend only the initial frame; Third Row: Attend only to the previous frame; Fourth Row: Attend to the initial and preceding frame (ours).
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B.2 Spatial eta
Figure 13: Ablation Spatial-ry. First Row: Spatial-r on; Second Row: v = 0.
Figure 14: Ablation Spatial-7 First Row: Spatial-1 on; Second Row: n = 0.
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B.3 Inversion
Figure 15: Ablation Inversion Mechanism. First Row: Without Inversion; Second Row: With
Inversion
Figure 16: Ablation Inversion Mechanism. First Row: Without Inversion; Second Row: With Inversion
Figure 17: Ablation Inversion Mechanism. First Row: Without Inversion; Second Row: With
Inversion
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C Obstacles, Different Physics and Additional Visual Results
In this section we showcase additional visual results of our method; all the generated videos can be found in the Supplementary Material. In Fig. [8 we show an example of poured glass with MOTIONCRAF (third row) and applying the same flow in image space (fourth row). In the first two rows of Fig. 18 we show the results of the f-flow physics simulator. Note that we simulate both the fluid as set of particles (Eulerian simulations)
specific position (blue balls in the first row of the figure) and two obstacles (orange objects) representing the glass and the jug. The corresponding optical flow that we used MOTIONCRAFT is visualized in the second row the figure.
As it can be seen, the optical flow applied to the image space produces some artefacts, such as deformations the glass and the smoothness the liquid due the stretching of the pixels. On the other hand, when the same flow is applied to the noisy latent space through our method, the resulted video appears more realistic, avoiding such deformations.
Since d-flow able to adopt both Eulerian and Lagrangian numerical solvers, we show the corre- sponding videos in Fig. (second and fourth row). While the former decomposes the fluid in set of particles, the latter models the fluid in the entire space as fluid field. In both cases we extract from the simulation the (eventually extrapolated) velocity field (first and third row in Fig. 19 and use as the optical flow in the latent space, resulting in two different videos.
Figure 18: Fluid simulation: pouring drink. First row: Eulerian simulation performed with 4-flow; Second row: resulting optical flow; Third row: MOTIONCAFFT; Fourth row: resulting video when optical flow is applied directly to pixel-space.
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Figure 19: Smoke simulation: Evaporating man. First and second row: Optical flow and video generated by MOTIONCRAFT with an Eulerian simulation. Third and fourth row: Optical flow and video generated by MOTIONCRAFT with Lagrangian simulation.
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D Text Prompts
In this section we state the text prompts used in the generated videos for our method and T2V0. Note that while MOTIONCRAFT is able to start from real or generated image (with almost zero error for the real image reconstruction), T2V0 needs a hyper-parameters tuning due to a high guidance scale (not supporting direct inversion of real images).
Fighting Dragons: "Two dragons fighting while breathing fires each other. The flames are blazing and majestic light. Theatrical, character concept art by ruan jia, thomas kinkade, and trending Artstation."
Melting Man (both versions): "transparent Shinkawa and Hyung-tae Kim, trending on ArtStation, dark fantasy, great composition, concept art, highly human made of water and foam, in the style of Pierre Koenig, red pigment, pastel paint, pink color scheme"
made by water and smoke, in style of Yoji
Satellite Scan: "a satellite image of a city"
Revolving Earth: "a close up of a picture of the earth from space."
Flock of birds: "a small flock bird flying in the sky at the sunset"
. Pouring drink: "wine falling on empty glass"
For the text prompts of Fighting Dragons and Melting Man we leveraged MagicPrompt (for which we credit Gustavo Santana), a tool for rewriting simple text prompts to create more appealing starting images with Stable Diffusion.
For each example, the negative prompt Po is equal to "poorly drawn, cartoon, 2d, disfigured, bad art, deformed, poorly drawn, extra limbs, close up, b&w, weird colors, blurry"
E Limitations and future work
In this section we discuss the limitations of the proposed approach. Being a zero-shot approach, MOTIONCRAFT relies on the pretrained text-to-imant to-inage model, i.e. Stable Diffusion, and it can inherit some limitations from it, such as not exact DDIM inversion. Hence, by exploiting other diffusion models we could improve our method as well.
Experimentally, we observed a global color shift, getting stronger in the last frames of the generated videos. We noted that the proposed MCFA strategy partially solved this, but a better solution could be attending all the previous generated frames (albeit resulting in memory and run-time complexity increase). Moreover, MOTIONCRAFT depends on the optical flow derived from physics simulations but there are some dynamics that may be difficult to simulate (e.g. the motion of dancer), thus limiting the generality of the generated videos. However, we speculate that it might be possible to devise generative model of optical flows conditioned being constrained by a physics simulator. This could readily provide inputs to MOTION and have the advantage of disentangling learning of motion from learning of content. future direction could also employ a better interaction between the image generator and the physics simulator, in order have closed feedback-loop framework leading to more physical fidelity in the generated frames. In this work we have shown videos generated by different physical simulations, but as future work we could also combine them generate more complex scenes with different physics mixed together.
starting frames and a prompt, while also
F Implementation Details and Licenses
We used the following hyperparameters throughout the work if not explicitely said otherwise. We set r = 400, the number of inference steps (both for DDIM inversion and for inverse diffusion) is set to 200 and the used model is runwayml/ wewttal--difffsiioo RAIL-M). All our experiments are done on single NVIDIA A6000 (48GB); video generation runs in minutes (1 (1-5min) on single GPU. Our provided code is available under MIT license. The Earth image a composite of six separate orbits taken on January 23, 2012 by the Suomi National Polar-orbiting Partnership satellite (Credit: NASA/NOAA).
(license CreativeML Open
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G Broader Impact
Synthetic video generation is a powerful technology that can be misused create fake videos, hence it is important to limit and safely deploy these models. From a safety perspective, we emphasize that MOTIONCRAFT does not add any new restrictions nor does it relax any existing ones with respect to our base text-to-ing -ittto--mmae model. Moreover MOTIONCRAFT, using existing text-to-image diffusion models, does not need extra training or adjustments. This means we avoid the large environmental costs associated with training new models. One possible broader impact of MOTIONCRAFT is its usage by scientists across various fields to visualize their simulations, thereby offering Al-based visualization of physical processes to wider scientific audience.
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Reviews:
[{"review_id": "eQIG8RDoLc", "reviewer": "Reviewer_ypn7", "summary": "The paper works on the zero-shot video generation task and proposes,  MotionCraft. It uses physics simulations to generate optical flow that follows physical dynamics. Then, optical flow is applied to warp the noise in the latent space with the stable diffusion model. This approach ensures coherent motion application and consistent scene evolution, avoiding artefacts and missing content typical in pixel space flow applications. Compared to the state-of-the-art Text2Video-Zero, MotionCraft shows both qualitative and quantitative improvements in generating videos with complex motion dynamics.", "questions": "How do you specify the region for simulating physical dynamics? \n\nWill the type of dynamic physics simulator affect the quality of the generated video?", "limitations": "The method is limited to specific types of dynamic simulators and may be hard to apply to generic real-world video generation.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The paper is well-motivated and well-written. \n2. The idea of using physics simulator to generate the optical flow which is then applied in latent space is very interesting. \n3. The qualitative results are impressive.", "weaknesses": "1. More quantitative comparison with baselines. Table 1 only reports the comparison with T2V0 on the generated videos. However, it is not clear which benchmark it is. Is it possible to compare with other baselines on more benchmarks, like MUG, MHAD?\n\n2. The method seems limited by specific types of dynamics, like fluid dynamics. It is not clear how to generate more general dynamics in real world. This may limit the potential application of the proposed method. \n\n3. The method is assumes that \"Optical Flow is preserved in the Latent Space of Stable Diffusion\" based on the observation of average correlations 0.727 between optical flows estimated in the RGB and noise latent spaces. Does this assumption hold true for generating realistic, pixel-wise precise motion in video with only 0.72 cosine simlarity?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "> More quantitative comparison with baselines. Table 1 only reports the comparison with T2V0 on the generated videos. However, it is not clear which benchmark it is. Is it possible to compare with other baselines on more benchmarks, like MUG, MHAD?\n\nWe appreciate the reviewer’s suggestion to include more quantitative comparisons with additional baselines.\n\nOur experimental setup follows that of the seminal paper of T2V0, which, at this time, is the only baseline for zero-shot video generation. Moreover, the nature of our approach introduces specific challenges in directly comparing with benchmarks such as MUG and MHAD. Our method, MotionCraft, utilizes optical flows derived from physical simulations to generate videos. As no benchmarks of this kind are available, we decided to compare T2V0 and MotionCraft on a new set of physics-based videos. This set of videos is composed of the 5 examples reported in Table 1. Additionally, among other newly generated videos in the Additional Results PDF, example 2 shows that MotionCraft can handle facial expression change videos similar to those present in the MUG dataset.\n\n> The method seems limited by specific types of dynamics, like fluid dynamics. It is not clear how to generate more general dynamics in real world. This may limit the potential application of the proposed method.\n\nWe argue that focusing on specific types of dynamics, like fluid dynamics, is a novel approach to the problem of zero-shot video generation. Moreover, fluid dynamics can be applied even to videos with content different from liquids or gases, as shown in the example 5 of Additional Results PDF, where the crowd moves according to a fluid simulation. However, the proposed approach based on physical simulations may not apply to all kinds of content to be generated. But, as we argue in the paper, the approach could be generalized by thinking of replacing the physics simulator with an animation software or 3D engine to generate the optical flows. One could even consider learning a dedicated optical flow generator. These are all interesting directions that require substantial future work that can leverage the evidence of effectiveness for the case of physics simulations shown in this paper. We will deepen the discussion of these aspects in the revised version of our manuscript.\n\n\n> The method is assumes that \"Optical Flow is preserved in the Latent Space of Stable Diffusion\" based on the observation of average correlations 0.727 between optical flows estimated in the RGB and noise latent spaces. Does this assumption hold true for generating realistic, pixel-wise precise motion in video with only 0.72 cosine similarity?\n\nWe agree with the reviewer that the value of the cosine similarity needs a comment.\n\nThis cosine similarity is computed between the flow estimated in the pixel space (between the two RGB frames) and, independently, the flow estimated between the corresponding latents. We argue that these two flows cannot be perfectly aligned since the VAE module of Stable Diffusion downsamples and encodes the image to the latent space. In addition, we think that 0.72 is a surprisingly high value, as it is measured in the noisy regime of the diffusion process ($\\tau=400$ over $1000$ steps).\n\nTo address the concern about generating pixel-wise precise motion, we conducted an additional experiment (Additional Results, experiment 2) to further validate our approach. We extracted the optical flow from a video and used it as input to MotionCraft. The results demonstrated that our method could reconstruct the initial video with higher fidelity than the reconstruction in the pixel space.\n\n> How do you specify the region for simulating physical dynamics?\n\nWe thank the reviewer for this comment that allows us to clarify a point. As explained in the methodology, there is a certain degree of manual input in setting up a physical simulation conditioned on the starting frame. For example, in the fluid simulation of the filling glass in the supplementary material, we extracted a semantic map from the latent of the first frame and labeled the glass walls as boundary regions.\n\n> Will the type of dynamic physics simulator affect the quality of the generated video?\n\nWe compared different types of physics simulators in appendix C, where the same dynamic is simulated with both an Eulerian and a Lagrangian numerical solver, resulting in two different videos. As we can see in this example, both methods provide plausible frames. This showcases the ability of MotionCraft to operate on very different types of physical simulators seamlessly, leveraging the image prior of the diffusion model to correct potential misalignments and produce visually coherent and high-fidelity videos.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "Qp4yoM762r", "reviewer": "Reviewer_cTbz", "summary": "The paper presents MOTIONCRAFT, a novel zero-shot video generation method that leverages physical simulations to create realistic and physically plausible videos. Unlike traditional video diffusion models that require extensive training and large datasets, MOTIONCRAFT uses a pre-trained image diffusion model, such as Stable Diffusion, and warps its noise latent space with optical flow derived from physical simulations. This approach ensures coherent motion and the generation of missing elements consistent with scene evolution.\n\n**Key Contributions:**\n\n1. **Innovative Approach:** Introduction of a zero-shot video generation method that uses optical flow from physical simulations to warp the noise latent space of a pre-trained image diffusion model.\n2. **Experimental Validation:** Demonstrates the effectiveness of MOTIONCRAFT through both qualitative and quantitative comparisons with the state-of-the-art Text2Video-Zero method, showing significant improvements.\n3. **Theoretical Insights:** Provides an analysis of the correlation between optical flow in the image space and the noise latent space, supporting the proposed method.\n4. **Versatility:** Showcases the ability of MOTIONCRAFT to generate videos with complex dynamics, including fluid dynamics, rigid body physics, and multi-agent interaction models, without additional training.\n5. **Technical Details:** Describes key techniques such as multi-frame cross-attention and spatial noise map weighting to ensure temporal and spatial consistency in the generated videos.\n\nOverall, MOTIONCRAFT represents a significant advancement in zero-shot video generation, combining the strengths of physical simulations and image diffusion models to produce high-quality, dynamic videos.", "questions": "- Is it possible to achieve better controllable video generation by handling optical flow in a manner similar to that mentioned in the Generative Image Dynamics ([https://generative-dynamics.github.io/](https://generative-dynamics.github.io/)) paper?\n- Can more coherent videos be generated through interpolation in optical flow?\n- Is it possible to generate long videos?", "limitations": "Refer to Weakness", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "Refer to Summary.", "weaknesses": "- There are now many approaches to zero-shot video generation, such as [https://openreview.net/forum?id=zOjW6yVYkE](https://openreview.net/forum?id=zOjW6yVYkE). The authors only compared their method with T2V0 (a relatively earlier method), which may make the experimental results insufficient. It would be better to include a more comprehensive comparison.\n- The current zero-shot video generation methods generally cannot achieve a very coherent video effect and can only generate keyframes. Although the method proposed in the paper largely ensures content consistency between consecutive frames, the generated videos still fail to achieve a highly coherent effect as seen in the demonstration.\n- Optical flow-based strategies often face limitations in certain specific situations. In complex environments, optical flow might not be effective. This aspect should be discussed and analyzed in the paper's main text. Moreover, the performance in different scenarios should be thoroughly evaluated using a variety of experimental results presented in the paper, instead of merely showcasing the method's validity through three handpicked examples.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "> There are now many approaches to zero-shot video generation, such as https://openreview.net/forum?id=zOjW6yVYkE. The authors only compared their method with T2V0 (a relatively earlier method), which may make the experimental results insufficient. It would be better to include a more comprehensive comparison.\n\nWe appreciate the reviewer's suggestion. Besides the work linked by the reviewer, we are unsure what other specific papers the reviewer has in mind for zero-shot video generation with diffusion models. At the time of submission, we ensured to include references to all relevant works available. Regarding the method mentioned by the reviewer, we note that this work primarily compares with T2V0 using a limited quantitative metric (text-image CLIP score) without considering frame alignment or temporal coherence. Additionally, since it does not have any code or videos released, we are unable to reproduce their results and compare them within our evaluation setting. Nonetheless, we acknowledge the importance of a broader comparative analysis. We will include the referenced work in our related work section in the camera-ready version of our paper.\n\n> The current zero-shot video generation methods generally cannot achieve a very coherent video effect and can only generate keyframes. Although the method proposed in the paper largely ensures content consistency between consecutive frames, the generated videos still fail to achieve a highly coherent effect as seen in the demonstration.\n\nIt is indeed a challenge for zero-shot video generation methods to maintain high temporal coherence. In particular, we found that the 64x64 resolution of the latent space is one limitation. This resolution restricts the accuracy and smoothness of the motion since it prevents sub-pixel movements during warping, resulting in less coherent transitions between frames. However, we have explored the use of Stable Diffusion XL (SDXL), which offers a larger latent space (128x128), allowing for more precise and smooth motion. By increasing the spatial resolution of the latent space, SDXL mitigates the limitations observed with the standard 64x64 latent space. See example 4 in the Additional Results. We will deepen the discussion of these aspects in the revised version of our manuscript.\n\n> Optical flow-based strategies often face limitations in certain specific situations. In complex environments, optical flow might not be effective. This aspect should be discussed and analyzed in the paper's main text. Moreover, the performance in different scenarios should be thoroughly evaluated using a variety of experimental results presented in the paper, instead of merely showcasing the method's validity through three handpicked examples.\n\nWe agree with the reviewer that optical flow in the pixel domain is not adequate for generating realistic video (for example, it is difficult to handle occlusions). However, the same optical flow in the latent space can produce realistic videos. Indeed, MotionCraft is able to exploit the diffusion model in order to fix the simplistic nature of the optical flow while maintaining its explainability and simulation ability. We will add some videos generated by warping the pixel space to prove this claim.\n\nRegarding the limited number of examples, we provide videos with new contents and dynamics in the Additional Results PDF (we are limited to 1 page as per NeurIPS FAQ). These additional examples have been evaluated and confirm the quantitative results presented in the paper.\n\n> Is it possible to achieve better controllable video generation by handling optical flow in a manner similar to that mentioned in the Generative Image Dynamics paper?\n\nThe Generative Image Dynamics method involves training a motion prior by modeling it as a dense Fourier volume. This representation of optical flow is particularly suited for oscillatory motions, while MotionCraft is able to handle both non-oscillatory and oscillatory motion (as seen in the sea waves in example 6). However, it should be possible to achieve better controllable video generation in a manner similar to GID, at the cost of learning an optical flow generator, because this module should be input dependent. This is, however, outside the scope of this work.\n\n> Can more coherent videos be generated through interpolation in optical flow?\n\nWe found that the coherence of generated videos is affected by both the temporal resolution of the provided optical flows as well as the spatial resolution of the latent space of the diffusion model.\n\nConcerning the temporal resolution, it is possible to run the physics simulator with a sufficiently small time step to match the desired frame rate. However, as mentioned in our response to Weakness 2, the primary limitation we encountered to represent fine-grained motion is the 64x64 spatial size of the latent space in the current Stable Diffusion model. Plase, see our response to Question 2 for further comments.\n\n\n> Is it possible to generate long videos?\n\nYes, it is possible to generate long videos using our method. From a theoretical point of view, the method complexity is linear in the number of frames to be generated, as explained in the manuscript. From a practical point of view, we demonstrate this capability in example 6 in the Additional Results, generating a coherent video with 200 frames. The key to generating long videos lies in the cross-attention mechanism we use, which ensures global consistency by attending to the first frame in the sequence and local consistency by attending to the previous frame. However, this cross-attention approach may introduce challenges when there are significant scene changes, as the mechanism maintains consistency with the initial frame. To address this, the frame-to-attend can be shifted periodically, or a weighted attention mechanism that decays over time can be used. These strategies can help enhance the video generation capability of our method for very long videos.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "YTKW903zwb", "reviewer": "Reviewer_zFVb", "summary": "In this work the authors propose MotionCraft, a new zero-shot video generator to craft physics-based and realistic videos. MotionCraft is able to warp the noise latent space of an image diffusion model, such as Stable Diffusion, by applying an optical flow derived from a physics simulation. The authors show that warping the noise latent space results in coherent application of the desired motion while allowing the model to generate missing elements consistent with the scene evolution, which would otherwise result in artefacts or missing content if the flow was applied in the pixel space. The authors compare the method with the state-of-the-art Text2Video-Zero reporting qualitative and quantitative improvements, demonstrating the effectiveness of the approach to generate videos with finely-prescribed complex motion dynamics.", "questions": "See the weakness.", "limitations": "See the weakness.", "rating": 5, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 3, "strengths": "1. This method does not need extra training, which is efficient.\n2. This method introduces explicit phisyics control to the field of video generation, which is novel.\n3. This method finds out that the optical flow is consistent between pixel space and latent space, which is interesting.", "weaknesses": "1. The main concern is about the experiments. This paper only have 5 video results in total, which is not sufficient. I am worrying that the method is highly unstable and not robust, thus the author cannot present more video results. If this is the case, I think this manuscript is not suitable for publication. If this is not the case, I think the authors should provide more generated results and I will be glad to raise my score.\n2. How long does it take to generate a single video? If the paper claims that the video can be generated within minutes, I think generating tens of videos in the supplemtary material would be a good idea.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "> The main concern is about the experiments. This paper only have 5 video results in total, which is not sufficient. I am worrying that the method is highly unstable and not robust, thus the author cannot present more video results. If this is the case, I think this manuscript is not suitable for publication. If this is not the case, I think the authors should provide more generated results and I will be glad to raise my score.\n\nWe understand the reviewer's concern regarding the number of video results presented in our paper. We would like to assure you that our method is stable and robust. To address this concern, we have generated additional video results, which are included in the Additional Results PDF. These supplementary videos showcase a diverse set of scenarios and dynamic simulations, further demonstrating the reliability and consistency of our approach. For example, we applied it to a different diffusion model (SDXL) without modifications, resulting in a video with higher resolution and smoothness (example 4 in Additional Results PDF). We also generated a video 200 frames long (example 6) showcasing the stability of the method. Furthermore, in example 2, we tested our method with a complex optical flow, estimated directly from a real video.\n\nHowever, we are limited to a 1-page additional PDF in the rebuttal, so we included all the videos that we could fit on this page. More video will be added in the supplementary materials upon acceptance. We believe that these additional results will provide a comprehensive validation of our method and alleviate any concerns regarding its stability and robustness. Code is also available to generate any additional videos.\n\n> How long does it take to generate a single video? If the paper claims that the video can be generated within minutes, I think generating tens of videos in the supplementary material would be a good idea.\n\nThe claims in the paper regarding the time to generate a video refer only to the video generation itself (all and only the steps in Pseudocode 1 in the manuscript). However, as explained in the methodology, there is a certain degree of manual input in setting up the physical simulation and conditioning it on the starting frame. For example, setting the type of simulation, the boundary conditions, or the initial state of the fluid often takes time beyond the actual runtime of the generative model.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:
Dear Reviewers and Area Chair,
 
We appreciate the valuable feedback and suggestions provided by the reviewers. We have carefully addressed the concerns raised and integrated additional experiments and clarifications to expand the original material in the suggested ways. Please find below a detailed point-by-point response to the reviewers' comments. We hope that these revisions and the additional results provided will demonstrate the robustness and effectiveness of our method.
 
Since the most critical point highlighted by the reviewers is the limited number of generated videos, we would like to note that we are limited to a 1-page additional PDF in the rebuttal, so we included all the videos that we could fit on this page. More videos will be added in the supplementary materials upon acceptance.
 
Thank you for your consideration.
Sincerely,
Authors of submission 16937

Meta-review: The paper received 2 borderline accepts and 1 weak accept.  The reviewers approved of both the problem setting and the general approach of defining a connection between a physics simulator and a video generator. They were however slightly concerned regarding the breadth of the experimental comparison, whether optical flow was the optimal representation to relate the results of the physics simulator to the video generation model, and the generality of the solution.

I agree with both the strengths and weaknesses expressed by the reviewers. The task of using a physics simulator to support and augment video generation is very interesting, but the representations used (optical flow) could have been investigated more thoroughly and more experiments included. I recommend Accept as poster.
Decision: Accept (poster)