FlowMo: Variance-Based Flow Guidance for Coherent Motion in Video Generation
Authors: Ariel Shaulov
Itay Hazan
Lior Wolf
Hila Chefer
Venue: NeurIPS 2025 poster ()
Keywords: video generation
diffusion models
generative models
Primary area: deep_learning

Abstract: Text-to-video diffusion models are notoriously limited in their ability to model temporal aspects such as motion, physics, and dynamic interactions. Existing approaches address this limitation by retraining the model or introducing external conditioning signals to enforce temporal consistency. In this work, we explore whether a meaningful temporal representation can be extracted directly from the predictions of a pre-trained model without any additional training or auxiliary inputs. We introduce __FlowMo__, a novel training-free guidance method that enhances motion coherence using only the model's own predictions in each diffusion step. 
  FlowMo first derives an appearance-debiased temporal representation by measuring the distance between latents corresponding to consecutive frames. This highlights the implicit temporal structure predicted by the model. 
  It then estimates motion coherence by measuring the patch-wise variance across the temporal dimension, and guides the model to reduce this variance dynamically during sampling. Extensive experiments across multiple text-to-video models demonstrate that FlowMo significantly improves motion coherence without sacrificing visual quality or prompt alignment, offering an effective plug-and-play solution for enhancing the temporal fidelity of pre-trained video diffusion models.

FlowMo: Variance-Based Flow Guidance for Coherent
Motion in Video Generation
Ariel Shaulov*
Itay Hazan Lior Wolf
Hila Chefer
School of Computer Science Tel Aviv University, Israel
Wan2.1-12 1.1.1
+o
"A woman performing challenging exercise"
"A dolphin jumping out of ocean waves"
Cog VideoX-SB 5B
+FlowMo
"A pair of flamingos wading through shallow water"
"A ballerina leaping through the air"
(b)
Figure Text-to-video results before and after applying FlowMo on (a) Wan2.1 and CogVideoX-SBB [2]. We present FlowMo, an inference-time guidance method to enhance temporal coherence in text-to-video models. Our method mitigates severe temporal artifacts, such as additional limbs (woman, 1st row, 2nd row), objects that appear or disappear (flamingo, 2nd row), and object distortions (woman, dolphin, 1st row), without requiring additional training or conditioning signals.
Abstract
Text-to-video diffusion models are notoriously limited their ability to model temporal aspects such as motion, physics, and dynamic interactions. Existing approaches address this limitation by retraining the model or introducing external conditioning signals to enforce temporal consistency. In this work, we explore
"Equal contribution.
Project page: https: attps://ariee httpe::/aaeeelaullloo github. 1o/FlowMo/ Correspondence Ariel Shaulov: arielshaul ovmmmmailllao.o.....oommmmm tau. i1, Itay Hazam: itay. hzn@gmail com.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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whether a meaningful temporal representation can be extracted directly from the predictions of pre-trained model without any additional training or auxiliary in- puts. We introduce FlowMo, novel training-free guidance method that enhances motion coherence using only the model's own predictions in each diffusion step. FlowMo first derives an the distance between latents corresponding to consecutive frames. This highlights the implicit temporal structure predicted by the model. It then estimates motion coherence by measuring the patch-wise variance across the temporal dimension and guides the model to reduce this variance dynamically during sampling. Extensive experiments across multiple text-to- eext-to-video models demonstrate that FlowMo sig- nificantly improves motion coherence without sacrificing visual quality prompt alignment, offering an effective plug-and-play solution for enhancing the temporal fidelity of pre-trained video diffusion models.
temporal representation by measuring
Introduction
Despite recent progress, text-to-video diffusion models remain far from faithfully capturing the temporal dynamics of the real world. Generated videos frequently exhibit temporal artifacts such as objects appearing and disappearing, duplicated or missing limbs, and abrupt motion discontinuities [3] These issues highlight the limited capability of text-to-video models reason about motion, physics, and dynamic interactions over time. To mitigate these shortcomings, prior works have proposed fine-tuning models with explicit motion-related objectives [3, conditioning the generation
4 [..
on external motion signals such as optical flow or pixel trajectories 6 7 8 91. or designing complex
model architectures tailored capture temporal dependencies
10
12
12 or introducing rigid external constraints that dictate motion [6] 77. limiting flexibility and generality. In this work, we propose an alternative strategy dubbed FlowMo, a training-free guidance method that improves temporal consistency using the model's own internal representations during sampling. FlowMo extracts latent temporal signal directly from the pre-trained model during inference and leverages its statistics to derive a guidance signal, without any architectural modifications, training, or external supervision.
However, these approaches require either retraining the model 3
Our method is grounded in the following key observation: the temporal evolution of individual spatial patches tends to be smooth when the motion is coherent. Namely, the shifts in the representation of each patch over time are expected to be relatively small, leading to low patch-wise variance across frames. In contrast, incoherent motion intuitively manifests as abrupt changes in appearance or structure, producing high temporal variance in the patches that display temporal artifacts.
Notably, measuring temporal relations in way that is disentangled from appearance information is challenging. As observed by previous works R the predictions of text-to-video models are biased toward appearance- based features. To obtain meaningful appearance-debiee -ebbiased representation, use the model's 's latent predictions to compute pairwise distances between frames. This enables us to measure the shifts in patch representations using patch-wise variance over time while neutralizing their shared appearance content. This is motivated by prior works demonstrating that the latent spaces of generative models capture semantically meaningful transformations, where simple vector
operations correspond to interpretable changes [13 14 15].
We explore the above intuition extensively in Sec. 3.2 First, we collect set of generated videos that exhibit significant motion. We categorize these videos into coherent and incoherent sets, and compute the patch-based variance over time given the appearance-debiased representations discussed above. Our experiments yield two complementary observations. First, we find a clear correlation between high patch-based variance and motion incoherence, indicating that measuring the shift in patch representations over time can serve as reliable metric to estimate coherence. Second, we observe both qualitatively and quantitatively that while coarse appearance-based features such as scene layout and spatial structure are established very early in the generation process, temporal information emerges only at later, intermediate denoising steps.
Motivated by these findings, we present FlowMo, a method that dynamically guides text-to-video diffusion models toward temporally coherent generations. At selected timesteps in the denoising process, we compute the maximal patch-wise variance over time, given the appearance-debiase latent prediction. We then optimize the model's prediction to reduce this temporal variance, thereby

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encouraging smoother, more coherent motion. This guidance is applied iteratively across timesteps, allowing FlowMo influence both coarse and fine motion dynamics in the generation process.
We demonstrate our method's effectiveness on two of the most popular open-source models, Wan2. 1- 1.3B [T] and Cog VideoX-5B (2). Across wide range of metrics, we evaluate the impact of our method on motion quality, overall video quality, and prompt alignment, using both the automatic evaluation metries proposed by VBench [16] and human-based assessments. In all cases, we find that FlowMo consistently and significantly improves the temporal coherence of the generated videos, while preserving the aesthetic quality, text alignment, and motion magnitude (see Fig.
Our results show that it is possible to extract meaningful temporal signals from the learned latent representations of text-to-vide video models. Such signals not only encapsulate the temporal structure of the generated videos but also serve as actionable guidance cues.
2 Related Work
Text-to-video generation Diffusion models have revolutionized visual content creation, starting with image generation 18 [9 and rapidly expanding to diverse applications such as text-to-image 31]. This success has spurred
synthesis [20, (2] and image editing [22
23 24
25
26
27
28,
29
30
their adoption for video generation, from cascaded diffusion models [32 33 34 35
36
37 38
39 40 41
to most recently Diffusion Transformers (DiT) 42 43] based on Flow Matching (FM)
44
45
which constitute the current state-of- of-the-art, and form the basis of our work.
Inference-time guidance has emerged as powerful technique to steer and refine the outputs
of generative models across various tasks without training [47 48 49
28 [0]. Such methods
typically optimize the model predictions based on an auxiliary loss. Inference-time guidance for
video generation has only recently emerged as promising research vector [51 [52. While our
work also explores inference-time optimization for video generation, existing objectives and guiding signals inherently differ from ours. Li et al. [5T] focus on steering video models using external motion priors, which requires access additional motion-specific inputs, while Wei et al. (52) propose to minimize a global 3D variance loss. In contrast, our method leverages the internal latent-space dynamics perform guidance without any auxiliary networks, perceptual objectives, or task-specific priors, making it lightweight and fully self self-supervised plug-and aad--ndd-lpla -dlp module.
Improving temporal coherence in video generation Temporal coherence remains a core challenge in video synthesis 55 12], and existing solutions generally fall into three categories. First, training with temporal objectives 11 53 54), which improves consistency but demands significant compute and access to training data. Second, guiding the generation with external motion signals such as optical flow or trajectories 6 g which enforce coherence but require external inputs and are restricted the conditioning motion. Third, architectures designed for temporal modeling (10 [1]
53 56 57 58), which are often complex and not easily applied to pre-trained models. In contrast,
FlowMo improves temporal coherence directly at inference time by leveraging the model's internal representations, without additional data, inputs, or retraining.
Closest to work, FreeInit (59] and VideoGuide [60] propose methods to reduce spatio-temporal incoherence in video generation. However, both were designed for earlier UNet-based models trained with DDPM or DDIM samplers [61 45), which suffered from severe signal-to-noise ratio (SNR) mismatches between training and inference [59] In contrast, modern Transformer-basee FM architectures are substantially more robust, rendering these techniques less effective. For completeness, we include a comparison to FreeInit (which can be reasonably adapted to DiT')) in App. A In our experiments, we find that applying FreeInit to DiTs results in drop in key metrics such as the overall video quality, as well as significant drop in the amount of generated motion.
3 Method
3.1 Preliminaries: Flow Matching in a VAE Latent Space
Following common practice state-of-the-art image and video generation models 62
we
consider models that leverage FM 44 to define the objective function and operate in the learned
3

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latent space of Variational Autoencoder (VAE) for efficiency. The VAE consists of an encoder- decoder pair (E, D), where maps input data I ~ X' from the pixel space lower-dimensional latent representation = = {(r) 2, and 'D yields a reconstruction a R D(z). Given pre-trained VAF, FM learns a transformation from a standard Gaussian distribution in latent space 2g ~N(0,) T), to target distribution 21 observed from applying & on the data.
At each training step, FM draws timestep t [0, 1], and obtains noised intermediate latent by interpolating between 2g and 21, namely & = (1 - t) #1 t- z0. The model ug is then optimized to namely:
predict the velocity Ut dt
dzy 20
frM (00.)= [1u0(2s, t) (zo =))13]
(I)
Once trained, samples can be generated from an initial noisy latent 2n (0, 7) by applying sequence of denoising steps over discrete schedule. At time 4, 21, denoised to produce St;+, by
applying ct,,, = (1 of,) Zz, ot (2(zt, 44), where or, is an interpolation coefficient determined by the scheduler.
3.2 Motivation
In the following, we conduct qualitative and quantitative experiments to motivate the construction of FlowMo. The experiments in this section are conducted on Wan2.1-1.3B [ for efficiency.
We begin by describing the latent representation on which FlowMo operates. As mentioned in Sec. 3.1 at each denoinsing step, the model prediction ug. == uo(=,, t) is estimate of the velocity 2t, which represents the direction from the noise distribution to the latent space distribution. To extract a temporal representation from the prediction, we propose debiasing operator A, which computes the di-distnece between consecutive latent frames to eliminate their common appearance information. Formally, A: R FFx X + R( I)xW XXXC is defined as:
Vf E [F-1], Vw [W], Wh E [M], Vc E [C] (Aua,)) f.m (I(u),)) (t - (. s.w.hell II
Next, we describe the motivational experiments conducted to examine the statistical characteristics of our proposed latent space.
Quantitative motivation. Our central hypothesis is that temporally coherent motion corresponds to a form of local stability in u0,1- Specifically, in videos with smooth and consistent motion, object trajectories evolve gradually, yielding lower temporal variance in ug,t- Incoherent motion, in contrast, introduces abrupt changes, manifesting larger fluctuations and higher patch-wise variance in the latent predic- tions. Formally, given u0,t, we define its temporal patch-wise variance tensor o² E IR XC as the variance across frames per patch and channel, i.e. Vw [W], vh E [M], Vc [C],
Mean Patch-wise Variance g2
(59 videos)
0.58
Cobment (61 videos)
0.66
0.54
0.62
0.60
0.58
Timestep
Figure 2: Quantitative motivation. We mea- sure the mean temporal variance of spatial patches for coherent and incoherent videos. Incoherent videos portray higher variance. The separation is visible from step 5 onward. 95 95%-confidence interval was computed using the seaborn python package.
h, V J~|F-111 11] (A...))......)
where V(X)= = [X - B[
To empirically validate our hypothesis, we conducted user study wherein several hundred generated videos were rated on a 1-5 scale for both coherence and perceived amount of motion (higher is more mo- tion/better coherence). To isolate the effects of motion magnitude on video coherence, we focused on videos with a substantial amount of motion (rated 2 3), and compared those labeled as completely incoherent (1), or completely coherent (5). As illustrated in Fig. 2 a clear negative correlation emerges: low-coherence videos consistently exhibit higher variance. This supports our intuition that temporal patch- patch-wise variance is meaningful measure of perceived coherence.

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Notably, the separation in variance becomes prominent from approximately the fifth generation timestep onward. Next, we wish to conduct a qualitative experiment to motivate this phenomenon.
Qualitative motivation. To qualitatively explore the process of motion generation in text-to-video models, we visualize the evolution of the model's latent space prediction across the generation steps.
Frame
Frame 14
Frame 20
First, observe that by Sec. 3.1] the model prediction Ug estimates the velocity 24 = 2g - 21. We can thus obtain an estimation of the fully denoised latent, ž1, at any intermediary step t as follows:
I
1 = 2 02 U0tt:
(4) I
where is the signal signal-to-noise ratio at step t, which defined by the noise scheduler.
Figure 3: Qualitative motivation. We visual- ize the model prediction per timestep across the generation. Coarse spatial information is determined in the first steps (0-4), whereas motion is determined around steps 5-8, and refined in later steps.
Note that 2 a latent-space representation where channels do not represent RGB information. We thus arbitrarily select the first channel, to obtain 21,00 E FxHW and visualize the grayscale video via:
31,00 ming.
V VaL.o = 255
InaF, (2) n.nF,,,.(W,,.0 (2),00)
The resulting visualizations V representative timesteps are presented in Fig. 3 As can be observed, coarse spatial information begins emerge from the first generation step, where the training bar and some of the outline of the person are visible. By step 4, most of the structure of the scene already determined. Conversely, the motion appears be added the scene between steps and 8, as evidenced by the strong similarity between all frames in times 0,4, whereas step 8 shows significant variance between these same frames (e.g.. the person bends down between frames 14 and 20). Visualizations on additional timesteps and latent channels are provided in Appendix B Note that the above supports the quantitative experiment presented Fig. 2 Since motion emerges only around the later initial steps of the denoising process (4-8), we would expect our variance-based metric to be meaningful only in the steps that depict measurable differences over time.
In App. C we show quantitative evidence that, in addition to enhancing coherence, FlowMo reduces the variance in generation steps that correspond the above intuition.
3.3 FlowMo
Motivated by the previous section, Algorithm I outlines the FlowMo guidance mechanism, ap- plied within a single FM denoising step. We perform the FlowMo guidance at specific timesteps (7..... Te), corresponding to the early-to-mid stages of generation, following the motivation pre- sented in Fig.
Each denoising step I; begins by obtaining the model prediction ua,,, given an input text prompt P. encourage alignment between the prediction and the textual prompt, Classifier-free guidance (CFG) (4) is first employed with scale of (Line
we are not in refinement step, we jump Line 14 in which we perform a standard FM step to obtain the next latent 2444 as a linear combination of the current latent and the predicted velocity:
2, (1 ot.) 24, 0t, Wo.
where ot, is time-dependent coefficient representing the signal-to-noise ratio.
If, however, t; E {T, a FlowMo refinement step is performed (Line 5 to Line 12 We first compute the appearance-debbased representation, Aug,t, defined in Equation (Line
Subsequently, drawing on the motivation presented Fig. 2 we calculate the temporal variance
22 hh for each spatial patch (w, h, e) as defined in Equation (Line 6). These patch-wise variances
5

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are then averaged across the channel dimension to produce a single spatial map Such indicating motion coherence score per patch (Line
Ve E [W], wh E [H] Sw,h Bewiey lo
Σ o whe
C
The final FlowMo loss C is then determined by the maximal value in this map, thereby targeting the most maamically-incoheree patch (
Algorithm 1 A Single FlowMo Denoising Step
Input: A text prompt P, timestep 4i, set of iterations for refinement (Ti,,... TeJ, and a trained Flow Matching model FM.
C w [.[[W],a<[H]
max
Sw,h-
(8)
Intuitively, this formulation encourages the model produce prediction vig,, wherein the latent space distances of each spatial patch over time are smoother, resulting in more coherent and gradual transitions in the generated video.
Output: A noised latent 24z+1 for the next timestep t
1: U..../P < FM (4
2: 00,4 +- FM 1, 0)
3: u0,t; < u0.1;10 + p (.. IP (0,1;10)
Inspired by existing guidance mechanisms that optimize spatial information [47]. we propose to the loss in Eq. 7 to optimize the input latent to the diffusion step. 2t, (Line (9). Intu- modify
4: if t4 E ffI....,TTe Je) then
5: Compute (Aug,r, as in Equation 2
6: Compute o² in Equation 3
itively, this allows our optimization low-level features in the generated video, includ- ing the coarse motion. Thus, the optimization is performed as a gradient descent step:
7:
Sw,h + E 02 wuhhi
44hh
8:
t 1mmmax 1W Sw,
9:
Zt, 21, 17 V
10:
UP, + FM t. P)
11:
M0,1, + FM (21 44, 0)
Zt; = =t, V C,
12: 20,t1 < u0,1,1 p (u,,1; IP u0,,,10)
where 77 is the learning rate. Following this re- finement, we repeat the denoising step 1, with the optimized latent 2t, (Lines T0 T2
13: end if
14: St; + - (1- =4, 0zg u0..
15: Return 26;12
Experiments
We conduct qualitative and quantitative experiments to demonstrate FlowMo's effectiveness. Our experiments evaluate the improvement in temporal coherence enabled by method, well as its ability to maintain or even enhance other aspects of the generation, such as appearance quality and text alignment. We provide code and website with video results in the supplemental materials.
Implementation details We employ two of the most popular publicly available text-to- video models: Wan2.1-1.3B [ and CogVideoX-a (2] using their officially provided weights and default configurations. Motivated by the insights from Sec. 3.2 apply Foow in the first 12 timesteps of the generation, since these are responsible for coarse motion and structure. All our experiments employ learning rate of 0.005, using the Adam optimizer, on two NVIDIA H100 GPUs, with 80GB memory each. 1 is evaluated at resolution of x80, and VideoX at 480 720, both generating 81 frames at 16 frames per second, resulting 5-second videos.
4.1 Qualitative Results
Figures T 4 contain representative results demonstrating the impact of FlowMo on pre-trained text-to- video models. As can be observed, our method mitigates severe temporal artifacts that are common text-to- video models. For example, the generations tend display extra limbs (women in Fig. Ta) and Fig. 4 2nd, 3rd row), distortions of objects over time (dolphin in Fig. Ta) [a) and deer in Fig. 4th
row), and objects that suddenly appear or disappear (flamingo in Fig. [(b) and rope, violin Fig.
2nd, 3rd row). These results demonstrate that temporal artifacts correspond to abrupt changes in the latent representations of video patches. This, in turn, drives our optimization process to encourage
smoother representations of the affected patches, resulting in improved temporal coherence.

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Wan2 1-1.33
+FlowMo
"A roulette wheel in dimly li room or casino floor" A boy with glasses flying a kite in grassy field
Wan2.1-11 1..3
+FlowMo
"A boy skipping rope in backyard"
"A senior couple dancing sunset pier
(a)
Cog CogVideoX-SI SB
+o
"A figure skater gliding across the ice"
"A violinist performing solo stage'
CogVideo
Mo
"A deer leaping over a fallen log"
"A teenager skatehoarding down handrail"
(b)
Figure 4: Qualitative results. Text-to-video results before and after applying FlowMo on (a) W [1] and (b) Cog (2]. FlowMo mitigates severe temporal artifacts, e.g., extra limbs (women, 2nd, 3rd row), objects that appear or disappear (2nd, 3rd row), and distortions (4th row).
4.2 Quantitative Results
We employ both the VBench benchmark [16] and human-based evaluations, which serve as standard evaluation protocols for measuring the quality of text-to-video generation 2 65 66 67 68)
7

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Wam2.1-1.33
Cog V5d
14.9%
79.9%
-7.2%
Text alignment
15.6%
75.7%
88.7%
31.1%
54.9%
11.00
Quality 31.7%
51.3%
17.1%
44.3%
39.5%
-6..2%
Motion
43.0%
39.4%
17.6%
0
20
40
60
80
160
20
40
60
80
100
Win Rate
Ours
Both
Baseline
Win Rate
Figure 5: User study conducted on Wan2.1-1.3B [ (left) and Cog VideoX-55 [2 (right) using VideoJAM-bench [3) designed specifically to evaluate motion coherence. Our method significantly improves temporal coherence in all models, while maintaining or improving the visual quality and the text alignment of the resulting videos. 95%-confidence intervals were calculated using Dirichlet sampling, assuming multinomial distribution with Laplace smoothing applied to the counts.
Table 1: VBench evaluation results. A comparison of the overall video quality before and after applying Fo on Wan2.1-1.33. I and CogVideoX-555 22 using VBench [16]. We enclose both the motion-speciife and the aggregated scores. FlowMo consistently improves the Final Score representing the overall video quality by at least 5%.
Motion Metries
Aggregated Scores
Motion
Dynamic Degree
Semantic Score
Quality Score
Final Score
Models
Smoothness
W-n2.1-1.3B FlowMo
96.43%
83.21 %
84.70% 89.11 %
65.58%
75.14%
98.56
81.96%
73.58
81.34 % (+6.20 %)
CogVideoX-SB
95.01 %
65.29 %
70.03 %
60.83%
65.43%
FlooMoo
97.29 %
63.92%
69.26%
72.11% %
70.69 % (+5.26 %)
User study. We conduct a human preference study using the VidcoJAM benchmark [3] which was specifically designed to test motion coherence. For each prompt, generate pair of videos (with and without FlowMo) with a fixed seed in the setting described above, and randomly shuffle the order of the results. Each prompt responses per baseline. Annotators were asked to compare the videos based on their alignment to the text prompt, the aesthetic quality of the videos, and the motion quality (see App. D)
evaluated by five different participants, resulting in 640 unique
The results, presented in Fig. 5 demonstrate a consistent human preference for FlowMo-guidee videos across all criteria. Specifically for Motion Coherence, FlowMo was favored in 44.3% of comparisons for Wan2.1 (ys. 16.2% for baseline) and 43.0% for CogVideoX (vs. 17.6% for baseline). A similar trend observed for Aesthetic Quality, where FoowMo was preferred in 31.1% % of Wan2.1 pairs (vs. 14.0% for baseline) and 31.7% of Cog VideoX pairs (vs. 17.1 % for baseline). Interestingly, FlowMo also showed improved Text-Vise Video Alignment, with preference rates of 14.9% for Wan2.1 (vs. 7.2% for baseline) and 15.6% for Cog VideoX (vs. 8.7% for baseline).
These findings highlight that Fo not only enhances temporal coherence but also contributes positively to the overall perceived video quality and faithfulness to the input prompt.
The results of the automatic metrics on the VBench benchmark [6] are summarized in Tab. [ We enclose both the motion-based metries, and the aggregated metries, which constitute an average of all the benchmark dimensions, and measure the overall quality of the generations. A full breakdown of all metries provided in App.
Automatic metrics.
Notably, FlowMo significantly improves the Final Score by 6.2%, 5.26% for Wan, Cog VideoX, respectively. This metric represents the overall quality score, considering all the evaluation dimensions. This improvement is supported by gains in the Quality Score (Wan2.1: 1: +8.0%; Cog VideoX: +1 1.28%) and Semantic Score for 1an2.1 (+4.41%) with negligible decrease of 0.77% for Cog VideoX.
Considering the motion metrics, FlowMo boosts Motion Smoothness (Wan2.1: 1:: +2.13%; Cog VideoX: +2.28%), which is a key metric that evaluates the motion coherence. Finally, note that some decrease

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to the dynamic degree is expected. This is since temporal artifacts such as objects appearing and disappearing increases the amount on motion the video.
In summary, both human evaluations and automated VBench metrics consistently demonstrate FlowMo's effectiveness in improving motion coherence and overall video quality.
4.3 Comparison with FrecInit
We compare FlowMo to FreeInit (59], the most conceptually related method. The full comparison between FlowMo and FreeInit is provided in App.
qualitative comparison between FlowMo and the adapted FreeInit is presented in Fig. 6 These examples highlight FlowMo's superiority in generating visually coherent motion. For instance, in the top-left example, FlowMo successfully generates plausible marching motion, whereas Freelnit produces disappearing feet and less convincing movement. Similarly, in the top-right example, FlowMo depicts coherent walking, while the rendition produced by Freelnit suffers from partially disappearing feet and less natural gait. The bottom-left example shows FlowMo maintaining the integrity of the man and rope, while in the video refined with FreeInit, the rope distorts and disappears and the man has less stable form. Finally, in the bottom-right example, FlowMo maintains consistent orientation, whereas the front and back sides of the person flip spontaneously in the version generated with FreeInit. Overall, these visual examples show that FlowMo demonstrates a significant advantage in producing more coherent and artifact-free motion compared to FreeInit.
FreeInit
FlowMo
"A person lifts one knee high in marching motion"
"A clase-up of person's 's feet as they walk"
Freeinit
Flow
"A man jumping rope a dark stage"
"Young Adult Male Doing Handstond the beach"
Figure 6: Qualitative results. Text-to-video results of FreeInit (59 (Ist, 3rd row) and FlowMo (2nd, 4th row) when applied on Wan2.1-1.3B [ FlowMo better mitigates severe temporal artifacts, e.g. distortions and object that appear and disappear.
We further compare FlowMo to the adapted FreeInit method through human preference study and quantitative benchmarks. Human evaluators consistently favored FlowMo-guides videos over FreeInit and the baseline across Motion Coherence (38.7% vs. 23.4%)) Aesthetic Quality (28.) % vs. 14.8%), ), and Text- Video alignment (16.5% vs. 5.2%). Quantitative results on VBench corroborate these findings: FlowMo improves Motion Smoothness by +3.1%% and Overall Quality and Semantic Scores by +7.36% and +3.20% respectively, achieving Final Score of 81 334% compared FreeTnit's 75.06%. Full per-dimension comparisons, and the full implementation details are provided in App. A

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4.4 Ablation Study
We ablate the primary design choices of FlowMo. namely using the patch with the maximal variance the loss (Eq. [). the appearance debiasing op- erator (Fq.2), 2) and the choice of steps to apply the optimization (1-12).
"A kásio Rippingg therigh banihoo fowees"
"Pikachu with Charmandeer comptfre"
FlomMe
Wan21-1.
Results of the ablation study on Wan2.1 are reported in Fig. 7 For each prompt, we enclose the result with FlowMo (1st row), Wan2.1 (2nd row) and the ablations (3rd-5th row). Replacing the maximum with the mean (3rd row) significantly weakens the effect, likely because most patches are static, leading to a smaller loss and diminished gradients. Removing the debiasing operator (4th row) yields a similar effect. This can be attributed to the fact that, as observed by previ- works [3, predictions by text-to- video models tend to be appearance- based, reducing the influence of mo- tion on the loss. Finally, applying FlowMo across all steps (5th row) in- troduces artifacts, as the optimization interferes with high frequencies and fine details in steps where motion is already determined.
Mem
WIO Dabiss
Figure 7: Ablation study. We ablate the main design choices of FlowMo, i.e., using the maximal variance for the objective (3rd row), using the appearance-debiasing operator (4th row), the selection of the optimization steps (5th row), and show that FlowMo is significantly superior to all variants.
4.5 Limitations
While our method enables substantial improvements in motion coherence and overall quality of generated videos, it still has few limitations. First, due to the calculation and propagation of gradients by our method (Alg. [. there some slowdown in the inference time. On average, generating a video with FlowMo takes 160.67 seconds compared to 99.27 seconds without it, corresponding to x 1.82 increase. This overhead could be mitigated by integrating FlowMo into the training phase, eliminating the need for gradient-based optimization at inference time.
Second, since FlowMo does not modify the model weights, it is bounded by the learned capabilities of the pre- pre-trained model. While it can improve the coherence of motion predicted by the model, it cannot synthesize motion types the model has not learned represent. We believe this limitation can be addressed by incorporating motion-basee objectives based on the model's internal representations during training, encouraging richer temporal understanding in generative video models.
5 Conclusions
Can we extract meaningful temporal representations from a model with limited temporal understand- ing? In this work, we propose new approach to address temporal artifacts in text-to-video models. Instead of relying on external signals, additional data, or specialized architectures, we repurpose the model's 's own learned representations as a source temporal guidance. Specifically, we find that the semantic latent space learned by text-to-video diffusion models implicitly encodes valuable temporal information. Through extensive analysis (Sec. (3.2), we show that distances between pairs of frames in this latent space correlate with intuitive measures of temporal artifacts, such as patch-wist variance over time. Building on these insights, we implement an inference- that encourages smoother transitions in the latent space, and observe that this maps to smoother behavior in pixel space as well, significantly boosting motion coherence while preserving and even improving other aspects of the generation. We hope this work sparks further interest in exploring the temporal properties of semantic latent spaces and encourages the development of methods that improve temporal coherence by looking inward rather than outward.
guidance method
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A Comparison between FoowMo and FreeInit
In this appendix, we compare FlowMo with Freeinit 55 which is most closely related to our method.
FreeInit was designed for earlier UNet-based models that employ DDPM or DDIM 66 45 Its approach is motivated by the observation that such models often exhibit significant spatio- nemio-tempooal inconsistencies in scene elements across frames (e.g.. character identities and backgrounds changing between frames). Their primary observation is that these models exhibit discrepancies in signal-to- noise ratios (SNR) between training and inference phases, causing temporal artifacts. contrast, modern Transformer-basee
architectures, as used in our work, are generally more robust to these inconsistencies due to more powerful architectures, more stable training frameworks (using FM), and larger training datasets. Thus, these models are able to maintain consistent appearance across frames and are less susceptive to these types of artifacts.
To provide fair comparison, we adapted FreeInit for use with FM-based DiT models. This involved re-noising a denoised latent and combining this re-noised latent with random noise to initialize the low-frequency components, before repeating the denoising process, as per FreeImit's methodology. We then conducted both quantitative (user study and VBench automatic metrics) and qualitative comparisons between FoowMo and our adapted Freelnit. The experiments are demonstrated hereafter.
All experiments were done the Wan2.1-1. 1-1.3B model, for efficiency. The experimental setting for the vanilla baseline and FlowMo-guided model the same as in Sec. [ FreeInit was implemented based on its publicly available open-source code [59] and its default configuration, namely employing the butterworth filter with n = 4, d, = de 0.25. To remain comparable with our work, we performed one refinement iteration with each of the methods.
Implementation details.
A.1 User Study
Consistent with the experiments presented in the main paper, we compare FlowMo to the FreeInit baseline using both the VBench benchmark [6 and human evaluation results.
Wan2.1 1-1.3B vs FlowMo
FlowMo FreeInit
14.9%
77.9%
7.2%
Text alignment
16.5%
78.3%
5.2%
31.1%
54.9%
14.0%
Quality
28.1 %
57.1%
14.8%
44.3%
39.5%
16.2%
Motion
38.7%
38.0%
23.4%
0
20
40
60
80
100
20
40
60
80
100
Win Rate
Ours
Both
Baseline
Win Rate
Figure 8: User studies conducted on Wan2.1-1.3B II using VideoJAM- -ench 3 The studies compare three variants of the model: vanilla (Wan2.1-1.3B). with FlowMo, and with FreeInit. Our method significantly outperforms the baselines both studies. 95%-conffience intervals were calculated using Dirichlet sampling, assuming multinomial distribution with Laplace smoothing applied to the counts.
We conducted a human preference study that compared vidcos generated by Wan2. 1-1.3B guided by FlowMo with those guided by FreeInit. Vidcos from both models were sampled given prompts from the VideoJAM benchmark in the same setting described in Sec. 4.2 of the main paper.
The results, presented in Fig. clearly indicate strong human preference for FlowMo across all evaluated categories, comparison FreeInit well as the vanilla Wan2.1-1.3B model. Comparing FreeInit and FlowMo, for Motion Coherence, FlowMo was preferred in 38.7% 38.7% of comparisons, substantially more than FreeInit (23.4%). In terms of Aesthetic Quality, FlowMo was chosen in 28. 1 % of pairs, nearly double the preference for FreeInit (14.8%). Furthermore, FlowMo also outperformed Freelnit in Text-Vides Alignment, with preference rate of 16.5% compared to FreeInit's 5.2%. These results demonstrate that human evaluators find FlowMo-guided videos to be
22

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significantly more coherent, aesthetically pleasing, and better aligned with textual prompts than those guided by the adapted FreeInit.
A.2 VBench Benchmark
Table 2: VBench evaluation results per dimension. Each column represents model variant, Wan2.1 (Baseline), with FlowMo, and with FreeInit. Rows correspond to the 16 VBench evaluation dimensions. While FlowMo significantly increases the overall quality of the videos (+6.20%), ), Freelnit reduces it (-0.08%), and is unable to compare with the Baseline and FlowMo in any of the dimensions.
Dimension
Wan2.1-1.3B
Baseline
FlowMo
FreeInit
Subject Consistency
95.61% %
96.54%
93.71% %
Background Consistency
97.25%
97.02%
97.12%
Temporal Flickering
99.15%
98.93%
97.77%
Motion Smoothness
96.43%
98.56%
96.54%
Dynamic Degree
83.21 %
81.96%
67.01 %
Aesthetic Quality
56.77%
58.03%
50.99%
Imaging Quality
61.01%
64.89%
57.19%
Object Class
91.37%
95.35%
92.11 %
Multiple Objects
77.98%
82.27%
73.26%
Human Action
98.27 %
97.23%
97.98%
Color
87.94%
87.28%
86.53%
Spatial Relationship
75.21%
78.42%
76.52%
Scene
49.84%
49.41%
48.32%
Appearance Style
20.95%
28.45%
21.59%
Temporal Style
26.35%
27.30%
24.24%
Overall Consistency
23.65%
25.53%
22.13%
Semantic Score
84.70%
89.11 %
85.91 %
Quality Score
65.58%
73.58%
64.22%
Final Score
75.14%
81.34% (+6.20%)
75.06 (-0.08%)
We further evaluate FlowMo against the adapted FreeInit using the VBench benchmark. The detailed results per dimension are presented in Tab. 2]
The VBench metrics [6] corroborate the user study findings, showing FlowMo's s superiority. First, observe that across the comprehensive suite of VBench metrics detailed in Tab. the adapted Freelnit does not achieve a superior score to both FlowMo and the baseline in any individual dimension.
Considering the main metrics related to motion coherence, FreeInit achieves only a marginal improve- ment in Motion Smoothness (+0.1 11 over bascline) compared to FlowMo's substantial +2.13% gain. Critically, FreeInit significantly degrades the Dynamic Degree by -16.20% from the baseline (from 83.21 % 67.01 %), whereas FlowMo maintains comparable dynamic level (81.96% This large reduction in motion by FreeInit suggests that its apparent coherence might stem from producing less dynamic videos, which are inherently easier to keep coherent, rather than genuinely improving the quality of complex motion. Furthermore, Freelnit performs worse than both the baseline and FlowMo in several other important quality aspects. For instance, Aesthetic Quality (50.99%) is lower than both baseline (56.77 (56.77% and FlowMo (58.03%) Similar trends are observed for other important qualitics, c.g. Temporal Flickering (FrecInit: 97.77% vs. FlowMo: 98. 93%, Baseline: 99.15%), Imaging Quality (FrecInit: 59.19% vs. FlowMo: 64.89%), Appearance Style (FrecInit: 21.59% vs. FlowMo: 28.45%), ), Temporal Style (FreeInit: 24.24% vs. FlowMo: 27. 27.30%), and
Overall Consistency (FrecInit: 22. 13% vs. FlowMo: 25.53%).
Finally, FlowMo significantly outperforms Freelnit in the aggregated VBench metrics. FlowMo achieves a Final Score of 81. 81.34%, a +6.20% improvement over the baseline, while Freelnit scores 75.0 75.06% slightly below the baseline. Similarly, FlowMo leads Quality Score (73.58% vs. Freelnit's 64.22%) and Semantic Score (89.11% vs. FreeInit's 85.91 %). These results underscore that FlowMo provides a more effective and well-rounded improvement to video generation quality compared to the adapted FreeInit modern FM-based DiT architectures.
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B Additional Qualitative Motivation Results
To complement the qualitative observations in the main paper, we present additional visualizations of the latent-space predictions 31,c across timesteps during the generation process. The two figures below show grid of frames from six different time indices (10-20) and representative diffusion steps (0-18), providing spatio-temporal view of how motion emerges over time within the latent space.
Fig. displays predictions for channel O, used in the main paper, while Fig. TO shows results for randomly selected channel (channel 7). In both cases, observe that coarse spatial structure appears in early steps, while coarse motion emerges primarily between steps 4 and 8. Although motion is 10 onward. its coarse features are determined earlier,
refined later steps, seen timesteps making the first timesteps the most crucial for coherent motion generation. These patterns reinforce our interpretation that motion is added into the generation during these intermediate steps, which underpins our focus on this range for motion-aware optimization in FlowMo.
Frame
Frame 12
Frume
Frame 16
Frame 18
Frame 20
I
L6
1.
F-1
12
14
16
1-88
Figure 9; A visualization of channel (selected arbitrarily, and used in the main paper) of the latent prediction at different timesteps of the generation.

---

Frame
Frame 12
Frame
Frame 16
Frame
Frame
AAAAAM
M
1-
F88
1-10
-12
114
Fi
1-8
Figure 10: A visualization of channel (selected randomly) of the latent prediction at different timesteps of the generation.
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C
The Effect of Fo on Patch-Wise Variance
This section demonstrates the alignment between FlowMo's s optimization mechanism and our motivat- ing insights from Sec. 3.2] Fig. [T] plots the maxi- mal patch-wise temporal variance (FlowMo's loss,
Max Patch-wise Variance O²
Without FlowMo
1.3
With FlowMo
1.2
Equation (7) for videos generated with and without FlowMo guidance.
1.1
1.0
We observe that the results demonstrate strong relation with the conclusions from 3.2 First, the application of FlowMo results in a significant reduc- tion and stabilization of this maximal variance, which particularly evident from approximately timestep 5 onward. This observation is consistent with our ear- lier finding (Fig. 2 that the variance characteristics of coherent and incoherent videos begin to diverge this stage.
0.9
15
20 Timestep
25
30
35
40
Figure 11: FlowMo effect on patch-wise variance. We plot the maximal temporal vari- ance of spatial patches for videos with and without applying FlowMo guidance, and ob- serve that our method significantly reduces and stabilizes the variance in the generation steps that impact motion the most by our anal- ysis from Sec. 3.2 95%-confidence inter- val was computed using the seaborn python package.
Second, FlowMo's optimization is applied during the initial 12 timesteps of the generation process. This targeted intervention aligns with our qualitative mo- tivation (Fig. 3). which indicates that coarse motion patterns are predominantly established within these early stages of the generation. As can be observed, applying the optimization at these steps indeed stabi- lizes the maximal variance in all other, non-optimized steps as well.
Consequently, Fig. illlustrate that FlowMo guidance leads to a notable decrease in the maximal patch-wise temporal variance. Videos generated with FlowMo exhibit consistently lower variance, especially within the critical timesteps 5-15, compared to the higher and more fluctuating variance observed in videos generated without FlowMo. This empirically validates that FlowMo operates as intended by reducing the target variance metric during the crucial phases of motion formation.
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D
User Study: Instructions Provided to Participants
As part of the evaluations we performed on our method, conducted a user study, described in
Sec. 4.2 The study was designed to assess human preferences on videos generated with and without FlowMo, using the videoJAM benchmark [3, which focuses on motion coherence.
The study was conducted using Google Forms. For each prompt, participants were shown a pair of videos-one with FlowMo and one without-generaace with the same random seed (1024). The order of the videos was randomized to avoid positional bias. Each pair was evaluated by five different participants, resulting in 640 responses per baseline.
Participants were asked to evaluate the videos based on three criteria: text alignment, aesthetic quality, and motion coherence. The instructions provided annotators reproduced below, followed by screenshot of the interface used:
Hello!
We need your help to read caption, and then watch generated videos. After watching the videos, we want you to answer a few questions about them:
Text alignment: Which video better matches the caption?
Quality: Aesthetically, which video is better?
Motion: Which video has more coherent and physically plausible motion?
(Do note: it is OK if the quality is less impressive as long as the motion looks better.)
User Study: Wan2.1
Hello!
We need your help to read caption, and then watch two generated videos.
After watching the videos, we want you to answer a few questions about them:
alignment:
matches caption?
Quality: Aesthetically, which video better?
Motion: Which video has more coherent and physically plausible motion? Do note, it is OK if the quality less impressive as long as the motion looks better.
Indicates required question
Figure 12: Screenshot of the Google Form used in the user study.
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E VBench Metrics Breakdown
Table VBench evaluation results per dimension. Each column represents model variant, with and without FlowMo. Rows correspond to the 16 VBench evaluation dimensions.
Dimension
Wan2.1-1.3B
CogVideoX-SB
Baseline
+ FlowMo
Baseline
+ FlowMo
Subject Consistency
95.61%
96.54%
95.79%
97.02%
Background Consistency
97.25% %
97.02%
96.53%
97.53%
Temporal Flickering
99.15%
98.93%
99.23%
96.21 %
Motion Smoothness
96.43%
98.56%
95.01%
97.29%
Dynamic Degree
83.21 %
81.96%
65.29%
63.92%
Aesthetic Quality
56.77%
58.03%
55.51%
58.29%
Imaging Quality
61.01%
64.89%
58.91
58.75%
Object Class
91.37%
95.35%
82.72%
88.41 %
Multiple Objects
77.98%
82.27%
60.17%
61.27%
Human Action
98.27% %
97.23%
97.81%
95.69%
Color
87.94% %
87.28%
82.75%
80.82%
Spatial Relationship
75.21%
78.42%
67.89%
67.23%
Scene
49.84%
49.41%
51.55%
54.13%
Appearance Style
20.95%
28.45%
23.53%
30.29%
Temporal Style
26.35%
27.30%
25.04%
31.26%
Overall Consistency
23.65%
25.53%
26.43%
24.28%
Semantic Score
84.70%
89.11%
70.03%
69.26%
Quality Score
65.58%
73.58%
60.83%
72.11%
Final Score
75.14%
81.34% (46.20%)
65.43%
70.69 (45.26%)
In Sec. 42 we reported the aggregated VBench [16] metrics, as well as specific metrics that correspond motion coherence and magnitude. Here, provide the complete breakdown across all 16 individual evaluation dimensions for both Wan2.1 and Cog
Tab. compares the baseline models with their FlowMo-guided counterparts. FlowMo leads to consistent improvements key dimensions, including Subject Consistency, Motion Smoothness, and Object Class, while maintaining or slightly improving aesthetic and perceptual metrics such as Aesthetic Quality, Appearance Style, and Spatial Relationship. Although small decrease is observed in Dynamic Degree, this aligns with our expectation that reducing motion artifacts also reduces spurious motion.
Critically, mentioned in the main text, FlowMo consistently and significantly boosts the overall quality metric (Final Score) by at least 5% across all models. This clear indication of the positive impact our method has on the overall quality of the produced viseos.
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Additional Quantitative Ablation Results
Table 4: Comparison of bascline(WAN2.--1.3B) FlowMo, and ablations across VBench metrics.
FlowMo achieves the best Motion Smoothness and the highest overall Final Score.
Dimension
Mean
W/O Debias
Steps 0-30
Baseline
+FlowMo
Subject Consistency
94.26%
95.02%
83.56%
95.61%
96.5%%
Background Consistency
97.69%
96.72%
92.24%
97.25%
97.02%
Temporal Flickering
99.02%
99.45%
91.82%
99.15% %
98. 98.93%
Motion Smoothness
97.53%
98.01% %
80.42%
96.43%
98.56%
Dynamic Degree
82.99%
82.12%
72.98%
83.21%
81.96%
Aesthetic Quality
53.81
54.65%
43.27%
56.77%
58.03%
Imaging Quality
59.22%
58.72%
49.71%
61.04%
64.89%
Object Class
92.89%
90.74%
74.33%
91.37%
95.34%
Multiple Objects
78.01 %
78.48%
58.92%
77.98%
82.27%
Human Action
98.51%
98.08%
77.89%
98.27%
97.23%
Color
86.23%
86.98%
82.73%
87.94%
87.28%
Spatial Relationship
77.85%
76.36%
72.90%
75.21%
78.42 %
Scene
47.77%
48.62%
40.98%
49,44
49.41 %
Appearance Style
22.03%
21.22%
16.04%
20.95%
28.45%
Temporal Style
27.01%
26.76%
22.58%
26.35%
27.30 %
Overall Consistency
23.81%
24.92%
15.87%
23.65%
25.53%
Semantic Score
82.35%
82.15%
69.27%
84.09%
89.11
Quality Score
66.27% %
67.51% %
3
65.58%
73.58 %
Final Score
74.76%
76.31%
58.17%
75.14%
81.34%
In Sec. 4.4 reported the show qualitative results for our ablation study. Here, we provide the complete breakdown across all 16 individual evaluation dimensions for Wan2.1.
Tab. Lub._shoee shows quantitative comparison of VBench metrics between the WAN2.1-1.3B baseline, Fo, and the following ablations: Mean (i.e., regulating mean patch-wise variance of the debiased latent), W/O Debias (i.e., regulating max patch-wise variance the un-debiased latent), and Steps 0-30 (applying optimization over the first 30 steps, instead of all 50, due to computational and time constraints).
In accordance with the qualitative results presented in the paper (Fig. 7), FlowMo demonstrates the best Motion Smoothness, with roughly 50% more improvement over the best ablation. It also achieves the strongest performance across the three aggregated metrics: +5.86 % on Semantic Score, +6.07% % Quality Score, and +5.03% Final Score compared to the closest ablation. As for Dynamic Degree, applying optimization over 30 steps leads to significant drop, whereas the other ablations, and FoowMo itself, show no meaningful degradation, indicating that motion magnitude is largely preserved.
The quantitative metrics are consistent with our motivation and theoretical justification (see Sec. 3.2 and Appendix E). Replacing the max operation with a mean significantly weakens the effect of the optimization, was also argued theoretically above. Removing the debiasing operator results in a comparable degradation, which aligns with prior observations that text-to-video models tend to prioritize appearance features, which overshadow motion in the loss signal (e.g., ( Lastly, applying the optimization across the first 30 denoising steps leads to clear performance drop. This because the coarse denoising steps primarily determine motion, structure, and overall layout. In later steps, these aspects are already fixed, and the loss, although still valid, can only influence high-frequency details. As result, applying the optimization at later stages tends introduce artifacts rather than improve motion quality. This observation aligns with findings from prior works (e.g.. [47 69)), which similarly emphasize the importance of applying optimization during the early denoising stages.
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G On Choosing to Optimize Maximal Patch-Wiss Variance
We provide both intuitive and theoretical justifications for the choice of the max operator in our optimization.
Intuitive justification. Artifacts are typically a local phenomenon dominated by specific spatiotem- poral locations in which the patch statistics are abnormal (compared the training set). Using the mean operator dilutes the impact of these anomalies, as it is dominated by the majority of patches. In contrast, their presence can be captured by a max operator, making it natural choice to detect and mitigate inconsistencies.
Theoretical justification. The following lemmas justify optimizing the maximum patch-wise variance to keep generated latents in distribution.
Lemma G.I. Noising of real videos keeps patch-wise temporal variance bounded by a dataset- dependent constant C, which bounds patch-wise variance for all patches of all videos in the training data.
Since the model was trained on a finite dataset of real-valued latents, such a constant C' exists. Assuming the dataset consists of natural videos, and since VAEs minimize latent variance, C is likely to be relatively small. Recall that noising a latent of real video 2o to timestep is done by:
St a4 + VT- e e~ (O,
(10)
Thus, the temporal variance of each patch p given by:
(pr: = (1 - ãi) Var(ep);
(11)
and hence the maximum patch-wise variance of all samples during training is bounded.
Lemma G.2. Consider the denoising process starting from pure Gaussian noise. Suppose that in early timesteps (i.e., when is small), each patch of the denoised latent remains approximately Gaussian but with unknown variance due to guidance, decoder mismatch, or score error, i.e., x., NO, of)). with op varying across space. Then, the maximal patch-wise variance is Olo high probability (w.h.p.). where Nj. Nw. and Nn, are the number of frames, width, and height of the latent, respectively.
with
Empirically, this assumption holds in early denoising timesteps: the denoised latent remains approxi- mately Gaussian, and patch-wise variances exhibit spatial variability consistent with the stated form. Intuitively, this holds because at high noise levels, the per-pixel variance distribution is heavy-tailed, so outliers are likely to occur. Formally, given the assumptions above, the temporal variance each patch is distributed x where Ny is the number of latent frames. The maximal patch-wise variance is thus the maximum over such N Nw distributions, which lies in the Gumbel domain and satisfies the property in the lemma.
Hence, as the number of patches N grows, local outliers (i.e., patches with high patch-wise variance) appear with neglligiee probability.
Lemma G.3. A global stability condition for the numerical integration step in the denoising process requires that [Jpl Up S C, where Jp is the Jacobian at patch p. Up its patch-wise variance, and C the Courant number.
Let f(x) denote a linearization of the denoising step. A stability condition for solving the ODE numerically is the CFL condition, which requires every patch p to satisfy [Jp At < C. Otherwise, the numerical process could be unstable or fail to converge. If the CFL condition holds, the local step magnitude satisfies:
(12) leading to the stated global stability condition. If single patch attains a large Up. the product above cross the stability boundary, causing local overshoot that pushes that region off the training manifold.
Arpll R [Jp Up-
Corollary G.4. During training, patch-wise variance is bounded. However, when denoising pure Gaussian noise, high patch-wise variance is likely local phenomenon, which may drive generation out-of-din distrrbbbtt Minimizing the maximum patch-wise wise variance is thus a practical strategy to improve ODE stability and ensure generated latents remain in in-distribution.
30


Reviews:
[{"review_id": "W0gvasA2fT", "reviewer": "Reviewer_gJqQ", "summary": "This paper introduces a training-free inference-time guidance method to improve temporal coherence in text-to-video diffusion models. The key insight is that temporally coherent motion should exhibit low patch-wise variance across frames in the model's latent space.   \nThe paper computes appearance-debiased temporal signals by measuring L1 distances between consecutive latent frames. Then the paper measures the motion coherence by calculating patch-wise variance across the temporal dimension as a proxy. By gradient-based optimization of the input latent during specific denoising timesteps, the maximal patchwise variance is minimized and thus the temporal coherence is improved.   \nThe method is evaluated on Wan2.1-1.3B and CogVideoX-5B models, showing consistent improvements in motion coherence while maintaining visual quality and text alignment.", "questions": "1. Timestep Generalization: How sensitive is the method to the choice of optimization timesteps? Have you explored adaptive timestep selection based on the model's temporal dynamics?\n2. Computational Efficiency: Have you investigated more efficient optimization strategies (e.g., fewer gradient steps, approximate gradients) that could reduce the computational overhead while maintaining effectiveness?", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n\n1. The insight of the paper is valuable. The core insight that temporal coherence correlates with low patch-wise variance in latent space is intuitive and well-supported by both qualitative and quantitative analysis. This finding is well-supported by experiments in the Section3.2. \n2. The proposed method is training-free, making it a practical plug-and-play solution for existing models.\n3. The evaluation is comprehensive. The paper includes thorough experiments with both automatic metrics (VBench) and human evaluations, showing consistent improvements across multiple criteria.\n\n\nWeaknesses\n1. The method would cause a significant 2.39× increase in inference time due to gradient computation and optimization steps. \n2. The choice of maximizing over patch-wise variances (Equation 8) appears somewhat ad-hoc. While ablations show it works better than mean aggregation, the theoretical justification could make the paper stronger.\n3. The selection of timesteps 1-12 for optimization is based on empirical observation rather than principled analysis. Different models or architectures might require different timestep ranges.", "was_revised": true, "final_justification": "Thanks for the author's response. Most of my concerns are resolved and I will maintain my initial score as borderline accept.", "rebuttal": "We thank the reviewer for the thoughtful feedback and for recognizing our core insights, design, and evaluation. \n\n## Runtime speedup\n\nIn response to the reviewer’s feedback, we made small implementation changes that preserve correctness. Specifically, we replaced redundant operations and removed unnecessary computation (e.g., replacing loops over tensors with built-in PyTorch functions). The code changes did not change the results – we verified on all samples from our project’s website that the obtained outputs are bit-exact identical before and after the change. These optimizations led to a x1.29 speedup, reducing the mean runtime from 234.30s to 180.67s. As a result, FlowMo now incurs an overhead of only x1.82 (down from x2.13) relative to the baseline.\n\n## The choice of maximal patch wise variance\n\nWe provide both intuitive and theoretical justifications for the choice of the max operator in our optimization.\n\nIntuitively, artifacts are typically a local phenomenon that is dominated by specific spatiotemporal locations in which the patch statistics are abnormal (compared to what exists in the training set). Using the mean operator dilutes the impact of these anomalies, since it is dominated by the majority of the patches. However, their presence can be captured by a max operator, making it a natural choice to detect and mitigate inconsistencies. \n\nTheoretically, the following lemmas justify optimizing the maximum patch-wise variance to keep generated latents in-distribution.\n\n**Lemma 1**. *Noising of real videos keeps patch-wise temporal variance bounded by $ 1 + V_{\\max} $, where $ V_{\\max} $ is a dataset-dependent constant that bounds patch-wise variance for all patches of all videos in the training data.*\n\nFirst, note that $ V_{\\max} $ exists since the model was trained on a finite dataset of real-valued latents. Furthermore, assuming the dataset consists of natural videos, and since VAEs minimize latent variance, $ V_{\\max} $ is likely to be relatively small.\n\nNow, recall that noising a latent of a real video $ z_0 $ to timestep $ t $ is done by:\n\n$$ z_t = \\sqrt{\\alpha_t} z_0 + \\sqrt{1 - \\alpha_t} \\epsilon \\quad \\text{where } \\epsilon \\sim \\mathcal{N}(0, I) $$\n\nThus, the temporal variance of each patch $ ij $ is given by:\n\n$$ V(z_t[ij]) = \\alpha_t V(z_0[ij]) + (1 - \\alpha_t) = 1 + \\alpha_t (V(z_0[ij]) - 1) \\leq 1 + V_{\\max} $$\n\nHence the maximum patch-wise variance of all samples during training is bounded.\n\n**Lemma 2**. *Consider the denoising process starting from pure Gaussian noise. Suppose that in early timesteps (i.e., when $ \\alpha_t $ is small), each patch of the denoised latent remains approximately Gaussian but with unknown variance due to guidance, decoder mismatch, or score error, i.e., $ z_{k, i, j} \\sim \\mathcal{N}(0, s_{ij}) $, with $ s_{ij} $ varying across space. **Then**, the maximal patch-wise variance is $ \\Omega\\left( \\frac{\\log(W \\cdot H)}{F} \\cdot \\max s_{ij} \\right) $ w.h.p., where $F,W,H$ are the number of frames, width, and height of the latent, respectively.*\n\nWe note that the assumptions in Lemma 2 are empirically satisfied in early denoising timesteps: the denoised latent remains approximately Gaussian, and patch-wise variances exhibit significant spatial variability consistent with the stated form.\n\nIntuitively, the lemma holds because at high noise levels, the per-pixel variance distribution is heavy-tailed, so outliers are likely to occur. Formally, given the assumptions in the lemma, the temporal variance of each patch is distributed $ V(z_t[ij]) \\sim \\frac{s_{ij}}{F - 1} \\cdot \\chi_{F - 1}^2 $, where $ F $ is the number of latent frames. The maximal patch-wise variance is thus the maximum over such $ \\chi^2 $ distributions, which lies in the Gumble domain and is known to satisfy the property in the lemma. \n\nHence, as the number of patches $ W \\cdot H $ grows, local outliers (i.e., patches with high patch-wise variance) appear with non-negligible probability.\n\n**Lemma 3**. *A global stability condition for the numerical integration step in the denoising process requires that $ \\eta_t \\Vert J_{\\max} \\Vert \\sqrt{(F-1) s_{\\max}} \\leq C $, where $J_{ij}=\\frac{\\partial \\epsilon_\\theta}{\\partial Z_{ij}}$ is the Jacobian at patch $ij$, $s_{ij} $ is its patch-wise variance, and $C$ is the Courant number.*\n\nLet $ z_{t-h} \\approx z_t - \\eta_t JZ $ be a linearization of the denoising step.\n\nA stability condition for solving the ODE numerically is the CFL condition, which requires every patch $ij$ to satisfy $\\eta_t \\Vert J_{ij} \\Vert \\leq C $. Otherwise, the numerical process could be expensive and not converge. If the CFL condition holds, the local step magnitude satisfies:\n\n$$ \\Vert z_{t-h}[ij] - z_t[ij] \\Vert \\leq \\eta_t \\Vert J_{ij} \\Vert \\Vert z_{ij} - \\bar{z}_{ij} \\Vert $$\n\n$$ = \\eta_t  \\Vert J_{ij}  \\Vert \\sqrt{(f-1) s_{ij}} $$\n\nTherefore, a global stability condition is as mentioned in the lemma. If a single patch attains a large $ s_{ij} $, the product above can cross the stability boundary, causing a local overshoot that pushes that region off the training manifold.\n\n**Corollary**. In training, patch-wise variance is bounded. However, when denoising pure Gaussian noise, high patch-wise variance is a likely local phenomenon, which may drive generation out-of-distribution. Minimizing the maximum patch-wise variance is thus a practical strategy to improve ODE stability and ensure generated latents $ z_t $ remain in-distribution.\n\n## Selection of timestamps 1-12\n\nWe justify the selection of timesteps 1-12 on both empirical and theoretical grounds.\n\nWe break down the question into two: why we started optimizing from the first timestep, and why we stopped after 12. First, notice that Lemma 2 above shows that large patch-wise variance, a precursor to temporal incoherence, can arise as soon as the latent remains close to Gaussian—i.e., from the very first timestep—so optimization should start as early as the first step. \n\nAs to why we stopped after 12 steps, section 3.2 shows, qualitatively and quantitatively, that coarse structure and global motion are set within the first dozen denoising steps. Figure 3 further indicates that these high-noise, “coarse” steps largely determine overall motion, making them optimal to apply FlowMo. This mirrors findings in image-based works (e.g., [1], [3]) which likewise identify early steps as critical for establishing coarse features. Furthermore, the same 1-12 range improves motion coherence on two very different models—Wan2.1 and CogVideoX (Secs. 4.1 – 4.2)—demonstrating robustness across architectures and datasets. \n\n## Adaptive timestep selection\n\nThank you for this valuable suggestion. First, we note that the use of a fixed intervention range is the standard practice in all other inference-time techniques we are aware of (e.g., [1], [2]). Nonetheless, adaptive selection is a promising direction for improving both runtime and output quality. In response to the review, we implemented a simple adaptive intervention strategy: if the maximum variance at a given step fell below 60 times the mean variance, we stopped the intervention early. The threshold of 60 was chosen based on the typical ratio observed at step 12 after a full 12-step intervention. This adaptive approach led to early stopping in most cases—typically between steps 8 and 10—and reduced average runtime by 20%. While performance metrics were slightly lower than in the fixed 12-step setup, we believe this initial result shows promise, and expect that more refined adaptive strategies could yield better results with relatively little effort.\n\n| Dimension | Baseline | + FlowMo | Adaptive timesteps |\n|---|---|---|---|\n| Motion Smoothness| 96.43% | **98.56%** | 97.25% |\n| Dynamic Degree | **83.21%**  | 81.96% | 82.04%  |\n| Semantic Score | 84.70% | **89.11%** | 86.12% |\n| Quality Score | 65.58% | **73.58%** | 70.11% |\n| Final Score | 75.14% | **81.34%** | 78.11% |\n\nAdditionally, initial experiments on a subset of the data suggest that interventions applied between 8 and 15 frames result in metric values within 1% of those from the fixed setup—substantially better than the 30-frame setting (see ablations in our response to reviewer MYjg or the no-intervention baseline).\n\n## Efficient optimization strategies (e.g., fewer gradient steps, approximate gradients)\n\nFollowing the review, we implemented approximate gradients (finite differences and random directional derivatives), but found that these lead to a substantial drop in video quality. Developing more efficient optimization techniques without compromising quality could be an interesting direction for future work.\n\nRegarding the number of gradient steps: please note that FlowMo uses a single gradient step (L192–200). \n\nRegarding implementation efficiency, please see above.\n\n---\n\nWe would be happy to engage further and clarify any additional questions.\n\n\n**References**\n\n[1] Attend-and-Excite: Attention-Based Semantic Guidance for Text-to-Image Diffusion Models\n\n[2] FreeInit: Bridging Initialization Gap in Video Diffusion Models\n\n[3] Image Generation from Contextually-Contradictory Prompts"}, {"review_id": "Jom1vkfb6d", "reviewer": "Reviewer_MYjg", "summary": "This paper aims to enhance motion coherence of text-to-video diffusion models in a training-free way. Text-to-video diffusion models often struggle to accurately capture temporal dynamics like motion and interactions. Existing solutions require retraining or external signals to improve temporal consistency, which can be resource-intensive and complex. FlowMo introduces a training-free guidance approach that leverages the model’s own predictions at each diffusion step to extract appearance-debiased temporal representations and dynamically guide the model to enhance motion coherence by reducing temporal variance. Comprehensive experiments on various text-to-video models show that FlowMo effectively boosts motion coherence without compromising visual quality or prompt alignment, providing an easy-to-integrate improvement for existing models.", "questions": "Suggestions:\n1. Discuss the cost-effectiveness of FlowMo and its proper applications.\n2. Compare FreeInit quantitatively and qualitatively in the main text. And it would be better if more training-free works could be taken into comparison.\n3. Add quantitative ablation results to make the paper claims solid.\n4. Conduct a careful writing check.", "limitations": "Yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. The quantitative and qualitative motivation analyses are interesting and convincing. The demos in webpage make it clear for readers to understand how the proposed method works.\n2. The proposed method is simple and easy to be implemented. The training-free design allows readers to validate the effectiveness of this method easily and inexpensively on their own tasks.\n3. The writing is easy to understand.\n\nWeaknesses\n1. Computation time is increased by x2.39 when using FlowMo, which will undermine the cost-effectiveness of the method in practical applications.\n2. The quantitative and qualitative comparisons with FreeInit should be conduct and displayed in the main text, since it is similar and related to this paper. Instead, this paper majorly compares FreeInit in appendix, which is not very clear for readers.\n3. The ablation study chapter is not very clear and precise, since there are no quantitative ablation results.\n4. There are some confusing statements. For instance, in terms of the line.3 of Algorithm.1, the first term of the right equation is written as conditioned on P, which is inconsistent with the definition of the CFG formula.", "was_revised": true, "final_justification": "Most of my concerns are addressed in the author's rebuttal except the runtime problem. I appreciate the authors' efforts to speed up the algorithm to fit it in real-world applications, but 1.82x runtime is still hard to be ignored, especially for a method which is claimed to be training-free. \nGiven the novelties and practical impacts of this work, I would keep my initial score for this work.", "rebuttal": "We thank the reviewer for the encouraging feedback and are glad they found the motivation analysis convincing, the method simple and accessible, and the writing clear.\n\n## Runtime speedup\n\nIn response to the reviewer’s feedback, we made small implementation changes that preserve correctness. Specifically, we replaced redundant operations and removed unnecessary computation (e.g., replacing loops over tensors with built-in PyTorch functions). The code changes did not change the results – we verified on all samples from our project’s website that the obtained outputs are bit-exact identical before and after the change. These optimizations led to a x1.29 speedup, reducing the mean runtime from 234.30s to 180.67s. As a result, FlowMo now incurs an overhead of only x1.82 (down from x2.13) relative to the baseline.\n\n## Moving FreeInit to the main text.\n\nThank you. Following your suggestion, we will move both the quantitative and qualitative comparisons of FreeInit from the appendix into the main text. \n\n## Additional quantitative ablation results.\n\nThe table below shows a quantitative comparison of VBench metrics between the WAN2.1-1.3B baseline, FlowMo, and the following ablations: Mean (i.e., regulating mean patch-wise variance of the debiased latent, as opposed to max), W/O Debias (i.e., regulating max patch-wise variance of the un-debiased latent), and steps 0-30 (applying optimization over the first 30 steps, instead of all 50, due to computational and time constraints). \n\nIn accordance with the qualitative results presented in the paper (Fig. 6), FlowMo demonstrates the best Motion Smoothness, with roughly 50% more improvement over the best ablation. It also achieves the strongest performance across the three aggregated metrics: +5.86% on Semantic Score, +6.07% on Quality Score, and +5.03% on Final Score compared to the closest ablation. As for Dynamic Degree, applying optimization over 30 steps leads to a significant drop, whereas the other ablations—and FlowMo itself—show no meaningful degradation, indicating that motion magnitude is largely preserved.\n\nThe quantitative metrics are consistent with our motivation and theoretical justification. First, replacing the maximum operation with a mean significantly weakens the effect of the optimization, as was also argued theoretically above. Removing the debiasing operator results in a comparable degradation, which aligns with prior observations that text-to-video models tend to prioritize appearance features, which can overshadow motion in the loss signal (e.g., [4]). Lastly, applying the optimization across the first 30 denoising steps leads to a clear performance drop. This is because the coarse denoising steps primarily determine motion, structure, and overall layout. In later steps, these aspects are already fixed, and the loss, although still valid, can only influence high-frequency details. As a result, applying the optimization at later stages tends to introduce artifacts rather than improve motion quality. This observation aligns with findings from prior works (e.g., [1], [3]), which similarly emphasize the importance of applying optimization during the early denoising stages. \n\n| Dimension             | Mean   | W/O Debias | Steps 0-30 | Baseline | + FlowMo |\n|----------------------|--------|------------|-----------|----------|----------|\n| Subject Consistency  | 94.26% | 95.02%     | 83.56%    | 95.61%   | **96.54%**   |\n| Background Consistency | **97.69%** | 96.72%     | 92.24%    | 97.25%   | 97.02%   |\n| Temporal Flickering  | 99.02% | 99.45%     | 91.82%    | **99.15%**   | 98.93%   |\n| Motion Smoothness    | 97.53% | 98.01%     | 80.42%    | 96.43%   | **98.56%**   |\n| Dynamic Degree       | 82.99% | 82.12%     | 72.98%    | **83.21%**   | 81.96%   |\n| Aesthetic Quality    | 53.81% | 54.65%     | 43.27%    | 56.77%   | **58.03%**   |\n| Imaging Quality      | 59.22% | 58.72%     | 49.71%    | 61.01%   | **64.89%**   |\n| Object Class         | 92.89% | 90.97%     | 74.33%    | 91.37%   | **95.35%**   |\n| Multiple Objects     | 78.01% | 78.48%     | 58.92%    | 77.98%   | **82.27%**   |\n| Human Action         | 98.51% | 98.08%     | 77.89%    | 98.27%   | **97.23%**   |\n| Color                | 86.23% | 86.98%     | 82.73%    | **87.94%**   | 87.28%   |\n| Spatial Relationship | 77.85% | 76.36%     | 72.09%    | 75.21%   | **78.42%**   |\n| Scene                | 47.77% | 48.62%     | 40.98%    | **49.84%**   | 49.41%   |\n| Appearance Style     | 22.03% | 21.22%     | 16.04%    | 20.95%   | **28.45%**   |\n| Temporal Style       | 27.01% | 26.76%     | 22.58%    | 26.35%   | **27.30%**   |\n| Overall Consistency  | 23.81% | 24.92%     | 15.87%    | 23.65%   | **25.53%**   |\n| **Semantic Score**   | 83.25% | 85.12%     | 62.97%    | 84.70%   | **89.11%**   |\n| **Quality Score**    | 66.27% | 67.51%     | 53.37%    | 65.58%   | **73.58%**   |\n| **Final Score**      | 74.76% | 76.31%     | 58.17%    | 75.14%   | **81.34%**   |\n\n## Inconsistency with CFG Definition.\n\nThank you for pointing this out. We will revise line 3 In Algorithm 1 to match the correct CFG structure:\n$ u_{\\theta, t_i} \\gets u_{\\theta, t_i \\mid \\emptyset} + \\rho \\cdot (u_{\\theta, t_i \\mid P} - u_{\\theta, t_i \\mid \\emptyset} ) $\n\n## Cost-effectiveness of FlowMo and its proper applications.\n\nFlowMo is designed to be cost-effective: it requires no additional training and introduces only a modest runtime overhead (which is now x1.82) during inference. This makes it practical for applications where motion quality is critical, such as content creation or video refinement, while preserving efficiency.\n\n## Additional training-free baselines \n\nIn addition to the training-free methods that we have included in our study, the only relevant method that we could not include is VideoGuide. This is due to the incompatible architecture, since this method was developed for a U-net based architecture and is not easily adaptable (see lines 96-103). \n\nWe are happy to conduct further comparisons upon request.\n\n## Conduct a careful writing check.\n\nWe will conduct a thorough review of the writing to improve clarity and resolve any ambiguities in the final version of the paper.\n\n---\n\nWe sincerely thank you for your insights and feedback. We would be glad to answer any follow-up questions and continue the discussion.\n\n\n**References**\n\n[1] Attend-and-Excite: Attention-Based Semantic Guidance for Text-to-Image Diffusion Models\n\n[2] FreeInit: Bridging Initialization Gap in Video Diffusion Models\n\n[3] Image Generation from Contextually-Contradictory Prompts\n\n[4] VideoJAM: Joint Appearance-Motion Representations for Enhanced Motion Generation in Video Models"}, {"review_id": "YxkA8bPhYy", "reviewer": "Reviewer_mc6Y", "summary": "The paper focuses on enhancing the temporal coherence of text-to-video diffusion models. The authors introduce FlowMo, a novel training-free guidance method that aims to improve motion coherence without additional training or external inputs. The main contributions include the Appearance-Debiased Temporal Representation to measure the distances between consecutive frame latents, and Motion Coherence Estimation to guide the model towards reducing temporal inconsistencies during sampling. Experiments conducted on VBench and VideoJAM-bench show reasonable improvements over the baselines without FlowMo.", "questions": "1. The questions in weaknesses part.\n2. How well does FlowMo perform on models with different architectures or on tasks requiring more nuanced temporal reasoning?\n3. Could external factors, such as the quality or specificity of the input text, affect the performance of FlowMo in generating temporally coherent videos?", "limitations": "yes", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 1, "originality": 2, "strengths_and_weaknesses": "Strengths:\n+ Tested across various models like Wan2.1-1.3B and CogVideoX-5B to showcase the method's generalizability.\n+ The method does not require retraining or external conditioning signals, making it a versatile solution for improving existing models.\n+ The paper is mostly clear and easy to follow.\n\nWeaknesses:\n- The technical contribution is limited. As a training-free method, the main idea of FlowMo is to improve the temporal consistency by explicitly reducing the difference between consecutive frames. In this way, this method is more like a trade-off between temporal consistency and dynamic degree. It is evidenced by the degraded Dynamic Degree metric of FlowMo on VBench. Therefore, the technical contribution of this paper is limited.\n- The ablation study is needed. The proposed FlowMo is a manually designed rule to refine diffusion model prediction. There are many manually-determined designs in FlowMo including the refinement steps, the calculation of patch-wise variance  and FlowMo loss. The ablation study of how these designs influence the performances should be included.\n- The officially reported total score of Wan2.1-1.3B on VBench is 84.26%. However, in this paper, the performance of Wan2.1-1.3B is improved from 75.14% (without FlowMo) to 81.34% (with FlowMo). I speculate that this large gap may be caused by different inference settings (e.g., output resolution, prompt refinement). Since the performance of Wan2.1-1.3B baseline is much lower the official version, the conclusion in this paper is not convincing enough.\n- The results might be influenced by external factors such as the complexity of the input text prompts or the diversity of the generated content. For the prompt that requires large motion or complex transition, the continuous constrain may affect the results.\n- The longer inference time than baseline may limit the application of FlowMo on larger model.", "was_revised": true, "final_justification": "Thank you for your response. Some of my concerns have been well-addressed, particularly regarding the dynamic degree and ablation studies, which will lead me to consider increasing my rating.\nFurthermore, I still highly recommend conducting experiments with a higher-performing implementation of the WAN baseline. The significant performance gap between the officially-released performance and the performance measured in this paper could weaken the paper's contribution.\nFinally, regarding the authors' statement in their response, \"our experiments were carefully designed to cover all types of motion,\" I find this claim to be too absolute and suggest toning down the description in this regard.", "rebuttal": "We thank the reviewer for highlighting the method’s generalizability across models and its versatility as a training-free, plug-and-play refinement.\n\n## Trade-off between temporal consistency and dynamic degree\n\nPlease note that this is addressed directly in both the motivational experiments and the main results of the paper, showing that FlowMo improves temporal coherence without meaningfully compromising motion dynamics.\n 1. In our motivation (Sec. 3.2, L. 144–152), we specifically analyze high-motion videos and find that patch-wise variance correlates with coherence even when motion is high, indicating our loss targets coherence, not reduced dynamics.\n 2. In our main results (Sec. 4.2, App. A.2, Table 2), we show that FlowMo reduces Dynamic Degree by less than 1.5% across both models, a negligible drop given the overwhelming benefit to the overall Quality Score (Wan2.1: +8.0%, CogVideoX: +11.25%). In contrast, FlowMo’s closest baseline, FreeInit, causes a 16.2% drop in Dynamic Degree (see L. 568-574, Appendix A). This is a further indication that our method does not incur a significant drop in dynamic degree, even compared to its closest baselines.\n 3. Finally, note that Dynamic Degree reflects motion *magnitude*, not *coherence*; for instance, completely incoherent motion (e.g. flickering) can inflate Dynamic Degree scores. Thus, slight reductions in this score are expected when coherence improves.\n\nTherefore, rather than exploiting a trade-off between the two measures, FlowMo improves coherence without compromising dynamic degree. \n\nTo provide a clear overview, we briefly summarize the core contributions of our work:\n - We present a systematic analysis of motion in video diffusion models (Sec. 3.2), revealing that motion often emerges in later denoising steps, distinct from appearance features. We justify our insights both quantitatively and qualitatively. We further show that patch-wise variance is a strong predictor of temporal coherence, even in high-motion videos (Fig. 2, L. 144-154).\n - We propose FlowMo, a training-free, inference-time method that significantly improves temporal coherence *with minimal impact on motion dynamics*. It is lightweight, plug-and-play, and requires no retraining.\n - We demonstrate strong cross-model generalization across Wan2.1 and CogVideoX (which differ in architecture, training data, and base performance) highlighting the robustness and broad applicability of our approach.\n\n## Justification of design choices.\n\nDue to the character limit, we are unable to include the full response here. We kindly refer the reviewer to our response to Reviewer gJqQ, where we provide a theoretical justification for using the maximum operator in FlowMo’s loss. That response also includes both empirical and theoretical justifications for the choice of the 1–12 timestep range.\n\nFurthermore, the table below shows a quantitative comparison of VBench metrics between the WAN2.1-1.3B baseline, FlowMo, and the following ablations: Mean (i.e., regulating mean patch-wise variance of the debiased latent, as opposed to max), W/O Debias (i.e., regulating max patch-wise variance of the un-debiased latent), and Steps 0-30 (applying optimization over the first 30 steps, instead of all 50, due to computational and time constraints). \n\nIn accordance with the qualitative results presented in the paper (Fig. 6), FlowMo demonstrates the best Motion Smoothness, with roughly 50% more improvement over the best ablation. It also achieves the strongest performance across the three aggregated metrics: +5.86% on Semantic Score, +6.07% on Quality Score, and +5.03% on Final Score compared to the closest ablation. As for Dynamic Degree, applying optimization over 30 steps leads to a significant drop, whereas the other ablations—and FlowMo itself—show no meaningful degradation, indicating that motion magnitude is largely preserved.\n\nThe quantitative metrics are consistent with our motivation and theoretical justification. First, replacing the maximum operation with a mean significantly weakens the effect of the optimization, as was also argued theoretically above. Removing the debiasing operator results in a comparable degradation, which aligns with prior observations that text-to-video models tend to prioritize appearance features, which can overshadow motion in the loss signal (e.g., [2]). Lastly, applying the optimization across the first 30 denoising steps leads to a clear performance drop. This is because the coarse denoising steps primarily determine motion, structure, and overall layout. In later steps, these aspects are already fixed, and the loss, although still valid, can only influence high-frequency details. As a result, applying the optimization at later stages tends to introduce artifacts rather than improve motion quality. This observation aligns with findings from prior works (e.g., [1], [3]), which similarly emphasize the importance of applying optimization during the early denoising stages. \n\n| Dimension             | Mean   | W/O Debias | Steps 0-30 | Baseline | + FlowMo |\n|----------------------|--------|------------|-----------|----------|----------|\n| Subject Consistency  | 94.26% | 95.02%     | 83.56%    | 95.61%   | **96.54%**   |\n| Background Consistency | **97.69%** | 96.72%     | 92.24%    | 97.25%   | 97.02%   |\n| Temporal Flickering  | 99.02% | 99.45%     | 91.82%    | **99.15%**   | 98.93%   |\n| Motion Smoothness    | 97.53% | 98.01%     | 80.42%    | 96.43%   | **98.56%**   |\n| Dynamic Degree       | 82.99% | 82.12%     | 72.98%    | **83.21%**   | 81.96%   |\n| Aesthetic Quality    | 53.81% | 54.65%     | 43.27%    | 56.77%   | **58.03%**   |\n| Imaging Quality      | 59.22% | 58.72%     | 49.71%    | 61.01%   | **64.89%**   |\n| Object Class         | 92.89% | 90.97%     | 74.33%    | 91.37%   | **95.35%**   |\n| Multiple Objects     | 78.01% | 78.48%     | 58.92%    | 77.98%   | **82.27%**   |\n| Human Action         | 98.51% | 98.08%     | 77.89%    | 98.27%   | **97.23%**   |\n| Color                | 86.23% | 86.98%     | 82.73%    | **87.94%**   | 87.28%   |\n| Spatial Relationship | 77.85% | 76.36%     | 72.09%    | 75.21%   | **78.42%**   |\n| Scene                | 47.77% | 48.62%     | 40.98%    | **49.84%**   | 49.41%   |\n| Appearance Style     | 22.03% | 21.22%     | 16.04%    | 20.95%   | **28.45%**   |\n| Temporal Style       | 27.01% | 26.76%     | 22.58%    | 26.35%   | **27.30%**   |\n| Overall Consistency  | 23.81% | 24.92%     | 15.87%    | 23.65%   | **25.53%**   |\n| **Semantic Score**   | 83.25% | 85.12%     | 62.97%    | 84.70%   | **89.11%**   |\n| **Quality Score**    | 66.27% | 67.51%     | 53.37%    | 65.58%   | **73.58%**   |\n| **Final Score**      | 74.76% | 76.31%     | 58.17%    | 75.14%   | **81.34%**   |\n\n## VBench results on Wan2.1\n\nWhile the official VBench score for Wan2.1-1.3B is reported as 84.26%, the exact inference settings (e.g., resolution, prompt formulation) used to obtain that result have not been publicly detailed. We suspect the performance gap is due to our use of 480p resolution, which is lower than the model’s maximum supported resolution (720p, as stated on the official website). Due to computational limitations, we were unable to run our experiments at the higher resolution. Please note that all our experiments were conducted using the publicly released code and checkpoints, and we followed the default configurations as provided in both the Wan2.1 and VBench repositories. Our goal was to ensure consistency and reproducibility, and under these conditions, FlowMo demonstrates clear and meaningful improvements.\n\n## Influence by external factors.\n\nWe would like to kindly emphasize that our experiments were carefully designed to cover all types of motion, with various complexities, prompts, and settings. Firstly, the VBench dataset includes a wide variety of prompts, ranging from simple to complex, and from static scenes to high-motion scenarios. Secondly, we enclose studies conducted on VideoJAM-bench [2] (Fig. 5,8, L. 247-253), which was carefully and specifically designed to examine motion, and includes highly complex motion types such as gymnastics, physics, rotations, etc. Across these diverse and comprehensive benchmarks, FlowMo consistently shows strong performance and improved temporal coherence, further supporting its robustness to prompt complexity and motion diversity while improving temporal consistency.\n\n## Runtime speedup\n\nIn response to the reviewer’s feedback, we made small implementation changes that preserve correctness. Specifically, we replaced redundant operations and removed unnecessary computation (e.g., replacing loops over tensors with built-in PyTorch functions). The code changes did not change the results – we verified on all samples from our project’s website that the obtained outputs are bit-exact identical before and after the change. These optimizations led to a x1.29 speedup, reducing the mean runtime from 234.30s to 180.67s. As a result, FlowMo now incurs an overhead of only x1.82 (down from x2.13) relative to the baseline.\n\n---\n\nThank you once again for your helpful observations and careful review. We would be pleased to further clarify any remaining points or engage in additional discussion.\n\n\n**References**\n\n[1] Attend-and-Excite: Attention-Based Semantic Guidance for Text-to-Image Diffusion Models\n\n[2] VideoJAM: Joint Appearance-Motion Representations for Enhanced Motion Generation in Video Models\n\n[3] Image Generation from Contextually-Contradictory Prompts"}, {"review_id": "sOL7gqRBcI", "reviewer": "Reviewer_tGek", "summary": "This paper presents a training free method for producing coherent videos from a pretrained video generation flow matching model. The idea is to introduce a refinement optimization when sampling the denoising steps that encourages more coherent frame to frame motions.", "questions": "The overall idea of the work is simple and nice. But the core idea of adding a refinement optimization based on frame to frame variance in patches seems like it should be tested not just at inference time, but also in the context of training. I would enourage the authors to include in the rebuttal some results for incorporating it into training. How good are the resulting videos in terms of coherence? What is the inference runtime in this setting?", "limitations": "Yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths: \n\n* Training-free\n* The paper does a nice job of showing why a patch-based variance reduction approach can be an effective refinement strategy. I appeciate the experiment described in Section 3.2.\n\nWeaknesses:\n\n* The refinement optimization introduces a 2.39x increase in runtime to perform the gradient descent step. This is very briefly mentioned in the limitations section of the paper. I think this needs to be brought up as part of the results and evaluation. The authors mention that this optimization could also be made more efficient by incorporating it into training. I think the work would be stronger if it showed how adding it to training improves results.", "was_revised": true, "final_justification": "Based on the strengths outlined above and the rebuttal I recommend acceptance.", "rebuttal": "We thank the reviewer for their recognition of the training-free design and the effectiveness of our patch-based variance reduction approach.\n\n## Runtime speedup\n\nIn response to the reviewer’s feedback, we made small implementation changes that preserve correctness. Specifically, we replaced redundant operations and removed unnecessary computation (e.g., replacing loops over tensors with built-in PyTorch functions). The code changes did not change the results – we verified on all samples from our project’s website that the obtained outputs are bit-exact identical before and after the change. These optimizations to a x1.29 speedup, reducing the mean runtime from 234.30 seconds to 180.67 seconds. FlowMo now incurs an overhead of only x1.82 (down from x2.39) compared to baseline.\n\n## Adding FlowMo during training.\n\nThank you for the insightful suggestion. First, we note that integrating our refinement into training is a promising direction for future research, since prior works like [1] show that inference-time objectives (e.g., [2]) can be effectively adapted into training, and obtain similar gains. Since FlowMo is similar in spirit to these image-based inference-time optimizations, we believe it will yield similar benefits when applied to pretraining or fine tuning.  \nHowever, attempting this is infeasible under the limits of our current computational resources; we only have access to two H100 GPUs, and backpropagating through larger batches with latent gradients would be significantly more demanding than our inference-time setup.\n\nWe appreciate your time and constructive feedback. We would be happy to address any further questions or concerns you may have during the discussion period.\n\n\n[1] Separate-and-Enhance: Compositional Finetuning for Text2Image Diffusion Models\n\n[2] Attend-and-Excite: Attention-Based Semantic Guidance for Text-to-Image Diffusion Models"}]

Author rebuttal:

Meta-review: This paper introduces a practical, training-free method for improving temporal coherence in video diffusion models. The core idea of minimizing patch-wise variance is well-motivated, theoretically grounded, and validated across multiple datasets and models. The reviewers appreciated the clarity, systematic analysis, and cross-model generalization.

The main weakness is runtime overhead. While the authors reduced it from 2.39× to 1.82× (and to 1.58× with adaptive stopping), some reviewers (notably MYjg) still find this overhead problematic for real-world applications. Reviewer mc6Y expressed concerns about the potential reduction of dynamic degree. He/she also noted a baseline discrepancy with official Wan2.1 performance. The authors attributed this to resolution limitations in the released model. Concerns about ablations and theoretical justification were largely resolved during rebuttal.

Reviewer tGek recommended acceptance after rebuttal. Reviewer mc6Y recommended borderline accept as the concerns about dynamic degree is resolved, but emphasized that the authors should compare with higher-performing implementation of the WAN baseline. gJqQ and MYjg both maintained borderline accept due to runtime overhead, though they acknowledged that the authors addressed most other concerns. 

Overall, the paper is seen as a technically solid, practical contribution, albeit with some remaining efficiency and evaluation concerns. The runtime concern, while valid, the AC believes that it is sufficiently mitigated, and the work will be of interest to the video generation community.
Decision: Accept (poster)