Physics-Driven Spatiotemporal Modeling for AI-Generated Video Detection
Authors: Shuhai Zhang
ZiHao Lian
Jiahao Yang
Daiyuan Li
Guoxuan Pang
Feng Liu
Bo Han
Shutao Li
Mingkui Tan
Venue: NeurIPS 2025 spotlight ()
Keywords: AI-Generated Video Detection;  Diffusion Models; Maximum Mean Discrepancy
Primary area: deep_learning

Abstract: AI-generated videos have achieved near-perfect visual realism (e.g., Sora), urgently necessitating reliable detection mechanisms. However, detecting such videos faces significant challenges in modeling high-dimensional spatiotemporal dynamics and identifying subtle anomalies that violate physical laws. In this paper, we propose a physics-driven AI-generated video detection paradigm based on probability flow conservation principles. Specifically, we propose a statistic called Normalized Spatiotemporal Gradient (NSG), which quantifies the ratio of spatial probability gradients to temporal density changes, explicitly capturing deviations from natural video dynamics. Leveraging pre-trained diffusion models, we develop an NSG estimator through spatial gradients approximation and motion-aware temporal modeling without complex motion decomposition while preserving physical constraints. Building on this, we propose an NSG-based video detection method (NSG-VD) that computes the Maximum Mean Discrepancy (MMD) between NSG features of the test and real videos as a detection metric. Last, we derive an upper bound of NSG feature distances between real and generated videos, proving that generated videos exhibit amplified discrepancies due to distributional shifts. Extensive experiments confirm that NSG-VD outperforms state-of-the-art baselines by 16.00\% in Recall and 10.75\% in F1-Score,  validating the superior performance of NSG-VD. The source code is available at \url{https://github.com/ZSHsh98/NSG-VD}.

Physics-Driven Spatiotemporal Modeling for AI-Generated Video Detection
Shuhai Zhang' Zihao Lian's
Jiahao Yang Daiyuan Li' Guoxuan Pang"
Feng Liu'
Bo Han? Shutao Li
Mingkui Tan
South China University of Technology. UUniversity of Science and Technology of China
Key Laboratory of Big Data and Intelligent Robot, Ministry of Education, "Pazhou Lab University of Melbourne, Hunan University, 'Hong Kong Baptist University
Abstract
Al-generated videos have achieved near- car--eefect visual realism (e.g.. Sora), urgently necessitating reliable detection mechanisms. However, detecting such videos faces significant challenges modeling high-dimensional spatiotemporal dynamics and identifying subtle anomalies that violate physical laws. In this paper, we propose physics-driven Al-generated video detection paradigm based on probability flow conservation principles. Specifically,
propose statistic called Normalized Spatiotemporal Gradient (NSG), which quantifies the ratio of spatial probability gradients to temporal density changes, explicitly capturing deviations from natural video dynamics. Leveraging pre-trained diffusion models, we develop an NSG estimator through spatial gradients approximation and motion-aware temporal mod- eling without complex motion decomposition while preserving physical constraints. Building on this, propose NSG-based video detection method (NSG- VD) that computes the Maximum Mean Discrepancy (MMD) between NSG features of the test and real videos detection metric. Last, we derive upper bound of NSG feature distances between real and generated videos, proving that generated videos exhibit amplified discrepancies due to distributional shifts. Extensive exper- iments confirm that NSG- VD outperforms statc-of-the-e baselines by 16.00% in Recall and 75% in FI-Score, validating the superior performance of NSG-VD. The source code is available at https:/ httpp:////tttiee /ggthub.. com http://SSHhh/GGG--AA
Introduction
The rapid advancement of generative models [1, 5, 6], particularly diffusion-based frameworks (e.g., Sora [3]), has achieved unprecedented capabilities in synthesizing photorealistic video content. While these breakthroughs enable transformative applications in content creation for creative indus- tries [7, 8, 9, 10], they simultaneously pose critical societal risks through malicious manipulation (e.g., deepfake disinformation [11, 12, 13. 14. 15, 16, 17], synthetic media fraud [7, 18]). As Al-generated videos become increasingly realistic in both spatial and temporal domains, developing effective video detection methods becomes critically urgent for preserving societal trust digital media.
fundamental challenge for Al-generated video detection lies modeling the spatiotemporal dynamics of video evolution. Intuitively, natural videos inherently obey physical laws like motion co- herence and texture continuity [19, 20). while Al-generated videos often exhibit subtle yet systematic inconsistencies in spatiotemporal coherence [21]. This observation raises a crucial question:
How can we model intrinsic spatiotemporal dynamics of natural videos to expose synthetic anomalies?
Equual contribution. Email: shuhaizhangshz.e @ gmail.com, lianzihaolzh@ @gmail.commmmmmmmmm Corresponding author. Email: mingkuitan @ sesuteedu.cc shutao Lintato__@@aaa hnu.edu.cn
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Probability p O
Velocity
Appcarance
4
Motion
Video Frumes
Video Frames
(Appearance, Motion)
Real
Op(x.
+ (x=(px)))=x(x0))) 0)
Fake
(a) Traditional Spatiotemporal Modeling
(b) Physics- Drivvn Spatiotemporal Modeling (Ours)
Figure I: Comparisons of traditional and physics-driven paradigms for spatiotemporal modeling in AI -eggerrrte video detection. (a) Traditional methods [22, 23, 24] often rely on specific artifacts
like appearance consistency and optical flow- base motion modeling, struggling with highly realistic content yet physically implausible (e.g., Sora). (b) Our physics-driven approach explicitly models video dynamics via physics conservation laws, effectively identifying violations of physical laws.
Two critical difficulties arise: 1) Video content inherently contains complex spatial domain correla- tions (e.g., texture structure) and temporal domain dependencies (e.g., motion trajectories), requiring modeling frameworks that jointly capture both spatial structures and temporal dynamics characteris- ties. 2) Al-generated videos are rapidly approaching the perceptual quality of natural videos, with discrepancies that may become vanishingly subtle in both visual appearance and temporal evolution.
Existing Al-generated video detection methods primarily rely on local feature inconsistencies (e.g., optical flow-based motion modeling [22], appearance consistency modeling [23]) or supervised learning with large-scale datasets [25, 24, 26, 27J. However, they often ignore physics-driven constraints governing spatiotemporal evolution inherent natural videos. This limitation exhibits inherent vulnerabilities when confronting synthetic anomalies that violate physical laws, e.g., non- physical motion patterns in Sora- geraeeeeertte videos [3] (Figure 1-a), leading to inferior performance.
In this paper, we propose physics-driven paradigm based on probability flow conservation principles [28, 29]. By modeling video dynamics as fluid mechanics, we formulate video evolution through a probability flow velocity field governed by continuity equations (see Figure 1-b and Section 3.1). This reveals a key insight: natural video dynamics preserve the product between the velocity field and the ratio of spatial probability gradients to temporal density changes. Inspired by this, we introduce Normalized Spatiotemporal Gradient (NSG) statistic, which quantifies the ratio of spatial probability gradients to temporal density changes. NSG captures fundamental discrepancies in how videos adhere to physical constraints while eliminating reliance on specific artifacts, enabling sensitive detection even when visual differences are imperceptible to humans or conventional models.
To enable practical estimation, we develop an NSG estimator leveraging pre-trained diffusion models' inherent gradient estimation ability [30, 31] ]]]]]] Section 3.2. By approximating spatial gradients with learned score functions (i.e., the gradient of the log probability density) from the diffusion models and temporal derivatives through motion-aware temporal dynamics via a brightness constancy constraint [32], our method avoids explicit flow computation while preserving essential physical constraints. This estimator eliminates reliance on complex motion modeling by thysics-inspired priors while maintaining sensitivity to subtle spatiotemporal inconsistencies inherent to synthetic content.
Building on this foundation, we propose an baGed video detection method (NSG-VD) in Section 3.3, which computes the Maximum Mean Discrepancy (MMD) [33, 34] between NSG features of real videos and the test video as the detection metric, as illustrated in Figure 2. We further theoretically derive an upper bound of the distance between NSG features of real and generated data in Section 3.4, showing this bound expands with increasing distribution shifts in generated videos. This implies that the MMD between NSGs of real videos tends to be smaller than that between real and generated videos, establishing the theoretical basis for the effectiveness of NSG-VD, Extensive experiments show that NSG-VD achieves 16.00% higher Recall and 10.75% higher Fl-score than baselines, validating the superior performance of NSG-VD. Our contributions are summarized as:
A physics-driven NSG statistic: We formulate the video evolution through probability flow velocity field with a continuity equation and propose a novel statistic Normalized Spatiotemporal Gradient (NSG) that explicitly models spatiotemporal dynamics of vidcos. By quantifying the ratio

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of spatial probability gradients to temporal density changes, NSG fundamentally captures violations of physical continuity in AI Al-generteed videos without reliance on -seecicc- supervision.
A diffusion-guiie guuiedd NSG estimation with physical priors: We develop an NSG estimator by spatial
gradients approximation and motion-aware temporal dynamics modeling using pre-trained diffusion models. By avoiding explicit flow modeling and instead enforcing brightness constancy constraints, method achieves effective NSG approximation without domain-speciftt motion modeling.
An Al-generated video detection method with theoretical and empirical justifications: We propose an NSG-based video detection method (NSG-VD) VD), which quantifies distributional shifts in NSG features using Maximum Mean Discrepancy (MMD). We derive an upper bound of NSG feature distances between real and generated videos, proving that generated videos exhibit amplified discrepancies under distribution shifts. Empirical results also show the superiority of our NSG-VD.
2 Related Work
AT-Generated Video Detection. Early generated video detection methods primarily focus on identifying synthetic facial videos. Yang et al. [35] and Amerini al. [22] exploit auxiliary facial motion cues (landmark dynamics vs. optical flow) for deepfake detection. Gu et al. [36] separately model spatial and temporal inconsistencies, and introduce a vertical slicing feature fusion mechanism to establish a more comprehensive spatial-temporal representation. Wang et al. [23] propose an
alternating-to frermatigg--rezingg strategy with spatiotemporal augmentation for facial consistency modeling. Xu et al. [24] transform consecutive frames into a predefined layout via masking/resizing to enable efficient spatiotemporal modeling. Peng et al. [37] integrate multi-fcature fusion of facial perspectives, textures, and attributes. While most methods utilize facial priors, their reliance on domain-speciff features limits their generalizability to more general Al-generated content detection.
With the rapid advancement in video generation, detecting general Al-generated content has become challenging. Bai et al. [38] fuse frame-level and optical flow predictions detect spatial-temporal anomalies. To jointly capture spatiotemporal cues, Ma et al. [39] and Chen et al. [25] propose Transformer- and mamba-based frameworks model spatiotemporal relationships in video frame features for detection. Song et al. [40] exploit the cross-modal perception and reasoning in vision- language large models to learn general forgery features. Despite this progress, these methods mainly focus on appearance inconsistencies, while overlooking the intrinsic spatiotemporal dynamics cues, thereby struggling to tackle visual cues from diverse video generative models.
Diffusion Models. Diffusion models [41, 30, 42, 31] have emerged as powerful probabilistic generative models, benefiting from their diffusion-denoisinn paradigm that perturb data into noise through Gaussian processes and reconstruct samples via iterative denoising. Intuitively, the high- quality and diverse generative capabilities of diffusion models come from their ability capture and exploit the distributional characteristics of natural data, enabling effective discrimination between natural samples and outliers. Motivated by this, growing body of research has leveraged diffusion models for the detection of adversarial [43, 44, 45] and generated samples [46, 47, 48]. wherein the score model emerges as a powerful discriminative tool. Nevertheless, it remains challenging to simultancously capture and integrate spatiotemporal features when relying solely on score models.
3 Modeling Spatiotemporal Dynamics for AI-Generated Video Detection
Al-Generated Video Detection. Let P be Borel probability measure separable spatiotemporal metric space X'c, where T is the number of frames and d is the spatial dimension. Given independent and identically distributed (i.i.d)) samples (x= y from the real video distribution P. we aim to determine whether each sample (() in (g= m ly=1 originates from F.
Challenges for Video Detection. The complex spatiotemporal dynamics in high- -igh-dimensional video data often require modeling both spatial irregularities (e.g., unnatural textures) and temporal inconsistencies (e.g., implausible motions). Moreover, the diversity of generative paradigms (e.g.. diffusion models [1] and generative adversarial networks [49]) introduces heterogeneous distribution shifts that exhibit as subtle statistical inconsistencies rather than explicit artifacts. These challenges are further worsened by rapidly evolving generative techniques (e.g., Sora [3]), which continuously produce novel spatiotemporal patterns surpassing existing detection mechanisms.
3

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Inter-frame Differences
Normalized Spatiotemporal Gradient
plach
Temppral Derivative
(MD stres)))
Video Franess
a log
[G(xx*)
x P
Pxlogp(x
G -0,bgg((x + 6(x*)
Spatial Gradient
Sg
Vy Vxlngr(x e)
Model
Figure 2: Overview of the proposed NSG-VD VD. Given reference set of real videos {xx*) and test video x"", we estimate their spatial gradients Vx log p(x, t) and temporal derivatives ò, log p(x, t) via pre-trained diffusion model Sø, from which we derive their Normalized Spatiotemporal Gradients (NSGs) and calculate the MMD between NSG features of real and test videos as a detection metric.
Method Overview. To address these challenges, we propose a physics-driven method based on physical conservation principles to model spatiotemporal dynamics and introduce a novel statistic Normalized Spatiotemporal Gradient (NSG), which quantifies the ratio of spatial probability gradients to temporal density changes, capturing subtle anomalies in videos (Section 3.1). Leveraging diffusion models, we develop an effective NSG estimator by spatial gradients approximation and motion-avee aware temporal dynamics modeling (Section 3.2). Building on this, we develop an NSG- based video detection method (NSG-VD), which computes the Maximum Mean Discrepancy (MMD) between NSG features of the test video and real videos as a detection characteristic (Section 3.3), where its framework shown in Figure 2. Last, we theoretically show that the MMD between NSGs of real videos tends to be smaller than that between real and generated videos (Section 3.4).
3.1 Modeling Spatiotemporal Dynamics via Normalized Spatiotemporal Gradient
Detecting Al-generated videos requires capturing both spatial irregularities and temporal inconsisten- cies in synthetic content. Inspired by conservation laws in physics (e.g., mass or energy transport), we initially formulate the probability flow velocity field (xx, t) to model the evolution probability density p(x,t), t), which satisfics a continuity equation for global consistency across spatiotemporal domains. However, solving v faces challenges due its underdetermined nature (Eqn. (4)). To address this, we propose Normalized Spatiotemporal Gradient (NSG) g(x, t), dual field statistic of v combining both spatial gradients and temporal dynamics of p(x, t), as defined in Eqn. (6).
Probability Flow Velocity Field v(x. t). We begin to conceptualize the probability flow (also called probability current) the movement of probability mass of over time [50, 51]. To formalize this flow, we define the probability flow density J [xx l), analogous to fluid mechanics [52]]
J(x, t) p(x, t) v(x,t).
where p(x, t) denotes the probability density and v(x, t) represents the velocity field guiding the flow of probability mass. The conservation of probability mass [28, 29] implies the continuity equation:
0p(x,() Öt
+ Vx J(x, () = 0,
where V JJ= aJ: denotes the divergence of the vector field J [51]. This not a specciic ix; assumption but universal mathematical formulation of probability mass conservation, which holds for any time-evolving probability density p(x, t) [53, 29]. Intuitively, this equation shows that the rate of change in probability density O.p point equals the difference between inflow (negative divergence) or outflow (positive divergence) of the probability flow J. Substituting J(x, t) into Eqn. (2), dividing by p(x, t), and applying the chain rule log p(x, t). yields:
0 pox 1) + Vx v(x, L) + v(x,)) () Vx (og,(x = 0.
This expression reveals how the velocity field v(x, i) simultaneously encodes temporal evolution (0, log pxx, t)) and spatial gradients (Vx log p(x, t)) of the probability distribution.

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Normalized Spatiotemporal Gradient g(x, t) as Dual Field of v(x,t) t). To solve v(x, t), we focus on the dominant components of Eqn. (3). Assuming that the divergence term Vx V is subdominant in smoothly varying distributions (e.g., incompressible flow approximations [28, 54]), condition
commonly used in fluid dynamics [28] and quantum mechanics [55], Eqn. (3) simplifies to:
v(x,t) t) Vx logp(( 1) ~ -O, 1l..
Considering the non-uniqueness of solutions to v(x, 1) in Eqn. (4), we normalize both sides into
Vx log 1) v(x,t)
1.
(5)
- log p(x,
Definition 1. (Normalized Spatiotemporal Gradient (NSG).) The relation in Eqn. (5) reveals that natural video dynamics preserve the product between the velocity field and the ratio of spatial probability gradients to temporal density changes. We formalize this constrained ratio as the Normalized Spatiotemporal Gradient (NSG), defined as:
Vxlog p(x. t)
g(x, t) - log p(x, t) X
(6)
Here, A >> 0 prevents numerical instability. Eqn. (5) and (6) imply that g(x, () acts as dual field to (xx (), satisfying g g The formulation of g(x, 1) bypasses the ill-posed velocity v(x, inversion problem while preserving the critical information about spatiotemporal gradient dynamics.
Interpretation and Advantages. The NSG statistic gxx, t) quantifies the directional sensitivity of probability flow per unit temporal variation, driven by both spatial gradients (Vx log p(x. t)) and tem- poral derivatives (0, log p(x, f)). This statistic captures both spatial irregularities (via V log p(x. t)) and temporal inconsistencies (via Ô, log p(x. t)), enabling comprehensive analysis of video dynamics. Moreover, by modeling fundamental probability flow dynamics, NSG avoids dependencies specific artifacts, making it suitable for detecting generated videos across diverse generation paradigms.
3.2 Estimating NSG with Diffusion Models
The NSG statistic g(x, 1) in Eqn. (6) requires estimating two key components: the spatial gradients Vx pox, t) and the temporal derivatives 0 log t). Using diffusion models' inherent gradient estimation ability [30, 31J, we propose effective estimator combining spatial gradients from pre-trained diffusion models with motion-aware temporal dynamics using Eqn. (8) and (9), yielding:
So (x.) Xe+
g(x,t) R
So (x()))
At
where So denotes the learned score function from diffusion models and x, represents the /-th video frame. This estimator eliminates the need for explicit flow computation while preserving critical spatiotemporal dynamics through physies-inspired modeling. Below, we detail its derivation.
Spatial Gradients Estimation. Diffusion models [31, 56] explicitly learn a score network sy through score matching [30] or denoising diffusion modeling [41] approximate Vx log p(x, For a given video x at t-th frame, the spatial gradient is estimated by:
Vx log pepp(x 1) RJ So(x:),
8
where x, is the t-th frame of the video x. Here, we omit the diffusion timestep to make the notation clearer. This estimation allows direct computation of V log p(x, t) in NSG via single forward pass of the pre-trained diffusion model, eliminating the need for numerical differentiation.
Temporal Derivatives Approximation. To estimate è p(x, 1), we exploit the temporal coherence of video sequences under the brighiness constancy assumption [32], which posits that the probability density along motion trajectories remains constant. This leads to the following approximation:
Proposition 1. Under the brightness constancy assumption p(x + Ax, L. + At) R p(x,() () with small fraee-frame motion (At -> 0) and inter-frame displacement (Ax- -> 0), we have
a, log pogp(xt)) R Vx log log t) Ax
At
5

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3.3 Exploring NSG for Detecting Al-Generated Videos
To effectively distinguish Al-generated content from real videos, is crucial to design metrics that capture subtle distributional discrepancies in high-dimensional spatiotemporal features. Recent studies show Maximum Mean Discrepancy (MMD) [33]-a non-parametric statistic for distribution alignment-han has demonstrated remarkable capabilities in measuring distributional differences, e.g., Al- text detection [48, 46] and adversarial samples detection [57, 58). Building upon MMD's theoretical foundation and NSG's unique strength in modeling spatiotemporal dynamics, propose an NSG- based video defection method (NSG-VD) that integrates MMD with the NSG feature representation.
MMD Formulation with NSG Features, We aggregate NSG features across I frames in each (x denote a reference set of real videos and St -y}
video as (xx)=[g(x,, D Let Sp
represent a test video. The MMD [33] between Sp and St in terms of NSG is computed as:
2 MMD S o n² Σ l (G GU) (G))),G))
1 " [&]
2 E G (((aa) +he G (tess), G G(est), (10)
where G G(x and G (lest) G() NSG features extracted from real and test videos. The kernel & : 9 x G + E maps NSG features to a reproducing kernel Hilbert space (RKHS) Hs. such as the Gaussian kernel (a. b) = exp (- ||a - b11² / (20²)) Note that while MMD is conventionally used for distribution-level comparisons, recent studies [48, 46, 58] validate its efficacy in sangle detection by quantifying deviations from reference distributions. Crucially, while MMD provides viable solution for distributional comparison, the core advantage of NSG- VD stems from the NSG itself modeling fundamental spatiotemporal dynamics (see details in Appendix E.3).
2 Detection Protocol with MMD Metric. Let f(y: Sp, k) = I [MMD; > +): where is the
indicator function and is threshold for the decision. Given a test video y. compute the MMD with NSG against a referenced real video set and give the decision:
Fake, if [(;; ST, kw T) = 1,
f
(11)
Real, if fý;; Sp. ku, T) 0.
Optimization for NSG-VD. To enhance discriminative power, we use a deep kernel [34] for MMD:
(x, y) [(1 - e)x (dG(x), + c] 4 (G(x), G(y)),
(12)
where (x) = O (x))) is deep neural network, x and + are Gaussian kernels with bandwidths To and ao, and 6 E (0, 1). The kernel parameters w= Φ, os, σo} will be optimized by Eqn. (13) to maximize the detection ability. Considering the multiple-populatte distributions [48], we adopt multi-population aware optimization for the kernel training:
scenarios across diverse video
2
2
MPP. (Sp St KEw) 65 Sth kw) +
N
N
N
N
k arg max Rw
Σ
H
Σ
Hig
(13)
N
N
where Str" and Str denote the training real and generated videos, respectively, MPP (S Str x,) (x, kk xy).
N(N-1) Eie Hi and
3.4 Theoretical Guarantees for NSG-VD
The effectiveness of NSG-VD relies on ensuring the MMD between NSG features of real videos is smaller than that between real and generated videos. To formalize this, analyze the MMD formu- lation in Eqn. (10), where the key discrininative information lies in the cross-term & (G G (1est) since the first and third terms remain invariant for fixed reference sets. Under the Gaussian kernel, this cross-term is dominated by the exponential squared distance between NSG features. Note that v= log p(x,t)
analyzing -8, log +xX under practical distributions can be very difficult and infeasible, we adopt common practice [59, 60] by assuming Caussian-distriburee data to derive theoretical insights. Below, we first characterize the NSG statistics for real and generated videos under Gaussian assumptions.

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Proposition 2. Let the real video distribution be t(x,t) = NO (t) and the generated video distribution be ( respectively, where I E Rdxd is an identity matrix and μ=0 E & is the distribution shift and (1) the NSG g(x, 1) and g(y, t) satisfy:
x/o(1]2 x
~N(0,,(t)IL) Dx At (t( a(t)
g(x,t)
(d)):
D,(x)
o(t)
o(t) a(t)
g(y,)) \/o(1)2 y
~N(- ((1) (119))))) Dy(y) ~ x dā(l) a(t)
(d)
Dy(y)"
o(t)
(t) a(t)
where (x = A+ dā(t) 1x) Dy(y) = X+ da(t) (y(1)
o(t) & d at()), and p= a(t)a
||
a(t) a(t)
o(t)
a(ts
dt
x2 (d) is the central chi-squared distribution with d degrees of freedom and x2 22, ()) the noncentral chi-squared distribution with noncentrality parameter up and d degrees of freedom [61].
Proposition 2 reveals that the distribution shift in generated videos introduces deviations in both the numerator and denominator of the NSG, i.e., noncentral Gaussian and chi-squared distributions. To quantify this deviation, we derive an upper bound on the squared distance between NSGs:
Theorem 1. Let the real video distribution be x~N(O, a (1) and the generated video distribution be y~N Lt)) respectively, where Ldd is an identity matrix and 0f d the distri- bution shift. Given (xx)= t)}
denote -=1|u4]] (t) and assume -- log p(x, + 21
C O and -- ply. + Al 2 C > 0, with probability at least 1 5, we have
[GG()-G(y)II 0o (
T
T σ d) + log? σ ))
T
pdd + dl + 4 + log
(0 + (p+
Theorem reveals that the bound of the squared distance between NSG features of real and fake data will be smaller if the distribution shift term & = (t)² is closer to zero for a given 6. This formalizes the intuition that small distribution shifts produce small geometric distortions in NSG space, while significant deviations in synthetic content lead to large separations from real data. Under the Gaussian kernel, this implies that the real data have a larger k( (x)),, Gyy)) than the fake data since the distribution shift term o = 0 for real data. Therefore, when substituted into Eqn. (10), the MMD between NSG features of real videos is smaller than that between real and generated videos.
Experiments
Datasets. We evaluate our methods on the Gen benchmark [25], a large-scale dataset for Al-generated video detection that includes diverse real-world videos and synthetic content from multiple generative models. We use Kinetics-400 [62] as the real video source, SEINE [63] or Pika [64] as the Al-generated videos for training. The test set comprises MSR- VTT [65] and 10 diverse Al-generated datasets from different generation paradigms. More details are Appendix C.I.
Evaluation Metrics. We evaluate the performance of video detection on Recall, Accuracy, F1- [66] and AUROC [67] metrics. More details are provided in Appendix C.2. We use bold numbers to indicate the best results and underlined numbers to denote the second- best results in tables.
Baselines. We compare our NSG-VD with following baselines: TALL [24], NPR [27], STIL [36), and Demamba [25]. These baselines are implemented based on the codebase provided by Demamba [25].
4.1 Comparisons on Standard Evaluation
We start by comparing our NSG-VD with baselines using 10, 000 real videos from Kinetics-400 and 10, 000 generated videos from Pika (Table 1) and SENIE (Table 2) for training. respectively.
Results on Trained with Kinetics-400 and Pika. From Table 1, existing methods exhibit critical limitations. For instance, Demamba struggles with generative paradigms like HotShot (40.60% Recall) and Sora (48.21% Recall), while NPR shows unstable performance with Accuracy ranging from ..70 to 98. 20%. TALL fails on synthetic outliers (e.g.. 25.00% Recall on Sora) and STIL collapses completely on critical cases (e.g., 1.40% Recall on HotShot and 1.79% Recall on Sora), revealing limitations of their inherent dependencies on generator-specins artifacts.
7

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Table I: Comparisons with baselines on standard evaluation (%), where we train all models with 10, 000 real and generated videos from Kinetics-400 and Pika, respectively.
Method
Metric
Model
Morph Studio
Moon Valley
HotShot
Show1
Gen2
Crafter
Lavie
Sora
Wild Scrape
Avg.
Scope
Recall
87.00
93.60
98.80
40.60
48.40
98.00
88.40
59.00
48.21
58,20
72.02
DeMamba
Accuracy
91.70
95.00
97.60
68.50
72.40
97.20
92.40
77.70
72.32
77.30
84.21
91.29
94,93
97.63
56.31
63.68
97.22
92.08
72.57
63.53
71.94
80.12
AUROC
98.04
98.82
99.68
87.84
90.12
99.46
97.81
91.32
88.36
87.38
93.88
Recall
61.20
80.00
98.00
16.00
33.00
91.20
80.60
34.60
35.71
43,20
57.35
NPR
Accuracy
79.80
89.20
98.20
57.20
65.70
94.80
89.50
66.50
67.86
70.80
77.96
F1
75.18
88.11
98.20
27.21
49.03
94.61
88.47
50.81
52.63
59.67
68.39
AUROC
93.05
97.18
99.66
82,97
90.50
99.13
97.87
87.54
90.47
91.84
93.02
Recall
51.20
65.20
93.40
32.00
61.60
94,80
81.80
49.20
25.00
53.60
60.78
TALL
Accuracy
75.10
82.10
96.20
65.50
80.30
96.90
90.40
74.10
61.61
76.30
79.85
F1
67.28
78.46
96.09
48.12
75.77
96.83
89,50
65.51
39.44
69.34
72.63
AUROC
95.82
97.14
99.73
92,55
97.36
99.79
99.09
94.84
86.67
93.75
95.67
Recall
73.80
70.80
43.40
L.40
2,00
45.00
13.20
7.20
1.79
11.60
27.02
STIL
Accuracy
86,90
85,40
71.70
50.70
51.00
72.50
60
53,60
50.89
55,80
63.51
F1
84,93
82.90
60.53
2.76
3.92
62.07
23.32
13.43
3.51
20.79
35.82
AUROC
96.43
97.77
99.34
86.66
90.56
98.88
97.04
88,16
92.57
87,52
93.49
Recall
68.33
98.33
100.00
92.50
87.50
80.00
98.33 33
94.17
78.57
82.50
88.02
NSG-VD (Ours)
Accuracy
81.67
98.33
96.67
91.67
90.83
88.33
95.83
94.17
88.39
88.75
91.46
Fl
78.85
98.33
96.77
91.74
90.52
87.27
95.93
94.17
87.13
88,00
90.87
AUROC
92.26
98.66
98.15
94.45
96.38
94.83
98.16
97.41
96.40
94.73
96.14
Table 2: Comparisons with baselines a standard evaluation (%), where we train all models with 10, 000 real and generated videos from Kinetics-400 and SEINE, respectively.
Method
Metric
Model
Morph Studio
Moon Valley
HotShot
Show!
Gen2
Crafter
Lavie
Sora
Wild Scrape
Avg.
Scope
Recall
47,40
87.80
88.20
77.40
75.00
85.60
91.60
68.60
42.86
48.00
71.25
Accuracy
72.80
93.00
93.20
87.80
86.60
91.90
94.90
83,40
68.75
73.10
84,54
DeMamba
F1
63.54
92.62
92.84
86.38
84, 84
91.36
94.73
80.52
57.83
64.09
80.87
AUROC
88.29
98.39
98.76
97.84
96. 89
98.76
99.35
96.87
80.93
88.11
94.42
Recall
46,40
76.40
69,80
63.80
56.00
75.00
83.80
$8.80
35.71
27.40
59.31
Accuracy
71.40
86.40
83.10
80.10
76.20
85.70
90.10
77.60
66.96
61.90
77.95
NPR
F1
61.87
84,89
80.51
76.22
70.18
83.99
89.45 .43
72.41
51.95
41.83
71.33
AUROC
85.73
96.01
93.79
91.44
89.96
95.13
96.87
89.46
84.15
76.66
89.92
Recall
58.60
75.00
79.40
60.20
62.00
77.80
88.20
43.80
33.93
35,80
61.47
TALL
Accuracy
F1
73.43
78.80
87.00
85.23
89.
88.03
74.69
79.60
76.07
80.50
87.02
88, 40
93.23
93.60 23.60
71.40
60.50
50.00
66.07
52.34
67. 47.40
74.05
80.20
AUROC
97.10
98.12
98.63
96.37
96.45
97.76
99.38
94,80
83.35
89.45
95.
Recall
28.60
57.40
78.40 70
46.80
18. 80
66.40
69.00
24,80
14.29
19.00
42.35
STIL
Accuracy
64,20
78.60
89.10
73.30
59.30
83. 10
84.40
62.30
57.14
59.40
71.08
Fl
44.41
72.84
87.79
63.67
31.60
79.71
81.56
39.68
25.00
31.88
55.81
AUROC
95.53
97.91
99.40
96.49
92.79
98.06
98.86
91.00
92.79
86.58
94,94
Recall
91.67
100.00
100.00
100.00
100.00
98.33
100.00
97.50
94.64
89.17
97.13
NSG-VD (Ours)
Accuracy
82,50
88.33
89.58
84.58
86.25
87.08
86.63
87.92
89.29
78.33
86.05
F1
83.97
89.55
90.57
86.64
87.91
88.39
88. 24
88.97
89.83
80.45
87.45
AUROC
90.67
97.62
98.38
95.88
96.69
97.87
97.64
95.09
96.14
88.65
95.46
In contrast, our NSG-VD achieves state-of-the-art performance across all metrics, significantly outperforming baselines despite not being pre- trainedd on large-scale videos. Remarkably, NSG-VIL VD demonstrates exceptional reliability on challenging closed-source generators like Sora (78.57%) Recall vs. 48.21% for Demamba) and emerging paradigms like HotShot (92.50% Recall vs. 40.60% for Demamba), and maintains reliability across other diverse domains (e.g., MorphStudio, Moon Valley). Notably, our NSG-VD achieves 16.00% t average Recall and 10.75% 1 F1-score over Demamba, and 55.05% 1 Fl-score over STIL. These results confirm its generalization across both open-source and closed-source generated models, highlighting the advantages of physics-driven modeling.
Results on Trained with Kinetics-400 and SENIE. As shown in Table 2, our NSG-VD achieves superior detection performance across all metrics compared to baselines. Notably, it attains near- perfect Recall (2 98.33%) on models like Moon Valley, HotShot and Show while maintaining balanced performance across diverse domains (e.g., ModelScope, WildScrape). These results are consistent with the results on Pika Table 1, further demonstrating the effectiveness of our proposed method. In contrast, existing baselines exhibit pronounced limitations under this setting. Demamba's 's performance is more constrained (S 85.60% Recall on most models), and NPR's FI-score varies widely (41.8%% 89.43%). TALL shows instability models like Sora (33.93% Recall), while
8

---

Table 3: Comparisons with baselines under data-imbalanced scenarios (%), where train all models with 10, 000 real and 1, 000 generated videos from Kinetics-400 and SEINE, respectively.
Method
Metric
Model
Morph
Moon Valley
HotShot
Show!
Gen2
Crafter
Lavie
Sora
Wild Scrupe
Avg.
Scope
Studio
Recall
56.80
82.60
65.60)
78.20
81.00
53.40
33.93
43.20
64.09
Accuracy
78.10
89.90
91.00
82.50
81.60
88.80
91.20
76.40
65.18
71.30
81.60
DeMamba
F1
72.17
88.84
90.17
78.94
77.62
87.47
90.41
69.35
49.35
60.08
76.44
AUROC
93.01
98.17
98.90
96.42
95.36
98.38
98.77 74
95.50
86.51
87.49
94.85
Recall
25.40
52.20
42.40
26.00
21.40
48.20
66. 60
22.00
10.71
12.20
32.71
Accuracy
62.40
75,80
70.90
62,70
60,40
73,80
83.00
60.70
55.36
55,80
66.09
NPR
F1
40.32
68.32
59.30
41.07
35.08
64.78
79.67
35,89
19.35
21.63
46.54
AUROC
83.64
94.85
92.44
86.68
83.77
94.33
95.77
84.34
84.60
70.52
87.10
Recall
28.20
45.20
41.20
26.20
33.80
60.20
60.20
22.60
25.00
18.20
36.08
TALL
Accuracy
64.00
72.50
70,50
63.00
66.80
80.00
80.00
61.20
62.50
59.00
67.95
F1
43,93
62.17
58.27
41,46
50.45
75.06
75.06
36.81
40.00
30.74
51.40
AUROC:
93.34
94.56
94.25
91.64
91.63
94.99
97.60
91.46
84.92
85.20
91.96
Recall
25,80
64,80
68,40
46,20
29.20
67.20
70.00
44,40
26.79
25,00
46.78
STIL
Accuracy
F1
40.89
62.70
78.45
82.20
81.04
84.00
72.90
63.03
45.06
64.40
83.40
80.19
82.16
84, 80
72.00
61.33
42.25
63.39
39.87
62.30
61.43
73.21
AUROC
85,14
95.74
96.87
89.46
83.22
96,09
96.23
90.36
89.89
78.99
90.20
Recall
85,83
99.17
100.00
99.17
97.50
95.83
99.17
91.67
82.14
81.67
93,21
NSG-VD (Ours)
Accuracy
84.58
92.50
93.75
89.58
89.58
90.83
92.50
90.00
86.61
81.67
89.16
F1 84.77
92.97
94. 12
90.49
90.35
91.27
92.97
90.16
85.98
81.67
89.48
AUROC
90.76
98.18
18
95.03
95.48
96.97
96.53
95.11
95.73
87.13
94,91
STIL fails entirely on critical cases (e.g., 19.00% Recall on WildScrape). These failures highlight the fragility of artifact-based approaches in capturing subtle spatiotemporal inconsistencies.
Quantitatively, NSG-VD surpasses Demamba by 25.88% t in average Recall (97.13%) vs. 71.25%) and NPR by 16.12% f in average Fl-score (87.45% vs. 71.33%). On closed-source models like Sora, it achieves 94.64% Recall-nearly twice Demamba's 's (42.86%) and sextuple STIL's (14.29%) This improvement highlights NSG-VD's sensitivity to synthetic anomalies, especially in near- saaarpoooorealsticcccc videos (e.g.. Sora), where subtle spatiotemporal inconsistencies are amplified by the NSG but not effectively captured by baselines, indicating reliable detection across diverse generation paradigms.
4.2 Comparisons on Challenging lnbta-mmbalaeeed Scenarios
In real-world scenarios, natural videos are often abundant and accessible, while collecting sufficient Al-generated videos remains challenging due to rapidly evolving generation techniques. To thoroughly assess reliability under these conditions, we train all models using 10, 000 Kinetics-400 real videos and only 1, 000 SENIE-gencrated videos. As shown in Table 3, all baselines exhibit significant limitations. Demamba fails catastrophically on challenging generators like Sora (33.93% Recall) and WildScrape (43. 43..00% Recall), while NPR exhibits fluctuations in Accuracy (55.36% ~ 83. 83.00%) Recall) and Lavie (22.60% Recall), and STIL shows highly variable performance, e.g., 25.00% ~ 70.00% Recall. Such instability indicates over-reliance on synthetic data volume or sensitivity to superficial artifacts.
TALL fails completely on emerging paradigms like WildScrape (18. 20%
In contrast, NSG-VD achieves strong generalization across 10 diverse generations. Notably, NSG-VD attains superior performance on critical test cases: 82. 14% Recall on Sora (vs. 10.71 % ~ 33.93% for baselines) and 81.677 31.67% Recall on WildScrape (vs. 12.20% ~ 43.20%). Critically, NSG-V VDD achieves 20.12% t higher average Recall than Demamba and 38. 38.08%% t higher F1-score than TALL. These results confirm NSG-VD's reliable generalization from limited synthetic data without compromising discriminative power, demonstrating that adherence to universal physical principles outperforms domain-specific feature reliance even when synthetic training data is severely constrained.
4.3 Impact of Spatial Gradients and Temporal Derivatives for NSG-VD
To investigate the impact of the spatial gradients Vx p(x, t) and temporal derivatives O log p(x, t) for our NSG-VD, we evaluate these components as in- dependent detection statistics for Al-generated video detection. To this end, we train these separate models with 10, 000 real videos from Kinetics-400 and gen- erated videos from Pika. From Table 4, the spatial
Table 4: Impact of spatial gradients and tem- poral derivatives on average metrics (%).
Method
Recall Accuracy
F1
AUROC
Spatial Gradients
87.99
82.84
83,40
Temporal Derivatives
71.09
66.97
78.95
NSG-VD VD (Ours)
88.02
91.46
90.87
96.14

---

gradient achieves moderate performance (e.g,, 87.9 87.99% Recall, 83.40% Fl Fl-score), suggesting its ability to capture spatial anomalies, which may arise from its sensitivity localized variations in texture geometry. The temporal derivative, however, shows limited detection power (e.g. 60.35% Recall, 66.97 66.97% F1 Fl-sc)re) likely due to its sensitivity to transient noise dynamic modeling. In con- trast, our NSG-VD VD integrating both components achieves significantly enhanced performance (e.g., 88.02% Recall, 90.87% Fl-score). This demonstrates that the interplay between spatial gradients and temporal derivatives formalized via physical conservation principles is critical for video detection.
4.4 Impact of Decision Threshold for NSG-VD
We evaluate the decision threshold in Eqn. (11) for NSG-VD by testing т E [0.4, under the same settings as Table shown in Figure 3, our NSG-
1.00
0.95
VD maintains remarkably stable performance across a wide range of values without requiring tineggriiedd tuning. Specifically, NSG-VD consistently shows high detection performance as 7 E [0.7, 1.1] for average Recall, Accuracy and FI-Score across diverse gener- ators. These results indicate that NSG features create clear separation between real and fake distributions.
0.85
0.75
Recall
Accuracy
F1 soore
Decision threshold
We set 1.0 as the default throughout all settings.
Figure 3: Impact of decision threshold.
Conclusion
In this paper, we propose physics-driven Al-generated video detection paradigm by modeling spatiotemporal dynamics through the Normalized Spatiotemporal Gradient (NSG), a novel statistic based probability flow conservation principles. Leveraging pre-trained diffusion models, propose an NSG-based video detection method (NSG-VD) VD). Theoretical analyses and extensive experiments validate the superiority of our NSG-VD in detecting advanced generated videos.
Acknowledgements
This work was partially supported by the Joint Funds of the National Natural Science Foundation of China (Grant No. U24A20327), RGC Young Collaborative Research Grant No. C2005-24Y, RGC General Research Fund No. 12200725, and NSFC General Program No. 62376235.
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16

---

APPENDIX
Contents
Theoretical Analysis
18
A.I Basic Theorems and Corollaries Related to Statistics
18
A.2 Proof of Proposition
19
A.3 Derivations of Chain Rule the Conservation of Prohahility Mass
20
A.4 Derivations of Gradients in NSG
20
A.5 Proof of Proposition
21
A.6 Derivations of Upper Bounds for Gradients
21
A.7 Proof of Theorem
23
B More Related Work
27
More Details for Experiment Settings
27
C.I More Details on Datasets
27
C.2 More Details on Evaluation Metrics
27
C.3 Implementation Details on NSG-VD
28
C.4 Pseudo Code of NSG-VD
28
More Experimental Results
29
D.1 More Results on Standard Evaluation
29
D.2 More Results on Impact of Spatial Gradients and Temporal Derivatives
29
More Discussions on NSG-VD
30
E.1 Efficiency of NSG-VD.
30
E.2 Numerical Stability of NSG
................................
31
E.3 Impact MMD for NSG-VD
31
E,4 Impact Size Reference Set for NSG-VD
32
E.5 Impact Diversity of Real Vidcos in the Reference Set
33
E.6 Discussions on Assumption the Divergence Term
33
Limitations and Future Directions
33
Broader Impacts
34
Visualizations
35
17

---

A Theoretical Analysis
A.1 Basic Theorems and Corollaries Related to Statisties
We start to provide some basic theoretical results, laying the foundation for establishing the bounds of the statistics in Appendix A.6 and A.7.
Theorem 2. Let X (2, s) follow noncentral chi-squared distribution with d degrees of freedom and noncentrality parameter ip For any > the following tail bounds hold:
p(x - (d 4) 2 2/ (d 20)1 + 21 Se
p
S Se
Proof. The moment -ennerttgnn function of X satisfies
Flee (1 - 2-2s)//2 1/2).
The log-moment generating function of X - (d + 44 is:
log (d++))) = log E]e=*] - ssdd + 4p
d
log(1 25) + 1- 28
4p
s(d + s))
(14)
For < 8 < 1/2, we have
1
$²
log(1 1 - 2s)= S 1 28
(15)
2
which holds because the function (s)) = - - 1 log(1 11 - 2s)
T-2s satisfies (s(ss = - + 1-
2²
22-82
(1-2s)² - 0, implying maxp<<<1/22 (s) < (0+))) = 0, i.e. (s) S 0.
2.a
(1-24)
Substituting Eqn. (15) into Eqn.(14) we get
ds²
2,ps
(d + 2xpss²
log le (d++)) (d+++))) -
(16)
28
1
28
1 28
According to the result in [68], 3. 0, s.t.log B|ea2] < inequality holds:
[1]- then for t > 0, the following
vua
P(Z 2 el + 22 S St
Applying this result to Eqn. (16), we set 7 X (d+ 5), v 2(d + 22p) and 2, then
p(x - (d+ 2 3/d+ + 22)1 + 21 se
For 112 < 0, we have
log(1 22s) S s²
(17)
which holds because the function ((s) 5 1 log(1 -2s) -
52 satisties h'(s) = -11 1-2s -2s
I-25 2 implying 112-1/20000 (ss) (5 ) i.e. h(s) S O.
462
Substituting Eqn. (17) into (1n,, we get
2ops2
24p )s² S (d + 22)s²
log (x < ds² + 1- 2s
(d +
(18)
1 1 2s
According to the result in [68], if 3r > 0, s.t., log Ele inequality holds:
<
n5² 2
then for A <>> 0. the following
p(z Z S - -Vool St
18

---

Applying this result to Eqn. (18), we set -
- (d+ == 2(d 22p) then P p(x (d+ -2 se
Corollary 1. Given (d) a noncentralchi--quue squarreeed---sddddd distribution with degrees of freedom and the noncentrality parameter y,, with probability at least 1 - 8, we have
2
s V
4(d + 24) log
+ log
8
Proof. By Theorem 2, setting e- yields the following inequalities:
2
P (d + 2 ( (d 24p) log
+
log
5
8
2
2
8
P x (d
x (d+ - (d+ 2(+
24) log
0
2
Combining these inequalities, obtain:
[ x xx2ddtt2// (d+2 ( log
(3) 2 log
2
( 56.
2
P
X s d+p-2 2/ (d+ (d+2p) log
Taking the complement of the above event, have:
P d (d+ (d+2p) log (
(2)
(3)
2
< x S d (d+2p)
S
log log
+2 log
21 - 6.
By relaxing the lower bound of X, we conclude
P p X |x| s dttpt2 (d+2,) log
2
+2 log
>1 - 8.
A.2 Proof of Proposition 1
Proposition 1. Under the brightness constancy assumption p(x + Ax, 1+ At) R p(x,() with small
inter-frame motion (At > 0) and inter-frame displacement (Ax + 0), have
Vx log t) Ax
log log
(19)
Al
Proof. We apply the Taylor expansion logp(x + Ax, + Al) around (x, to first order:
log p(x + Ax, t + At) = log t) Vx p(x, t) Ax + θ log p(x, t) At o + At?),
where Ax| 2 + ?t represents higher-order infinitesimal terms.
By assumption, log ((x Ax, + At) s log (oog((x; t). Subtracting log p(x, t) from both sides:
Vx log p(x, t) Ax + θ logp(x t) At + Ax + Ar 0.
Under At + 0 and Ax + 0, obtain:
Vx log log t) Ax logp(x, At
Rearranging terms gives:
Vx Vxlogp(x, t) Ax
0 log x
At
19

---

A.3
Derivations of Chain Rule to the Conservation of Probability Mass
For 0g dt + + J= = O, we substitute J = pv and then divide the entire equation by (which is strictly positive everywhere in its support), yielding:
S.p + 1 Vx (Iv) = O.
p p
Applying the vector calculus product rule Vx (nv) pp(xx .v) +v. (Vxp) and the chain rule of calculus, p
02 0 logp and YxP
Vx logp, we obtain Eqn.(3):
a logp Vx vv Vxlogp= =0
This transformation does not alter the underlying fluid constraint--t is variable change making explicit how velocity couples to log-density's temporal and spatial gradients.
A.4 Derivations of Gradients in NSG
In the following, provide the specific forms of the terms V lolo t), - log p(x, t) + A and g(x, t) when the data are from Gaussian distributions, which will be used in Appendix A.5, A.6, A.7. Proposition 3. Given the real video distribution p(x, t) NN0, (t) and the generated video distribution q(y,t)= (p,, It)) with μ=0 and (t) the gradients Vx logp(x. t) and Vy log ply, are:
1 Ia),
Vx x logp(x,) 1) ot))
N(O,
(t))
Vy logp(y,t) o1)2 N'
( (t)
Proof. Recall that for Gaussian distribution p(z) = N(v,o²Ia) the probability density function is
p(z) (2mo2)a/2 exp (- (-16)- |
11
20²
The den-iiysity is Thus, we have
d log (2g@2
|| - 2/
log p(z) =
2
20
V. z log p(gp((z))))))))))()))
For the real video distribution p(x, 1) NO (1) we have 0. Taking the gradient w.r.t.
Vx log p(x, 1) = Vx (- ||x
o112 ~ N o(jja (
(1)2
For the generated video distribution q(y,t) = o() evaluated under ply. t)), the gradient w.r.t. y
(t)
Vy logply,))
y N ~ (-olt) a(t)2 I1
1
a(t)2
Proposition 4. Given the real video distribution p(x,t) t) NOO, LL) and the generated video distribution ()y,t)=N(H Lt) with μ70 and f0, the partial derivatives - log p(x, t) and -ô, log ply,t) t) are:
dā(l)
|x((((()
dā(l)
a(1)
D, logoog log
(d), at) a(t) att)
ot)
- logglyy,)) dô(()
(t)))
dõ(t)
a(t)
o(1)3 a(l) o(1) (d.
(1))
where a(t) d
[il dt (.)(t) and is the noncentral chi-squared distribution with noncentrality parameter yp [61].
0t)2-- Here, x² (d) is the central chi chi-rqd distribution and 2d, ()
20

---

Proof. We first derive the expression for the real video distribution p(x, t). The oog-density is
||x|2
log p(x, t) = - log((no((t)3) (t)
Taking the time derivative 0 (denoted by dot notation):
||x| de log p(x, t) = 2 (t) 2n (t)
d
a(t)3 (t))
(1) + (xx
o(t)
o(t)3
Thus, we get
dt((t)
[x||(((t)
dā a(t)
- 0, log p(x t)
o(1) o(t) (t)) x (d),
ot))
where the last formula is based on ||
o(()
x 12 (d).
For the generated video distribution
()) = (() under p(y, 1) with 3
alryz we have
-à, log loy. = dā(l) [1y1|2((1) dā(l) a(1)
(1) o(1}3 o()) o(t) x" (d, sp)
where the last formula is based on
y o(o)
12 (dd,
A.5 Proof of Proposition 2
Proposition Let the real video distribution be p(x, 1) NO (1) and the generated video distribution be q(y, t)=,, La)) respectively, where Is Rdxd an identity matrix and μ~0 E R is the distribution shift and a O,) the NSG g(x, f) and g(y,t) t) satisfy:
g(x, f) x/o(1}2 x
(N(00.01)1a)
D2 ~ A+ dā(l) 6(1)
(d):
D,(x)
a(t)
(t)) a(t)
//o(t)2 y
~N(- o(1) (1))))). Dyly) ~ X + dt a(t)
g(y,) () Dy(y)*
o1) a(1) x" (d, v),
a(1)2
where (x(x)= = A+ do(l) xx))
Dy(y)= = x+ do(e) [ a(1) A d Lo((), and x .
||
o() o(t)
(d) is the central chi-squared distribution with d degrees freedom and x² up) the noncentral
chi-squared distribution with noncentrality parameter ip and d degrees of freedom [61].
Proof. According to the definition of NSG,
V log p(x, t)
g(x, t) - log p(x, t) X"
(20)
we can substitute the results of V log p(x, f) in Proposition and - logp(x,)) f) in Proposition into Eqn. (20) and directly contribute the results.
A.6 Derivations of Upper Bounds for Gradients
Next, we present some propositions on the upper bounds that will be used Appendix A.7. Proposition 5. Given the real video distribution p(x, t) (O (+t) and the generated video distribution q(y. L)= (2)) with f= and a (1), let D,(x) = X - Ôr log p(x, 1) and
Dy(y)= 0, log ply, t), with probability least 1 6, we have
4 z [x)()) - Dy(y) < -- - 22(d+ 24) log + 2
4 z
dlog
+ 2 log 8'
where x
0(
21

---

Proof. From Proposition 4, we obtain
[ö(1)
-
|||| 11y]11
ot)3
where (()) A (t).
Let Z
2 [x a(r) x" (d) and W
Iyll त[t) x2 :p), where y
Il att)²
The difference becomes
Dx Dy(x)) = |o(1) a(t)
W Z|.
To bound IW - 2), we use concentration inequalities for chi-squared distributions by Theorem 2. For Z x" (d), have
Z - d2 2 dlog 3 +2log 1 8/
4'
P 2 - d -2 dlog 4 8
Combining these events, obtain
P 2 dlog $ s d 2 dlog +l 4
21 2
(21)
Similarly, for W ~ (d, :p), we have
P (d log log S W ds p 2 (d 24) log _ 22 1/2
2
(22)
2
Combining the bounds in Eqn. (22) and (21), have with probability 1 8:
W - Z| & & + 2 (d + 2:p) log + 2 looo 1 + 2 log
Substituting this into the expression for [x) (y)) completes the proof.
Proposition Given the real video distribution p(x, 1) NO, (1) and the generated video distribution g(y, 1) ()=N(p, (l)) with p=20 and a (1)+ the following inequalities hold with probability least
|x|
2 (2)
2
11
S d + $1
/Adlog
+ log
atty
||yl2
2
2
2)
I d 4++ 1 /A(d+ 24) log
+ 2 log
at))
8
8
3) |x-X|l Sd + 4(d 4(d++ vp) log
(2
2
+ 2 2og
(t)2
where :p
Proof. 1) Since (0, (I)
o(t) follows central chi-squared distribution x2) By the
|x|
concentration inequality for central chi-squared distributions (Corollary 1), with probability 1 1- 8:
|x|
(2 (5
S
d
+
Ad
+ 2 log
o(1) 2
lyll oto follows a noncentral chi-squared distribution x2d sp), where
2) For y |||| o(1
By Corollary 1, with probability 1 1-8. 8, we have
| S d ++ 4(d 2pp log + 2lo
2
2t)
22

---

3) Since x ~ ~N,0 II) and y ~ (u, (t)) their difference z satisfies:
x - ~ (o
Thus, |x-y||² follows a noncentral chi- -quared distribution x² (d, 1p/2,, where s/2 2r(()²
|| (t)2
By Corollary 1, with probability 1 - 6, we have
x x1
2 + log
2 8
S d + + [(d++)) 10g 8
(1)
A.7 Proof of Theorem
Given video x E Txd, its NSG Feature is G(x) (g(x,1))7= where gxx,t) is defined as: g(x, Vx ()
(23)
- - p(x, + X²
Here, À > 0 and p(x, () is the probability density of the real video parameterized by time t.
Note that Theorem 1 share common lower bound C' both (x log p(, L) and Dr(y)=X-O) 0 log fly,t). We first derive the conditions for D,(x)>C>> and Dy(y)>C>0 to hold in Proposition 7. The same analytical approach can be extended examine other cases.
Proposition 7. Let the real video distribution be x (O (t)) and the generated video distribution be ~ NN (t) respectively, where La E Raddd is identity matrix and + 0 E d is the distribution shift, we have D, > C>> 0 and Dy(y) > C > 0 with probability least -6, provided C and meet the following conditions:
Case 1 a(t) o(1)
> 0):
C= X ō(1)
20(1)
2
20(1)
+
d
+
log
(tt)
o(t)
(t)
8
A t(t)
(1(
(t)
2
9)
dlog
log
o(l)
o(1)
(1)
where x
||]l
o(1)2-
2) Case 2
a(t) [(0]
< 0):
C X 20(t)
2
o(t) / dlog
X 20(1)
2
dlog
a(t)
8
||y| cBef (d, 1p), where x0
||1!| c(f From Theorem 2, we have
Proof. Let W
P W (d () 2 (d+x)22 (d + 24) log (2)
2 )
8
2
8
2og
8
2"
(24)
8
(d +)) -2 (4p) log
5
(25)
1) Case 1
a(t) a
> 0):
23

---

Substituting Dy(y) = = a(0
(W- - d) into the bound Equ. (24):
a(t)
P P-D o(1)
(1( (t) 9 +
2
(1)
8
(t) ((a [ 24) log
+
log
-
8
(t))
8
2
Thus, the following inequalities hold with probability at least
5/2:
Dy(y) 2 A- (t)
2t(t)
2
26 (t)
2
o(t) 10 +
oft) V (d (d++2p) 24) log
+
log
(t)
8
(0)
2
(1)
(2)
2
(x(x) 2 + att) dlog
8)
+
o(t)
log
8
To ensure (x) C> 0 and (y > C > O, we can select C and À as:
-= 6(1) (0(
(0(1)
(t)) +++
d'log
+
log
ot))
(t)
8
a(t)
+ ()) (t)
(2)
(t)
2
>> o(l)
dllog
log
(1)
(1)
2)
Case 2 a(t ((D) 0):
Substituting Dy(y)= X a(t) (W- - d) into the bound Eqn. (25): a(1)
P Dy(s) S _ a(t) p
20(t) ol) 1p
2
o1) / (d 2,p) log
(5)
2
Thus, the following incqualities hold with probability at least 1 - -8/2:
Dy(y) 2 a(t)
(1(
2
1og (t) (d + 24p log
ott) 4
5
D,(x) 2 (t
[1)) V dloo (
To ensure D,(x) > C> 0 and Dy(y) > C > O, we can select C and À as:
C x 2t(
(t) |
dlog
A (t)
2
dd dlog
al)
Building upon the established Propositions 2, 5, 6 and 7, we next prove Theorem 1.
Theorem 1. Let the real video distribution be x0, (t) and the generated video distribution
be y~N(H, NN,,,NHHoo (()) respectively, where dxd is identity matrix and ERR is the distri- bution shift. Given ((x)= D)) denote -=|| (o(2 and assume -- log p( (x, 1) + A Z
C> >>00 0 and -a, logp(y, Aa C >
O, with probability at least 1- 8, we have
T
T (pp + d) + log² T ))
[GGx)--(y)|| 0o
pd + dl + sp + log 8
24

---

Proof. Based on the definition of G(x), we have
T
GG( - G(y)]l = Σ
(lg(x,)) 1) t)),
(26)
t=1
Next, we focus on the bound of g(x, 1) - g(y,1) 1))
Let D, (x) = A - 3 log pgg 1) and Dy(y) = À - 0 logply, (), by Propositions 3 and 4, we have
lg(x,t) g(y, t)
x/o(1)² \/o(1)2
D,(x) Dy(x)
x/o(t)3
x/o(t)?
x/o(t)² y/o(t)2 2
(x Dy(x)
Dy(y)
Dy(y)
x/o(1)2
x/o(1)2
+2 x/a(1)²
8/o(t)2 2
2
(x) Dy(y)
(y(y)
Dy
1
|xl1 +2
1
||x ||x- yl?
(x(x) Dy(y)
o(ly
Dy(y)
al1)1
Dy(y) - (x(x))
)
|x||
1
|x |x-
+2
Dx(x)D,(y)
(t)4
Dy(y)
at))
Dy(y)- - (x)
||x| 3
y||
(27)
C
(1)2
C
a(1)
For the first term in Eqn. (27), according to Proposition 5, with probability at least 1 25/3, we have
(x)
||x]
2
C³1
(1))
2
(0+ 2 (d 2:p) log o/2 + 2 dlog 1 + 2 log 1 (d 1--VAdd Adlog (9) 2 log (9)
(ta(t)2
2
( 4v (d + 2:)) log 12 + 2lo 13 (a+ 4d (9) 2 log (:)
(28)
Cto(t)2
For the second term in Eqn. (27), applying Proposition 6, with probability at least 1 - 5/3, we have
2 |x yl1
5 ))
(
I C²a(t)²
d + + |
4(d + p) log 8
+ 2 log
(29)
C
(t)+
For simplicity, let L log 1. Since log
$ = log 2 L, we have
(1((y) - (x)x)
||x 4 a(t)4
2
(x+ (d 2p) 2d 21)
+ 21)
-
Cto(t)2
2
S
Cla(1)2
(x+ 2p) + L+ -++2)))) 2L) (d d + L 2L)
(1 (5ip + 2d + 32) + 3L)
(10pd + 4d + 3L (5p + 4d) + +L
(30)
(t))(t)2
2
xx xx-yl y
4
(d+ +2
(d ++)pT + (T)T++21 2T.)
C
att)
CRo(tT²
2
(d+
10
(d+ 4) + 21.)
S C
2
4
(d+ 2
L(d + +
(31)
2
25

---

Combining Eqn. (30) and (31) and (27), and substituting L = log 12 with probability at least 1 5, we have
(lB(x,t) 1) g(y, t)1
(l)( (10ipd + 4d + 3L (5p + 4d) + +922 + C²a(1)2
dd+ 1f + L(d x +2) x2))
2
For further simplicity, note that 0² S (34 we obtain
llg(x, t) t)l
2
$
(t)( (10pd + 4d 2d + 40 + L. (17.p + 14d + 4) +
2
100p + 4d 2d + 4 + log
12 5
(17 14d + 4) + 9log"
12
(32)
(ta((t)
8
Summing over time steps = I,..., and replacing ö in Eqn. (32) into 8/T we get:
2T
12T 10pd 4d + 2d + log
12T
[[G())-G(y))
(17 + 14d + 4) + 9 llgg
Cla(1)2
8
8
Thus, we obtain the final results
T T (06(0) pd + dl + + log 8 (1 d) + log² 5 )
T
(G(()-G(y)) so
26

---

B More Related Work
Maximum Mean Discrepancy (MMD). Maximum Mean Discrepancy (MMD) is effective metric for two-sample testing to assess whether two samples originate from the same distribution [69, 33, 70, 34, 71, 72, 72, 73]. Originally introduced by Müller et al. [72] as instance of an integral probability metric, MMD admits several sample-based estimators. Partieularly, Gretton et al. [33] introduce the U-statistic estimator, which is unbiased for the squared MMD and achieves near- minimal variance among all unbiased alternatives. Further, Tolstikhin et al. [74] derive lower bounds on the estimation error of MMD under fimite samples when employing a radial universal kemel..
Building upon the traditional formulation of MMD, recent advancements incorporate learnable kernels to enhance its discriminative capability. Liu et al. [34] develop data-spliting strategy for kernel optimization and selection, effectively addressing the kernel adaptation challenges for complex-on scenarios. Kim et al. [75] propose an adaptive two-sample test designed for comparing two Hölder densities supported on the d-dimensional unit ball. In addition, Zhang et al. [48] introduce MMD-MP, multi-population aware optimization framework to further improve the stability of kernel-based MMD training. At present, MMD has been extensively applied to distributional measurement and discrepancy detection tasks across both textual and visual modalities [45, 48, 46].
C More Details for Experiment Settings
C.1 More Details on Datasets
GenVideo [25] is large-scale benchmark for Al-generated video detection, comprising 1.22 million real videos and 1.05 million Al-generated videos. The real video collection aggregates content from three established datasets: MSR-VTT (web video clips) [65], Kinetics-400 (human action videos) [62], and Youku-mPLUG (diverse online videos captured from Youku.com) [76]. The Al-generated portion features videos produced by 19 distinct generation models, including both open-source implementations (ZeroScope [77], 12VGen-XL [78]. SVD [1], VideoCrafter [7]. DynamiCrafter [8], Stable Diffusion(SD) [79], SEINE [63], Latte [80]. OpenSora [81], ModelScope [82]. HotShot [83], Show-1 [84]. Gen2 [85], Crafter [86]. Lavie [87]) and commercial closed-source systems (Pika, Sora, Moon Valley, MorphStudio). This dataset spans multiple generation paradigms, including text-to-vide video and image-to-video synthesis. Throughout all experiments, we filter videos with less than frames and only uniformly sample 8 frames for each video during training and testing.
C.2 More Details Evaluation Metrics
Video generation detection is inherently a binary classification task. Here, we introduce four fun- damental evaluation metries of binary classification: True Positive (TP) means correctly predicted positive instances (ground truth is positive, prediction is positive). True Negative (TN) means cor- rectly predicted negative instances (ground truth is negative, prediction is negative). False Positive (FP) means incorrectly predicted positive instances (ground truth is negative, prediction is posi- tive). False Negative (FN) means incorrectly predicted negative instances (ground truth is positive, prediction is negative).
AUROC denotes the Area Under the Receiver Operating Characteristic Curve [67, 88], which is widely used statistic for assessing the discriminatory capacity of distribution models. Formally,
AU = (P(())
where TP(()) (P()/CPO))))))))) + FN)()) is the true positive rate and FP(() FP(0/((P())) (t) false positive rate with a threshed t.
Accuracy (ACC) measures the model's s overall correctness in classification by calculating the ratio of correctly predicted instances (both true positive and true negative) to the total instances.
TP + TN
Accuracy TP+ + FF+FN
Recall [66] evaluates the model's ability to identify all relevant instances of class, measuring the proportion of true positives among all actual positive instances. It emphasizes minimizing false
27

---

negatives, ensuring comprehensive coverage of positive cases.
TP
Recall
TP + FN
Precision [66] quantifies the model's capability to avoid false positives by calculating the proportion of true positives among all predicted positive instances. ensures reliability positive predictions.
TP
Precision
T
F1-score [66] balances Precision and Recall using their harmonic mean, providing robust metric for scenarios with imbalanced class distributions. It penalizes extreme biases toward either precision or recall.
Precision Recall
Fl-score 2
Precision Recall
C.3 Implementation Details on NSG-VD
In our NSG-VD, employ the pre- praitrd diffusion model so of Guided Diffusion using the 256 256 unconditional checkpoint from the guided-diffusion library' following [56]. For a given video t-th frame, compute its score feature V log p(x, t) by diffusing 5/1, 000 and passing it through 8p- For the deep kernel @G. we employ a single-layer of Swin transformer [89], mapping input features of dimension 8 x 224 224 300-dimensional output.
diffusion timestep
We conduct our experiments on a server with 1x NVIDIA RTX 3090 GPU using Python 3. 3.10.17 and Pytorch 2.7. .0. We use Adam optimizer [90] to optimize the kernel parameters with batchsize 24, learning rate 0.0001, weight decay 0.1, dg = 0.1 and a 100. For the testing, we set the decision threshold - 1 in Eqn. (11). The overall algorithms for training and testing are in Alg, I and 2.
C.4 Pseudo Code of NSG-VD
Algorithm 1 Training deep kernel of MMD
Input: Real and generated videos S S
Algorithm 2 Detecting videos with NSG-VD
wa; < 10-10, learning rate for r = 1,2. Tmax do
Input: Referenced videos Sp testing videos St
decision f(-); deep kemel kw; threshold T; for x; in S6 do
kw +- kernel function using Eqn. (12);
M(w) + M.PP...Str sh";; kw);
Q++MMMD, (SF", fxx:; kw) using Equ, (10);
(w: (St str; kw) using Eqn. (13);
[x: SF Tw,T)= I > 7);
Jx(w) (w)/ (W((:::
Obtaining f(x:) using Eqn. (11);
+ V Adum JA (w):
end for
end for
Output: Predictions (x.)) of the testing
Output: KD
28

---

D More Experimental Results
D.1 More Results on Standard Evaluation
To demonstrate the statistical robustness and reproducibility of our proposed NSG-VD method, we report standard deviations of four metrics across 10 datasets with three different seeds (Table 5). The table shows that our NSG-VD achieves consistently high performance with minimal variance (e.g., 0.41% for Recall, 0.87% for Accuracy), indicating strong reliability and repeatability our methods.
Table 5: Standard deviations of NSG-VD with three different random seeds (%), where we train all models with 10, 000 real and generated videos from Kinetics-400 and SEINE, respectively.
Dataset
Recall
Accuracy
F1
AUROC
ModelScope
92.78 + 0.48
84.31 +: 1.88
85.54 + 1.54
92.49 + 3.07
MtrphStudio
99.44 + 0.96
86.53 2.64
88.10 2.14
97.08 + 0.92
MoonValley
100.00 + 0.00
87.64 + 0.64
89.00 0.50
99.05 = 0.30
HotShot
100.00 + 0.00
88.06 + 2.30
89.35 + 1.83
98.64 + 0.49
Show1 I
100.00 + 0.00
88.89 + 2.55
90.03 = 2.08
96.96 = 0,93
Gen2
98.61 + 1.73
87.08 + 2.20
88.43 + 1.86
95.27 + 2.17
Crafter
99.72 0.48
88.89 1 1.05
89.98 1 0.86
98.07 1 0.41
Lavie
98.61 0.96
88.75 2.17
89.77 1
95.32 + 2.92
Sora
94.05 + 1.03
84.12 1.97
83.85 - 1.56
93.10 = 1.36
WildScrape
91.67 + 2.21
85.41 + 2.60
86.29 + 2.37
92.75 + 0.31
Avg.
97.49 + 0.41
86.97 0.87
88.04 + 0.74
95.87 0.87
D.2 More Results on Impact of Spatial Gradients and Temporal Derivatives
To comprehensively analyze how spatial gradients and temporal derivatives contribute to detection performance across diverse generative paradigms, we include detailed results across 10 diverse generative paradigms in Table 6. The spatial gradients achieve strong performance across most generated models (e.g., 81.67% Recall on ModelScope, 97. 97.50% Recall on MorphStudio), with only minor performance gaps models like HotShot (72.23% Recall) and Show (74.17% Recall).
In contrast, the temporal derivatives show complementary strengths and relatively better detection capabilities on these challenging cases, notably achieving 75.40% Recall on HotShot and 77.60% Recall on Showl, 1, where temporal dynamics (c.g., rapid motion transitions in HotShot dataset) may play more pronounced role in exposing synthetic anomalies.
Notably, our proposed NSG-VD demonstrates superior reliability by integrating both components, achieving an average F1 -core of 90.87%, significant improvement over individual features. This highlights the complementary nature of spatiotemporal dynamics modeling, enabling consistent detection performance even when individual cues exhibit dataset-specific limitations.
Table 6: Impact of spatial gradients and temporal derivatives across 10 generated models (%), where we train all models with 10, 000 real and generated videos from Kinetics-4Di and Pika, respectively.
Method
Metric
Model Scope
Morph Studio
Moon Valley
HorShot
Show! 1
Gen2
Crafter
Lavic
Sora
Wild Scrape
Avg.
Recall
81.67
97.50
100.00
72.23
74.17
98.3 33
98.13
77.12
98.21
82.5 22.50
87.99
Spatial Gradients
Accuracy
77.50
89.58
$7.08
75.00
76.25
87.92
88.75
76.67
88.39
81.25
82.84
Fl
78.40
90.35
88.56
74.36
75.74
89.06
89.73
76.86
89.43
$1.48
83.40
AUROC
87.32
98.43
99.99
78.76
82.72
98.98
98
84.15
99.01
90.52
91.85
Recall
$2.60
40.20
58.40
75.40
77.60
49.00
72.40
47,20
60.71
70.00
60.35
Tmporal Derivative
Accuracy
79.90
77.30
Fl
61.74
50.89
66.29
78.05
79.43
58.75
76.13
57,21
66.67
74.55
66.97
AUROC
81.46
84.24
Recall
68.33
98.33
100.00
92.50 22.50
87.50
80.00
98.33
94.17
78.57
82. $2.50
88.02
NSG-VD (Ours)
Accuracy
81.67
98.33
96.67
91.67
90.83
88.33
95.83
94.17
88,39
88.75
91.46
Fl
78.85
98.33
96.77
91.74 74
90.52
87.27
95. 93
94.17
87.13
88. 00
90.87
AUROC
98.66
95.15
96.38
98.16
94.73
29

---

E
More Discussions on NSG-VD
E.1
Efficiency of NSG-VD
100
Method
All Params(M) 1
Tun. Params(M)
FI(%)
Better
De DeMamba-XCLIF
F1 Fl-score (%)
TALL
DeMamba
119.89
119.89
80.12
NPR
TALL
82.89
82.89
72.63
STIL
21.63
21.63
35.82
68.39
STIL
NSG-VD (Ouns)
20
40
60
80
100
120
140
Number of Tunable Parameters (M)
Figure 4: Comparisons with baselines in terms training costs and performance (%), where we train all models with 10, 000 real and generated videos from Kinetics-400 and Pika, respectively.
Performance vs. Training Cost Analysis. We compare the number of trainable parameters and detection performance of NSG-VD against state-of-the- baselines. As shown in Figure 4, our NSG-VD achieves 87% F1 Fc-se with only 0.25 M trainable parameters, demonstrating superior parameter e efficiency compared to methods like DeMamba (80.12% Fi-score, 119.89 M parameters) and TALL (72.63) 63% F1-score, 82.89 M parameters). This demonstrates that NSG- VD's physics-driven design enables high accuracy through minimal parameter tuning.
Existing baselines struggle balance parameter scale and performance. NPR achieves only 68.39% F1-score despite its minimal trainable parameters (1.37 M), while STIL requires 21.63 M parameters attain 35. 55.82% Fi-score- suboptimal trade-off compared NSG-VD's superior performance with 100x fewer parameters. These results underscore the limitations of conventional artifact-driver frameworks effective parameter budget utilization, further validating the importance our physics- guided spatiotemporal modeling paradigm for Al-generated video detection.
Performance Inference Time Analysis. We evaluate the efficiency of NSG-VD by analyzing
both detection performance and computational overhead under the same setting as Table 1. As shown in Table our NSG-VD achieves superior detection performance (e.g., 97.13% Recall, 87.45% F1-score) with practical inference latency of 0.3605s per video, which remains viable for non-real- time applications (e.g., judicial video evidence analysis) despite being slower than other baselines. This latency stems from our current implementation of pre- tre-trained diffusion models for gradient estimation-a design choice prioritizing theoretical validation over computational optimization.
Importantly, this current implementation prioritizes accuracy over speed to establish the theoretical and empirical validity of physics-guidee guided spatiotemporal modeling. Empirically, the inference speed can be greatly enhanced with minimal performance degradation by scaling the resolution of pre-traine tre-trained diffusion models, e.g., reducing resolution to 128 x 128 and 64 x 64 cuts inference time by 67.73% and 91.7%%, respectively, while retaining over 98.63% and 94.57% of the original AUROC (Table 7). This trade-off underscores the flexibility of our approach in balancing accuracy and efficiency according to application needs. Future work may further boost efficiency via diffusion model compression [91, 92, 93] or efficient architecture design [94, 95], highlighting NSG-VD' potential for practical deployment as video generation and detection requirements advance.
observe that
Table Comparisons with baselines terms of Inference time and performance, where we train all models with 10, 000 real and generated videos from Kinetics-400 and SEINE, respectively.
Method
Recall(%)
Accuracy(%}
F1(%) f AUROC(S)
Infer. Time (s) $
DeMamba
71.25
84,54
80.87
94.42
0.0311
NPR
59.31
77.95
71.33
89.92
0.0036
TALL
61.47
80.20
74.05
95.14
0.0044
STIL
42.35
71.08
55.81
94.94
0.0108
NSG-VD (64x64)
78.29
83.26
81.99
90.27
0.0298
NSG-VD (128x128)
84.93
86.99
86.25
94.15
0.1163
NSG-VD (256x256)
97.13
86.05
87.45
95.46
0.3605
30

---

E.2
Numerical Stability of NSG
Kinetics-400
SEINE
0.07
0.06
Frequency
0.05
0.04
0.03
0.01
0.00
-10
-10"
-10'
-101
-10"
10"
10a
10a
10*
Values a,log p(x, t)
Figure 5: Distribution of the values of temporal derivatives 0 log p(x, t) in the NSG statistic across 10, 000 real and generated videos from Kinetics-400 and SEINE, respectively.
To ensure the numerical stability the NSG statistic with the temporal derivatives O log p(x, f) in its denominator, we examine the distribution of values in 0 p(x, t) across 10, 000 real and generated videos from Kinetics-400 and SEINE, respectively. From Figure 5, nearly all values lie outside the critical near-zero range [-0.1, 0.1]. This indicates that almost no value in Ô log p(x, i) approaches zero in practice, effectively mitigating instability risks from division by vanishingly small values.
The observed distribution aligns with the physical intuition that temporal density changes in real synthetic videos inherently non-stationary, resulting in measurable temporal derivatives. Additionally, the regularization term >> 0 in the NSG denominator (Eqn. 6) further safeguards against edge cases where O log p(x, t) might marginally approach zero. These design choices collectively ensure robust numerical stability for NSG across diverse video distributions.
E.3
Impact of MMD for NSG-VD
To validate the inherent superiority of the NSG statistic independent of the training objective,
compare our framework trained with both Maximum Mean Discrepancy (NSG-VD) and standard binary cross-entropy loss (NSG-BCE) against baselines using BCE. From Table 8, NSG-BCE Mic-Beeaahheees superior performance across all metrics compared to state-of-the-ar baselines, even when adopting conventional training paradigm. For example, it achieves 77.67% average Recall and 82.70% Fl-score, significantly outperforming Demamba by 6.42% 1 in Recall and 1.83% t in Fl-score, and TALL by 16.20% t in Recall and 8.65% t in Fl-score. This demonstrates that the NSG statistic's ability to capture spatiotemporal dynamics remains effective regardless of the training objective.
Notably, NSG-BCE excels in challenging scenarios where other methods struggle. For instance, achieves 64.29% Recall on Sora (vs. 42.86% for Demamba) and 63. 60% Recall on WildSerape (vs. 48.00% for Demamba), highlighting its ability generalize beyond superficial artifacts. The performance gap widens further in NSG-VI VD (97.13% Recall), where MMD explicitly models distributional shifts by the NSG feature in a producing kernel Hilbert space and enables more precise separation between real and synthetic videos. These results confirm that the NSG statistic's physics- driven design captures fundamental spatiotemporal dynamics, providing intrinsic advantage over conventional features regardless of the training strategy.
31

---

Table 8: Impact MMD in our NSG-VE VD across 10 generated paradigms (%), where we train all models with 10, 000 real and generated videos from Kinetics-400 and SEINE, respectively.
Model
Morph Studio
Moon Valley
Wild Scrape
Method
Metric
HotShot
Show
Gen2
Crafter
Lavie
Sora
Avg.
Scope
Recall
47.40
87.80
88.20
77.40
75.00
85.60
91.60
68.60
42.86
48.00
71.25
Accuracy
72.80
93.00
93.20
87.80
86.60
91.90
94.90
83.40
68.75
73.10
84.54
DeMamba
Fl
63.54
92.62
92.84
86.38
84.84
91.36
94.73
80.52
$7.83
64,09
80.87
AUROC
98.76
99.35
96.87
80.93
88.11
94.42
Recall
46.40
58.80
27.40
59.31
NPR
Accuracy
71.40
86.40
83.10
80.10
76.20
85.70
90.10
77.60
66.96
61.90
77.95
61.87
84.89
80.51
76.22
70.18
83 99
89.43
72.41
51.95
41.83
71.33
AUROC
85.73
93.79
91.44
89.96
95.13
96.87
89.46
84.15
76.66
89.92
Recall
58.60
75.00
79.40
60.20
62,00
77.80 80.8
88.20
43.80
33.93
35.80
61.47
Accuracy
78.80
87.00
89.2
79.60
80.50
88 40
93.60
71.40
66.07
67.40
80.20
TALL
73.43
85.23
88.03
74.69
76.07
02
93.23
60.50
50.00
52.34
74.05
AUROC:
97.10
98.12
98.63
96.37
96.45
97.76
99.38
94,80
83.35
89.45
95. 14.14
Recall
28.60
57.40
78.40
46.80
18.80
66.40
69.00
24,80
14.29
19.00
42.35
Accuracy
64.20
78.60
89.10
73.30
59.30
83.10
84.40
62.30
$7.14
59.40
71.08
STIL
44,41
72.84
87.79
79.71
39.68
25.00
31.88
55.81
AUROC
95.53
97.91
99.40
96.49
92.79
98.06
98.86
91.00
92.79
86.58
94.94
Recall
53.40
96.40
94,80
90.60
77. .0.6
79.40 40
83.20
73,40
64.29
63.60
77.67
NSG-BCE (Ours)
Accuracy
72.70
94,20
93.40
91.30
84,80
70
87.60
82.70
74.11
77.80
84.43
F1
66.17
93.49
83.62
84.74
87.03
80,93
71.29
74.13
82.70
AUROC
84,67
98.79
97.77
96.90
92.69
93.00
93.86
91.32
83.58
87.99
92.06
Recall
91.67
100.00
100.00
100.00
100.00
98.33
100.00
97,50
94.64
89.17
97.13
NSG-VD (Ours)
Accuracy
82.50
88.33
89.58
84.58
86.25
87.08
86.67
87.92
89.29
78.33
86.05
F1
83.97
89.55
90.57
86. 64
87.91
88, 39
88.24
88.97
89.83
80.45
87.45
AUROC
90.67
97.62
98.38
95.88
96.69
97.87
97.64
95.09
96.14
88.65
95.46
E.4 Impact of Size of Reference Set for NSG-VD
We investigate the impact of reference size by evaluating subsets containing between 10 and 500 samples, with other settings remaining consistent with Table 1. Performance assessed using comprehensive criteria, including AUROC, Accuracy, F1 Score, and Recall. Intuitively, larger reference set enables more accurate estimation the underlying distribution of real videos, thereby supporting more stable and reliable detection. In contrast, smaller reference sets may introduce substantial sampling and estimation biases. As shown in Figure 6, our NSG-VD demonstrates consistently robust performance across varying reference set sizes, with the exception of extreme cases involving very limited samples (e.g., n 10). Consequently, we set 100 for all experiments.
1.00
0.95
0.90
Value
0.80
0.75
AUROC
0.70
Accuracy
F1 score
0.65
Recall
0.60
100
200
300
400
500
Size of reference set
Figure 6: Impact of reference set size for NSG-VD, where we train all models with 10, 000 real and generated videos from Kinetics-400 and Pika, respectively.
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E,5 Impact of Diversity of Real Videos in the Reference Set
We conduct additional ablation studies on real-domain mixed reference sets, revealing key strength of ASG-VD: strong generalization to unseen generated video domains when most real test samples are covered by the reference distribution. Specifically, we train on Kinetics-400 (real) and SEINE (generated) videos, and test MSR- VTT (real) and 10 generated videos using reference sets with varying ratios of ASSRVVTT and Kinetics-400. From Table even a small proportion (3 7) yields satisfactory performance 184.19% of Accuray, 81.12% of F1-Score) compared with baselines, which quickly saturates. This confirms that NSG-VI VD needs only modest in-domain real coverage, while the fake side can remain highly heterogeneous. These results will be included in our revision.
Table Performance under different domain coverage ratios between MSR-VTI and Kinetics-400.
Domain Coverage
0:10
3:7
5:5
7:3
10:0 (Full)
DeMamba
TALL
(MSR-VTT Kinetics-400)
(Low)
(Medium)
(Balanced)
(High)
Average Accuracy (%)
77.82
84.19
85.57
87.06
86.05
84.21
80.20
Averuge F1-Score (%)
75.68
81.12
83.36
85.41
87.45
80.87
74.05
E.6 Discussions on Assumption of the Divergence Term
We assume Vx v is subdominant in smoothly varying video distributions for three reasons: First, its direct estimation is ill- ill-posed in high-dimensional video data. Solving 0,x v(x,t) t) is an underdetermined inverse problem, and video noise (e.g., blur or compression) further amplifies estimation errors, making explicit divergence computation unstable and infeasible [32, 29J. Second, many physical flows approximate incompressibility (Vx v As 0), a simplification grounded in fluid dynamics [29] and quantum mechanics [55] that preserves physical interpretability. Third, our NSG remains robust even if Vx v & 0, as it captures cumulative spatiotemporal inconsistencies across all terms Eqn. (3). Experiments confirm the resilience of NSG-VD to deviations from this assumption.
F Limitations and Future Directions
While our proposed NSG-VD method demonstrates strong performance across diverse Al Al-generated vidco detection scenarios, several limitations and opportunities for future work remain:
Limitations. First, the current formulation of the NSG statistic relies on simplified physical as- sumptions (e.g., the incompressible flow approximation in continuity equations), which may fail to capture highly dynamic or discontinuous motion patterns in complex real-world scenarios. Second, the effectiveness of NSG-VD critically depends on the quality of pre-trained diffusion models used for score estimation; domain shifts or limited training data may degrade the reliability of estimated NSG features. Third, while NSG-VD achieves competitive performance, its reliance on diffusion models introduces computational overhead, making it less suitable for large-scale real-time detection tasks. Lastly, while our deep kernel design improves detection performance, architecture could be further optimized to better adapt to heterogeneous spatiotemporal patterns.
Future Directions. To address these limitations, future work could explore more sophisticated physi- cal models that account for compressible flows or discontinuous motion dynamics [54], enhancing complex scenarios. Additionally, developing effective domain- specific fine-tune the-tunin strategies [96, 97, 98, 99] could improve the reliability of score estimation under distribution shifts. For real-time deployment, investigating lightweight diffusion model compression techniques (e.g., pruning [91, 100], quantization [92, 93]) would reduce computational costs. Finally, advancing the design of the deep kernel network such as incorporating attention mechanisms [101] or hierarchical feature fusion could further optimize the MMDD-ased detection framework, enabling better performance for Al-generated video detection.
the NSG statistic's 's adaptability
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G
Broader Impacts
The development Al-generated video detection methods like NSG-VD has significant societal, ethical, and technical implications. Our work contributes to mitigating the risks of malicious deepfake content, such as misinformation, identity theft, and political manipulation, by enabling more reliable verification of video authenticity. By leveraging physics- informed principles, NSG-VD provides reliable framework for detecting synthetic videos that may otherwise evade traditional artifact-based detection methods. This could strengthen trust in digital media, support content moderation efforts, and aid legal or journalistic investigations involving video evidence.
physics-informed
This research aligns with broader efforts to establish trustworthy multimedia ecosystems. By bridging physics principles with machine learning, NSG-VD advances interpretable detection mechanisms a critical step toward auditing AI-generated content while fostering public awareness of synthetic media risks. We encourage interdisciplinary collaboration among researchers, ethicists, and legislators to ensure such technologies serve as safeguards rather than instruments of control.
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H
Visualizations
Demamba
NPR
TALL
STI.
NSG-YD (Ours)
Fake
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2300
Demamba
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Fake
Fake
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(Ours)
Real
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Figure 7: Results of the detection on real videos from the MSR-VTT dataset.
Demamba
(Ours)
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Demamba
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NSC-VD (Ours)
Demamba
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NSG-VD (Ours)
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Fake
Figure 8: Results of the detection on generated videos from the Crafter dataset.
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100
Demamba
NPR
TALL
STIL
NSG-VD (Ours)
MVVVOR
MLOB
WDOB
WDOR
WDOR
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NSG-YD (Ours)
Demamba
NPR
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NSG-VD (Ours)
Fake
Fake
Real
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Fake
Figure 9: Results of the detection on generated videos from the Gen2 dataset.
Demamba
NPR
TALL
STIL
NSG-VD (Ours)
Demamba
TALL
STIL
NSG-VD (Ours)
Real
Real
Real
Real
Fake
Demamba
TALI
STIL
NSG-VD (Ours)
Real
Real
Real
Real
Fake
Figure 10: Results of the detection generated videos from the HotShot dataset.
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Demamba
NPR
TALL
STIL
NSG-VD (Ours)
Fake
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Fake
Real
Fake
Demamba
NPR
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STIL
NSG-YD (Ours)
Demamba
NPR
TALL
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NSG-VD (Ours)
Figure 11: Results of the detection generated videos from the Lavic dataset.
Demamba
NPR
TALI
STIL
NSG-VD (Ours)
Fake
Real
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Fake
Demamba
NSG-VD (Ours)
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Demamba
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NSG-VD (Ours)
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Fake
Figure 12: Results of the detection generated videos from the ModelScope dataset.
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Demamba
NPR
TALL
STIL
NSG-VD (Ours)
Demamba
NPR
TALL
STIL
NSG-YD (Ours)
Demamba
NPR
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NSG-VD (Ours)
Fake
Fake
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Real
Fake
Figure 13: Results of the detection on generated videos from the Moon Valley dataset.
Demamba
NSG-VD (Ours)
Fake
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Real
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Fake
Demamba
TALL
STIL
NSG-VD (Ours)
Fake
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Demamba
NPR
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STIL
NSG-VD (Ours)
Figure 14: Results of the detection generated videos from the MorphStudio dataset.
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Demamba
NPR
TALL
STIL
NSG-VD (Ours)
Real
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Real
Real
Fake
Demamba
NPR
TALL
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NSG-YD (Ours)
Demamba
NPR
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NSG-VD (Ours)
Figure 15: Results of the detection on generated videos from the Showl dataset.
NSG-VD (Ours)
Fake
Real
Fale
Real
Fake
Demamba
NSG-VD (Ours)
Real
Real
Real
Real
Fake
Demamba
NPR
TALI
STIL
NSG-VD (Ours)
Real
Real
Real
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Fake
Figure 16: Results of the detection on generated videos from the Sora dataset.
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Demamba
NPR
TALL
STIL
NSG-YD (Ours)
Demamba
NPR
TALL
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NSG-VD (Ours)
Demamba
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NSG-YD (Ours)
Real
Real
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Fake
Figure 17: Results the detection on generated videos from the Seaweed dataset.
Demamba
NPR Real
TALL
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Demamba
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Demamba
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Figure 18: Results of the detection on generated videos from the Seaweed dataset.
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NSG-VD (Ours)
Real
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Demamba
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STII
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NSG-VD (Ours)
Real
Real
Real
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Fake
Figure 19: Results the detection on generated videos from the WildScrape dataset.
To further demonstrate the excellent performance of our NSG-VD, we present visual detection results on both real and generated videos across all 10 datasets. As illustrated Figures 7-19, both the baselines and NSG-VD demonstrate satisfactory detection on real video samples. For generated videos. the existing baselines achieve reasonable performance on early generation models (e.g.. Crafter, Gen2, and Moon Valley), but exhibit significant performance degradation when applied to more advanced generative models (e.g., Show Sora, and WildScrape). contrast, NSG-VD consistently achieves strong detection performance across all generation levels.
On this basis, we consider the recently proposed Seaweed [102] method (as shown in Figures 17, 18), which generates highly realistic long-form videos. All four baselines exhibit near-complete failure on this dataset, whereas NSG-VD continues to deliver effective detection performance.
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Answer: [Yes]
The paper provides complete theoretical results for the NSG feature lower bound (Theorem 1 in Section 3.4), including assumptions (e.g.. Gaussia-ddittriuteed real/fake videos and temporal derivatives constraints). The proof is detailed in Appendix A.7, including all mathematical derivations and references to supporting lemmas. All theorems and lemmas are numbered and cross-referenced, and proofs are accessible in Appendix A.
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Reviews:
[{"review_id": "dUKHK1GN1d", "reviewer": "Reviewer_oZqK", "summary": "The paper proposes a metric termed Normalized Spatiotemporal Gradient (NSG) and defines it as the ratio of spatial probability gradients to temporal density changes. This metric is used to capture deviations from natural video dynamics. The motivation for this metric is the insight that \"natural video dynamics preserve the product between the velocity field and the ratio of spatial probability gradients to temporal density changes.\"\n\nAn NSG estimator is designed using pretrained diffusion models. NSG-VD for video detection is then proposed using MMD between NSG features of test and real videos. It is claimed that generated videos have amplified discrepancies due to distribution shifts.\n\nThe performance of the proposed NSG-VD is shown to be competitive across numerous datasets using several quantitative metrics.", "questions": "- Are you assuming a Newtonian fluid in this work? Please clarify.\n\n- Why and when is log introduced in the flow equation? If you are replacing p(x, t) with log (p(x, t)), does it impact the basic fluid-flow assumption? A basic review of fluid flow field constraints does not contain logarithmic terms. Please explain.\n\n- Have you considered and compared your approach with the standard optical flow constrained equation? Please consider a comparison with optical flow given that the typical constraint imposed on it is the smoothness condition combined with the intensity motion.\n\n- Why is Figure 1-b chosen to convey the intuition for this approach? Firstly, it is synthetic. Secondly, the reader cannot possibly compute the terms on the left hand side and check if it is indeed zero. Please provide better illustrations since the proposed methods fully rests on this idea.\n\n- Can you please provide justification for the following assumption? \"Assuming that the divergence term is subdominant\nin smoothly varying distributions \"\n\n- Why is equation (7) referring to definitions made after it ((8) and (9))? Please rearrange the order.", "limitations": "Yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths:**\n- The premise that natural (real) videos have a unique spatiotemporal distribution and that the flow of probability mass is governed by fluid-type physics is interesting.\n\n- The results are encouraging.\n\n**Weaknesses:**\n- While the premise in indeed interesting, it is not sufficiently substantiated either empirically or analytically. It is not intuitive as to why natural videos are expected to obey equation (2). Without this clarity, readers will not be able to appreciate the contribution.\n\n- Further, the logarithm of the distribution is used to go from (2) to (3). This is again not justified. Specifically, since the work is physics-inspired, this transition must be justified in terms of its impact on modeling fluid flow. \n\n- The success of this method is dependent on the threshold $\\tau$. As with any threshold-based approach, the choice of the threshold has a direct impact on performance. There is no discussion of this. Further, the choice of the threshold is given in the supplementary material.\n\n- Please check for a typo in Table 4 (\"gredients\").", "was_revised": true, "final_justification": "Based on the responses and clarifications, the rating has been revised upwards. I still think that the overall idea, which is interesting, can be conveyed more clearly.", "rebuttal": "We thank the reviewer for the detailed comments. Responses are below:\n>Q1. While the premise in indeed interesting, it is not sufficiently substantiated either empirically or analytically. It is not intuitive as to why natural videos are expected to obey equation (2).\n\n**A1.** We appreciate the reviewer's insightful comment regarding the foundation of the continuity Equation (2), i.e., $\\frac{\\partial p}{\\partial t}+\\nabla_{\\mathbf{x}}\\cdot\\mathbf{J}=0$. This is not a video-specific assumption but a **universal mathematical formulation of probability mass conservation**, which holds for **any time-evolving probability density** $p(\\mathbf{x}, t)$. It is **general and well-established** in statistical physics ([r1], Eqn.(1.16), Page 12) and Fokker-Planck equation（[r2], Eqn.(4.103), Page 84), where $\\mathbf{J}=p \\mathbf{v}$ ensures global conservation of the total probability over time. This principle is **universally valid without video-specific assumptions**. In fact, other reviewers recognize this strong physical grounding:\n* The proposed approach is **intuitive**, drawing on the principles of probability flow conservation [*Reviewer 74ip*].\n* The method is **well-grounded in physical principles**, like the probability flow conservation; The authors support their approach with a theoretical analysis, which, despite its simplifying assumptions, provides a **solid justification** [*Reviewer 1Wda*].\n* The paper is **well-motivated**; A statistic based on probability flow conservation principles [*Reviewer iZEA*].\n\nTo clarify its relevance to videos, we highlight two perspectives:\n* **Analoging fluid mechanics to videos**. Just as the continuity equation describes local density change equals net inflow/outflow, we treat pixel probability density $p(\\mathbf{x},t)$ as a \"visual mass\" and motion as a flow field $\\mathbf{v}$. Here, $\\mathbf{J}=p\\cdot\\mathbf{v}$ quantifies probability flux driven by inter-frame motion. This analogy grounds foundational video models like optical flow ([r3], Sec. 4, page 3).\n* **Intuitive interpretation for video dynamics.** Natural videos are inherently continuous—objects move coherently and pixels change smoothly over time. This implies that \"visual probability mass\" redistributes conservatively along motion trajectories rather than appearing or vanishing abruptly. Equation (2) mathematically encodes this intuition from spatial redistribution $\\nabla_{\\mathbf{x}}\\cdot\\mathbf{J}$ and temporal evolution $\\frac{\\partial p}{\\partial t}$.\n\nWe will include this discussion in our revised version.\n\n[r1] Fluid dynamics: an introduction. Springer, 2014.\n\n[r2] Fokker-planck equation. Springer Berlin Heidelberg, 1996.\n\n[r3] Determining optical flow. Artificial intelligence, 1981.\n\n>Q2. Logarithm use in (2)→(3) is unjustified. Why introduce it? Does it impact fluid-flow assumptions?\n\n**A2.** The logarithm is **not an artificial introduction but a direct mathematical consequence** of applying the chain rule to the continuity equation, without altering the underlying physics. To clarify, for $\\frac{\\partial p}{\\partial t}+\\nabla_{\\mathbf{x}}\\cdot\\mathbf{J}=0$, we substitute $\\mathbf{J}=p\\mathbf{v}$ and then divide the entire equation by $p$ (which is strictly positive everywhere in its support), yielding: $$\\frac{1}{p}\\partial_t p+\\frac{1}{p}\\nabla\\cdot(p\\mathbf{v})=0.$$ Applying the vector calculus product rule $\\nabla_{\\mathbf{x}}\\cdot(p\\mathbf{v})=p(\\nabla_{\\mathbf{x}} \\cdot \\mathbf{v})+\\mathbf{v}\\cdot(\\nabla_{\\mathbf{x}}p)$ and the chain rule of calculus, $\\frac{1}{p}\\frac{\\partial p}{\\partial t}=\\partial_t\\log p$ and $\\frac{\\nabla_{\\mathbf{x}} p}{p}=\\nabla_{\\mathbf{x}}\\log p$, we obtain Eqn.(3)： $$\\partial_t\\log p+\\nabla_{\\mathbf{x}}\\cdot\\mathbf{v}+\\mathbf{v}\\cdot\\nabla_{\\mathbf{x}}\\log p=0.$$ Moreover, this transformation does **not alter the underlying fluid-flow constraint**—it is a variable change making explicit how velocity couples to log-density's temporal and spatial gradients.\n\n>Q3. Threshold τ affects performance, but its choice is undiscussed and in supplements.\n\n**A3.** Thanks for pointing out the importance of threshold selection. Our NSG-VD maintains **remarkably stable performance across a wide range of τ values** without requiring fine-grained tuning. As shown in Tables I, II, NSG-VD consistently high detection performance as $τ\\in[0.7, 1.2]$ for average Accuracy and F1-Score across diverse generators compared with DeMamba. These results indicate that NSG features create a **clear separation between real and fake distributions**. In practice, we set $τ=1.0$ as the default. We will add these results to the main text.\n\nTable I. Effect of τ on average metrics (Table 1 settings (%)) (vs. DeMamba: 84.21 Acc / 80.12 F1). \n|τ|0.4|0.5|0.6|0.7|0.8|0.9|1.0|1.1|1.2|1.3|\n|-|-|-|-|-|-|-|-|-|-|-|\n|Accuracy|78.16|84.95|88.63|90.62|91.03|91.60|91.46|90.48|89.44|87.55|\n|F1|81.80|86.59|89.37|90.82|90.88|91.21|90.87|89.43|87.82|85.17|\n\nTable II. Effect of τ on average metrics (Table 2 settings (%)) (vs. DeMamba: 84.54 Acc / 80.87 F1).\n|τ|0.4|0.5|0.6|0.7|0.8|0.9|1.0|1.1|1.2|1.3|\n|-|-|-|-|-|-|-|-|-|-|-|\n|Accuracy|50.45|60.81|69.04|75.11|79.05|83.31|86.05|88.97|89.36|78.08|\n|F1|66.87|71.82|76.29|79.97|82.52|85.47|87.45|89.60|89.12|70.64|\n\n>Q4. Are you assuming a Newtonian fluid?.\n\n**A4.** No, **our method does not assume Newtonian fluids** (which invloves  linear stress-strain relationship). We only leverage the continuity equation, a universal mass/probability conservation that holds for any continuous medium (**Newtonian/non-Newtonian** fluids, or abstract probability flows). This equation governs the fundamental relationship between density evolution ($\\partial_t p$) and spatial flux ($\\nabla\\cdot\\mathbf{J}$), independent of material-specific properties like viscosity. \n\n>Q5. Have you considered and compared your approach with the standard optical flow constrained equation?\n\n**A5.** We do not rely on the standard optical-flow constrained equation [r3] for two key reasons: **fundamental limitations in exposing AI-generated anomalies** and **computational/robustness concerns**. Moreover, our experiments show NSG-VD's superiority over optical-flow-based methods.\n* **Limitations of Optical Flow Modeling:**\n    - **Local intensity focus**: Optical flow focuses on local pixel intensity changes under a smoothness prior; as a low‐level motion estimator, it often misses the subtle distributional anomalies from modern generative models. \n    - **Cost and sensitivity**: Dense flow estimation is computationally costly and sensitive to noise and minor misalignments, exposing the limitation that the generated models exploit.\n* **Empirical superiority over optical-flow baselines:** We compare NSG‑VD with an SOTA optical flow method [r4] trained on the same Kinetics‑400+Pika splits. From Table III, NSG‑VD outperforms [r4] by **3.6%** in Accuracy and **8.81%** in F1‑Score. This substantial margin demonstrates the advantages of our physics‑driven NSG in capturing spatiotemporal distribution discrepancies over traditional optical-flow constraints.\n\nTable III. Comparisons with [r4] on average metrics (Table 2 settings (%)). \n|Method|Accuracy|F1‑Score|\n|-|-|-|\n|AIGVDet|82.45|78.64|\n|**NSG-VD (ours)**|**86.05**|**87.45**|\n\n[r4] AI-Generated Video Detection via Spatio-Temporal Anomaly Learning. PRCV, 2024.\n\n>Q6. Why is Figure 1-b chosen to convey the intuition? Provide better illustrations.\n\n**A6.** Figure 1-b  was intended purely as a conceptual schematic of probability-flow conservation (our theoretical foundation) **not as a direct validation**. To avoid confusion, we will  **connect the theoretical foundation with our practical detection mechanism**, e.g., placing the conservation equation alongside video frames to link theory to video dynamics and highlighting the NSG feature as the key discriminative metric derived from this principle. We hope this can bridge the abstract physics-inspired model to our detection mechanism, and welcome further suggestions to strengthen this intuition.\n\n>Q7. Can you please provide justification for the assumption of the divergence term?\n\n**A7.** We assume $\\nabla_{\\mathbf{x}}\\cdot\\mathbf{v}$ is subdominant in smoothly varying video distributions based on three considerations: 1) **its estimation is ill-posed** in high dimensions, 2) **many physical flows approximate incompressibility**, and 3) our NSG **remains robust** even if $\\nabla_{\\mathbf{x}}\\cdot \\mathbf{v}\\neq0$.\n* **Ill‑posed estimation:** Directly estimating $\\nabla_{\\mathbf{x}}\\cdot\\mathbf{v}$ is **provably ill-posed** for high-dimensional video data. Solving $\\partial_t\\mathbf{x}=\\mathbf{v}(\\mathbf{x},t)$ is an underdetermined inverse problem with infinite solutions. Video noise (e.g., blur, compression) further amplifies errors, making explicit divergence estimation unstable and computationally infeasible [r1, r3].\n* **Theoretical precedence**: The $\\nabla_{\\mathbf{x}}\\cdot\\mathbf{v}\\approx 0$ is well-established physical and theoretical grounding in fluid dynamics [r1] and quantum mechanics [r5], simplifying estimation while preserving physical interpretability.\n* **Framework robustness:** Unlike methods relying strictly on $\\nabla_{\\mathbf{x}}\\cdot\\mathbf{v}=0$, NSG-VD captures cumulative violations across all terms in Eqn. (3). Even if $\\nabla_{\\mathbf{x}} \\cdot \\mathbf{v}\\neq0$, its contribution is subsumed by NSG’s integration of spatiotemporal inconsistencies, with experiments confirming resilience to this assumption.\n\n[r5] Quantum mechanics: foundations and applications. Springer Science & Business Media, 2013.\n\n>Q8. Why is equation (7) referring to definitions made after it ((8) and (9))? Please rearrange the order. Please check for a typo in Table 4 (\"gredients\").\n\n**A8.** We will move (8)-(9) before (7) for clarity and correct the typos.\n\n---\n**We hope our response has clarified the confusion and addressed your concerns. We would greatly appreciate it if you could kindly reconsider your score. Thank you.**"}, {"review_id": "JxvmDo2rFe", "reviewer": "Reviewer_74ip", "summary": "The paper addresses the challenge of detecting AI-generated videos generated using diffusion models. Inspired from the principle of probability flow conservation in physics, the authors propose Normalized Spatiotemporal Gradient (NSG) statistics, which quantifies the ratio of spatial probability gradients to temporal density variations, enabling effective modeling of a video's spatiotemporal dynamics. Spatial gradients are estimated using a pretrained diffusion model, while temporal dynamics are captured through motion-aware techniques based on brightness constancy assumption avoiding the explicit flow computation.\n\nThe authors introduce NSG-based Video Detection (NSG-VD), which employs Maximum Mean Discrepancy (MMD) between features of real and test videos as a detection metric. Extensive evaluations are conducted on real videos from Kinetics-400 and generated videos from Pika and SEINE, using metrics such as Recall, Accuracy, F1-score, and AUROC, under both balanced and imbalanced data settings. The approach is compared against existing state-of-the-art methods.\n\nA theoretical justification is also provided, showing that NSG feature distances between real and generated videos are upper-bounded, and that generated videos exhibit amplified discrepancies under distribution shifts.", "questions": "Please refer to the points listed in the weaknesses above.", "limitations": "Yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 4, "significance": 4, "originality": 3, "strengths_and_weaknesses": "Strengths\n\n1. The paper identifies a relevant research problem that AI-generated videos often exhibit near-perfect visual realism while violating physical laws, making their reliable detection essential. The proposed approach is intuitive, drawing on the principles of probability flow conservation.\n2. The paper is well-motivated and clearly articulated, backed by extensive evaluations, theoretical analysis, efficiency studies, and visualizations. The proposed NSG-VD approach demonstrates strong performance in detecting AI-generated videos, achieving high Recall, Accuracy, F1-score, and AUROC under both standard and data imbalanced evaluation settings.\n\nWeaknesses\n\n1.  Does the proposed NSG-VD also take into account the camera motion along with the object motion in the videos? Does change in the spatiotemporal dynamics of the videos induced through camera motion accounted for in Equation 6 and Equation 7?\n2. An analysis of the types of pretrained diffusion models used to compute NSG \nstatistics and their impact on detection performance would provide valuable insight \ninto the generalizability of the proposed method.\n3. Can NSG-VD be applied to fully unsupervised scenarios?", "was_revised": true, "final_justification": "Most of my concerns regarding change in the spatiotemporal dynamics of the videos induced through camera motion, analysis of different pre-trained diffusion models for computing NSG statistics and applicability of NSG-VD to fully unsupervised scenarios have been satisfactorily resolved. Therefore, I will raise my current score and support its acceptance.", "rebuttal": "We thank the reviewer for the encouraging comments and suggestions. Responses are below:\n>Q1. \"...**intuitive**, drawing on the principles of probability flow conservation...\", \"the paper is **well-motivated and clearly articulated**, backed by **extensive evaluations, theoretical analysis, efficiency studies, and visualizations**\", \"...demonstrates **strong performance** in detecting AI-generated videos...\".\n\n**A1.** We sincerely appreciate your thoughtful and encouraging comments on our work. Your acknowledgment of the strong performance of NSG-VD and your recognition of our paper as well-motivated and clearly articulated are deeply appreciated. We are also grateful for highlighting our work backed by extensive evaluations, theoretical analysis, efficiency studies, and visualizations. The comments that remark on our approach are intuitive, drawing on the principles of probability flow conservation is especially motivating, encouraging us to further advance our research in this domain.\n\n>Q2. Does the proposed NSG-VD also take into account the camera motion along with the object motion in the videos? Does change in the spatiotemporal dynamics of the videos induced through camera motion accounted for in Equation 6 and Equation 7?\n\n**A2.** We thank the reviewer's insightful comment. The proposed NSG-VD inherently accounts for **both object motion and camera motion through its physics-driven formulation**. Here's how our approach handles camera-induced dynamics: \n* **Unified physical modeling**: Our physics‐driven formulation $\\frac{\\partial p}{\\partial t} + \\nabla_{\\mathbf{x}} \\cdot \\mathbf{J} = 0$ models the *net* spatiotemporal evolution of pixel probability density, which **naturally incorporates all motion components**--whether arising from objects, cameras, or their interaction. In this view, camera motion simply appears as a global coordinate transformation in the velocity field $\\mathbf{v}(\\mathbf{x}, t)$, which is absorbed into the probability flow $\\mathbf{J} = p\\mathbf{v}$ and preserved in continuity constraints.\n* **NSG's motion-agnostic property**: The NSG statistic $\\mathbf{g} = \\frac{\\nabla_{\\mathbf{x}} \\log p}{-\\partial_t \\log p + \\lambda}$ quantifies **relative changes** in probability density rather than absolute motion. Since camera-induced motion tends to produce a coherent, approximately uniform shift in the spatial gradient $\\nabla_{\\mathbf{x}}\\log p$ across the frame, NSG remains **invariant** to such global flows. Meanwhile, subtle violations of conservation, e.g., those introduced by AI synthesis, still manifest as localized deviations in this ratio, allowing NSG to remain sensitive to the anomalies.\n* **Implementation-level robustness**: Both components of our estimator naturally incorporate camera motion. The pre-trained diffusion model’s score function $\\nabla_\\mathbf{x} \\log p$ captures underlying texture geometry regardless of motion source, and our brightness-constancy–based temporal derivative $(\\mathbf{x}_{t+\\Delta t}-\\mathbf{x}_t)/\\Delta t$ reflects all observed pixel displacements from objects or the camera itself. Together, these ensure that NSG‑VD robustly handles combined object and camera motions without requiring any separate stabilization or motion‐segmentation preprocessing.\n\nWe will clarify this in the revised manuscript, emphasizing that NSG-VD’s strength lies in its ability to model generic spatiotemporal constraints that hold regardless of motion origin.\n\n>Q3. An analysis of the types of pretrained diffusion models used to compute NSG statistics and their impact on detection performance would provide valuable insight into the generalizability of the proposed method.\n\n**A3.** We thank the reviewer for this valuable suggestion regarding the pre-trained diffusion models. We discuss this with three key insights: 1) **framework agnosticism to score function sources**, 2) **diffusion model selection criteria**, and 3) **empirical consistency** across different pretrained diffusion models.\n\n* **Architecture‑agnostic framework**: Our NSG‑VD pipeline requires only access to the score function $\\nabla_{\\mathbf{x}}\\log p(\\mathbf{x},t)$. Once this gradient is obtained, regardless of the underlying diffusion architecture, we compute the NSG features $\\mathbf{g}(\\mathbf{x},t)$ (Eqn. 4) and train a **lightweight deep‑kernel** MMD detector on these features. This design decouples the detection mechanism from any specific diffusion implementation.\n* **Diffusion model selection criteria**: We prioritize **unconditional, pixel-space diffusion** models because they directly estimate $\\nabla_{\\mathbf{x}} \\log p(\\mathbf{x}, t)$ in the pixel domain—critical for capturing spatiotemporal dynamics in videos. In contrast, recent latent-space models (e.g., Stable Diffusion [r3], EDMv2 [r4]) perform diffusion in compressed latents, requiring additional decoding and Jacobian projections to recover pixel-space scores, introducing additional complexity and potential approximation errors. We view this as compelling future work. \n* **Empirical validation across diffusion models**: In our main experiments, we use an ImageNet‑pretrained Guided Diffusion model [r1] and achieve strong detection performance (Tables 1–2). To further validate generalizability, we supplement additional experiments with an Improved DDPM-based pre-trained diffusion model [r2] on the same dataset, obtaining **consistent performance** of 84.26% average Accuracy and 81.99% F1-score. These results confirm that NSG‑VD’s efficacy stems from the **universal gradient‑estimation capability** of diffusion models, not model‑specific design and that our current pixel‑space diffusion model is **sufficient to capture the spatiotemporal dynamics needed** for robust detection.\n\nWe will include these findings in the revised manuscript to highlight the framework’s generalizability and its current practical scope.\n\nTable I. Effect of different diffusion Models, with the same setting as Table 2 (%). \n|Method|Accuracy|F1‑Score|\n|-|-|-|\n|DeMamba (Baseline)|84.21|80.12|\n|NSGVD (Improved DDPM, 64x64)| 84.26|81.99|\n|NSGVD (Guided Diffusion, 256x256)|86.05|87.45|\n\n[r1] Diffusion Models Beat GANs on Image Synthesis.NeurIPS, 2021.\n\n[r2] Improved Denoising Diffusion Probabilistic Models. ICML, 2021.\n\n[r3] Scaling Rectified Flow Transformers for High-Resolution Image Synthesis. ICML, 2024.\n\n[r4] Guiding a Diffusion Model with a Bad Version of Itself. NeurIPS, 2024.\n\n>Q4. Can NSG-VD be applied to fully unsupervised scenarios?\n\n**A4.** We appreciate the reviewer’s insightful question regarding fully unsupervised scenarios. In principle, NSG‑VD can be applied in a fully unsupervised setup: 1）**using a Gaussian‑kernel MMD** on raw NSG features without any deep‑kernel training, and 2) **integrating unsupervised adaptation techniques** to learn discriminative mappings at test time.\n\n* **Unsupervised Gaussian-kernel MMD.** Our NSG‑VD framework can be run without labels by directly computing a Gaussian‑kernel MMD on the extracted NSG features. In this case, the detector still exploits spatiotemporal continuity violations but must operate on high‑dimensional features without a learned mapping, leading to reduced separability. From Table II,  Gaussian‑kernel MMD obtains 57.86% Accuracy and 61.67% F1‑Score, which is consistent with prior observations that untrained MMD can detect distribution shifts but underperforms learned kernels \\[r5, r6].\n* **Unsupervised adaptation for enhanced separability.** To bridge this gap in truly label‑free settings, one promising direction is to combine NSG‑VD with unsupervised domain adaptation [r7] or test‑time adaptation (TTA) methods [r8], e.g., self‑supervised alignment or contrastive tuning of the deep kernel on unlabeled video streams could automatically discover the most discriminative projections of NSG features. We consider this an exciting avenue for future work and will clarify these supervision requirements in the revised manuscript.\n\nTable II. Result of Gaussian‑kernel MMD with NSG feature, where the test setting is the same as Table 2 (%). \n|Diffusion Model|Accuracy|F1‑Score|\n|-|-|-|\n|Gaussian‑kernel MMD|57.86|61.67|\n|NSG-VD (ours)| 86.05|87.45|\n\n[r5] Detecting machine-generated texts by multi-population aware optimization for maximum mean discrepancy. ICLR, 2024.\n\n[r6] Maximum Mean Discrepancy Test is Aware of Adversarial Attacks. ICML, 2021.\n\n[r7] Do We Really Need to Access the Source Data? Source Hypothesis Transfer for Unsupervised Domain Adaptation. ICML, 2020.\n\n[r8] Tent: Fully Test-time Adaptation by Entropy Minimization. ICLR, 2021.\n\n---\n\n**We hope our response has clarified the confusion and addressed your concerns. We would greatly appreciate it if you could kindly reconsider your score. Thank you.**"}, {"review_id": "kA5SMv6PvY", "reviewer": "Reviewer_1Wda", "summary": "The paper addresses the challenge of detecting realistic AI-generated videos. The authors argue that existing methods that often rely on specific visual artifacts are becoming less effective. They propose a novel, physics-driven paradigm that models video evolution based on the principle of probability flow conservation, analogous to fluid dynamics.\n\nThe core contribution is a new statistic called the Normalized Spatiotemporal Gradient, which quantifies the ratio between spatial probability gradients and temporal density changes. The goal is to capture subtle violations of physical laws that are common in synthetic videos but absent in real ones. To practically implement this, the authors develop the NSG-based Video Detection method. This method uses pre-trained diffusion models to estimate the spatial gradients and approximates temporal derivatives using a motion-aware model based on the brightness constancy assumption. The final detection is performed by calculating the MMD between the NSG features of a test video and a reference set of real videos. A larger discrepancy suggests the video is AI-generated.", "questions": "1. Physical assumptions: Could you elaborate on the failure modes of the incompressible flow and brightness constancy assumptions in the context of modern generative models? Do you observe performance degradation on specific types of ``real'' and generated videos (e.g., those with fantasy elements, non-rigid object transformations, or explosive visual effects) where these physical approximations might be less valid?\n    \n2. Diffusion model: How sensitive is NSG-VD's performance to the choice of the pre-trained diffusion model? Would using a different or more powerful model (like Stable Diffusion) as the score estimator further improve results, or is the current model sufficient to capture the necessary dynamics?\n    \n3. Failure cases: The method shows impressive average performance. Could you provide some analysis of the most common failure cases? Understanding when NSG-VD fails (i.e., misclassifying a real video as fake, or vice-versa) would offer valuable insights into its limitations and areas for future improvement.\n    \n4. MMD reference set: Your analysis shows that performance stabilizes with a reference set size greater than 10. In a practical setting, how does the _diversity_ of the real videos in the reference set affect detection performance, in addition to its size?", "limitations": "Yes.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 4, "originality": 4, "strengths_and_weaknesses": "### Strengths\n\n- Originality: The paper introduces a fundamentally new approach to video deepfake detection. Moving from artifact-based detection to a physics-informed model that exploits spatiotemporal dynamics is a significant contribution, especially with the rise of physically implausible but realistic video generators.\n    \n- Theoretical foundation: The method is well-grounded in physical principles, like the probability flow conservation. The authors support their approach with a theoretical analysis, which, despite its simplifying assumptions, provides a solid justification for why NSG features should be discriminative for real vs. fake videos.\n    \n- Experiments: The method is tested on a large-scale, recent benchmark against multiple baselines. The results demonstrate superior performance not just on average, but specifically on challenging, closed-source models and in difficult data-imbalanced settings, which mimic real-world challenges.\n    \n- Parameter Efficiency: The proposed NSG-VD method is efficient in terms of trainable parameters. As shown in Figure 3, it achieves state-of-the-art results by fine-tuning only 0.25 million parameters, a fraction of what competing baselines require for full training.\n\n### Weaknesses\n\n- Computational overhead: A practical limitation is the inference time. The authors honestly report that NSG-VD takes approximately 0.36s per video, which is an order of magnitude slower than the baselines. While the authors position it for non-real-time applications and suggest future work, this currently limits its practical deployment.\n    \n- Physical assumptions: The methodology rests on key assumptions, such as the incompressible flow approximation ($\\nabla x \\cdot v \\approx 0$) and the brightness constancy assumption. While standard in other fields, the paper could benefit from a deeper discussion of scenarios where these assumptions might not hold for real and AI-generated videos (e.g., videos with chaotic motion, rapid lighting effects, or object dissolution), and how that would impact performance.\n    \n- Pre-trained model: The quality of the NSG features is directly tied to the score estimation from the pre-trained diffusion model. The experiments use a single diffusion model, therefore the robustness of the method to different diffusion model architectures or to a domain mismatch between the model's training data and the test videos is not fully explored.", "was_revised": true, "final_justification": "I appreciated the rebuttal to my and the other reviewers' concerns. I remain convinced of the paper's merits and will maintain my positive rating.", "rebuttal": "We thank the reviewer for the encouraging comments and detailed suggestions. Responses are below:\n>Q1. \"...a **fundamentally new approach** to video deepfake detection. ... exploits spatiotemporal dynamics is a **significant contribution**...\", \"...**well-grounded** in physical principles...provides a **solid justification**...\", \" ...demonstrate **superior performance**...\", \"...is **efficient** in terms of trainable parameters...\".\n\n**A1.** We are deeply appreciative of your constructive comments. Your recognition of NSG-VD as a new approach, acknowledgment of our contribution in moving from artifact-based to physics-informed detection, and noting its solid physical grounding, superior performance on large benchmarks motivate us to advance this research.\n\n>Q2. Computational overhead: The authors report that NSG-VD takes approximately 0.36s per video, which is an order of magnitude slower than the baselines. While intended for non-real-time use, this limits practical deployment.\n\n**A2.** We appreciate the reviewer’s concern regarding inference latency. We fully agree that the inference time is important for deployment while our current NSG‑VD prioritizes detection accuracy to validate the physics‑driven paradigm. We will clarify and extend our discussion as follows:\n\n* **Core contribution focus**: Our primary goal is establishing the **physics-driven paradigm's effectiveness** for AI-generated video detection. This requires high-fidelity gradient estimation from diffusion models, e.g., the 256×256 Guided Diffusion model [r1], which prioritizes theoretical validation over speed optimization. This achieves SOTA detection with higher latency.\n* **Acceleration via resolution scaling**: To explore speedups, we replace the 256×256 diffusion model with a 64×64 Improved DDPM [r2] and 128x128 Guided Diffusion recompute NSG features at lower resolution. From Table I, inference time reduces by over **10×** (0.36 s→0.0298 s) with only modest drops in Accuracy (86.05%→83.20%) and F1‑Score (87.45%→84.90%) at 64×64 resolution, showing a favorable trade-off for near-offline use.\n* **Future work**: As discussed in the manuscript, further acceleration is possible via diffusion model compression using lightweight architectures for score estimation, e.g., pruning [r3], quantization [r4]. These are important directions for future work.\n\nWe will include these acceleration results in the revised version.\n\nTable I. Comparisons with baselines on Inference time and performance (Table 2 settings(%)). \n|Method|Accuracy↑|F1‑Score↑|Infer. Time (s)↓| \n|-|-|-|-|\n|DeMamba (Baseline)|84.21|80.12|0.0311|\n|NSGVD (Improved DDPM, 64x64)| 84.26|81.99|0.0298|\n|NSGVD (Guided Diffusion, 128x128)|86.20|86.25|0.1163|\n|NSGVD (Guided Diffusion, 256x256)|86.05|87.45|0.3605|\n\n[r1] Diffusion Models Beat GANs on Image Synthesis.NeurIPS, 2021.\n\n[r2] Improved Denoising Diffusion Probabilistic Models. ICML, 2021.\n\n[r3] Structural pruning for diffusion models. NeurIPS, 2023.\n\n[r4] Ptq4dit: Post-training quantization for diffusion transformers. NeurIPS, 2024.\n\n>Q3. The method relies on incompressible flow and brightness constancy. When these fail in real or AI‑generated videos (e.g., chaotic motion, rapid lighting changes, non‑rigid deformations) and any observed performance drops?\n\n**A3.** We thank the reviewer's insightful comment on physical assumptions. While NSG-VD leverages established approximations (incompressible flow and brightness constancy) for tractability, it is designed to **remain robust even when these assumptions are imperfect**.\n\n* **Incompressibility approximation**. Unlike methods relying strictly on the divergence term $\\nabla_{\\mathbf{x}} \\cdot \\mathbf{v}$, our NSG formulation $\\partial_t\\log p+\\nabla_{\\mathbf{x}}\\cdot\\mathbf{v}+\\mathbf{v}\\cdot\\nabla_{\\mathbf{x}}\\log p=0$ aggregates multiple physical inconsistencies, including temporal change $\\partial_t \\log p$, spatial divergence $\\nabla_{\\mathbf{x}} \\cdot \\mathbf{v}$, and directional advection. Even if $\\nabla_{\\mathbf{x}} \\cdot \\mathbf{v} \\ne 0$, the NSG’s ratio $\\mathbf{g} = \\frac{\\nabla_{\\mathbf{x}} \\log p}{-\\partial_t \\log p + \\lambda}$ still exposes distributional shifts.\n* **Brightness constancy**. This is a **mild assumption**—pixel intensities change smoothly with motion. While real videos may violate it under lighting/specular changes, these are often **spatiotemporally coherent** (e.g., a lamp sweeping across the frame). In contrast, generative videos often exhibit **disconnected inconsistencies** (e.g., misaligned shadows), causing larger NSG violations. Moreover, estimating $\\partial_t\\log p$ via **multi-frame finite differences** and combining it with score‐based $\\nabla_{\\mathbf{x}}\\log p$ helps regularize such effects.\n* **Empirical validation**. We test NSG‑VD on challenging subsets with possible assumption violations: Sora (contains fluid/smoke), ModelScope（contains fast motion), MSR-VTT-Sports (contains rapid non-rigid motion), MSR-VTT-Vehicle (contains fast vehicle motion). From Table II, the average accuracy drops by 6.74% on these “stress” sets versus the full average, yet **remains competitive**, showing robustness under physically non-ideal cases.\n\nWe will include these analyses in our revised manuscripts.\n\nTable II. Effect of \"assumption-stress\" datasets (Table 1 settings (%)). \n|Dataset|Subset|Accuracy|\n|-|-|-|\n|Sora|Fluid/Smoke|88.39|\n|ModelScope|Fast motion|81.67|\n|MSR-VTT-Sports|Sports|84.80|\n|MSR-VTT-Vehicle|Vehicle|84.00|\n|All Subsets (avg.)|—|91.46|\n\n>Q4. Pre-trained model: The NSG feature quality depends on the score from a pre-trained diffusion model. As only one is used, robustness to different architectures or domain gaps isn’t fully explored. How sensitive is NSG-VD to the model choice? Would a stronger one (e.g., Stable Diffusion) help, or is the current model sufficient?\n\n**A4.** We thank the reviewer for the valuable suggestion on pre-trained diffusion models. We discuss this with three key insights: 1) **framework agnosticism to score function sources**, 2) **diffusion model selection criteria**, and 3) **empirical consistency** across different diffusion models.\n\n* **Architecture‑agnostic framework**: NSG‑VD only requires the score function $\\nabla_{\\mathbf{x}}\\log p(\\mathbf{x},t)$. Once it is obtained, regardless of the diffusion architecture, we compute NSG features $\\mathbf{g}(\\mathbf{x},t)$ and train a **lightweight deep‑kernel** MMD detector. This decouples the detection from any specific diffusion designs.\n* **Diffusion model selection criteria**: We prioritize **unconditional, pixel-space diffusion** models that directly estimate $\\nabla_{\\mathbf{x}} \\log p(\\mathbf{x}, t)$ in the pixel space—critical for capturing video dynamics. In contrast, recent latent-space models (e.g., Stable Diffusion [r3], EDMv2 [r4]) operate in compressed latents and require additional decoding and Jacobian projections to recover pixel-space scores, adding complexity and potential approximation errors. We view this as compelling future work. \n* **Empirical validation across diffusion models**: In the main experiments, we use an ImageNet‑pretrained Guided Diffusion model [r1] and achieve strong detection performance (Tables 1–2). We also test with an Improved DDPM model [r2] on the same dataset, yielding **consistent performance** of 84.26% average Accuracy and 81.99% F1-score (Table I). This confirms that NSG‑VD’s efficacy stems from **general gradient estimation**, not model‑specific design and that our current diffusion model is **sufficient to capture key spatiotemporal dynamics** for detection. \n\nWe will include these findings in the revised manuscript.\n\n[r5] Scaling Rectified Flow Transformers for High-Resolution Image Synthesis. ICML, 2024.\n\n[r6] Guiding a Diffusion Model with a Bad Version of Itself. NeurIPS, 2024.\n\n>Q5. Failure cases: The method shows impressive performance. Could you analyze when NSG-VD fails? This would offer valuable insights into its limitations and future improvement.\n\n**A5.** We agree that understanding failure modes is important. NSG‑VD commonly fails in scenarios mentioned in A2, e.g., videos with rapid lighting changes or high-speed motion, which may violate physical assumptions, e.g., brightness‑constancy or incompressibility approximations. We will include this analysis with representative examples in the revised manuscript.\n\n>Q6. How does the diversity of real videos in the reference set affect detection performance?\n\n**A6.** We sincerely thank the reviewer's valuable suggestion regarding the diversity of the reference set. We conduct additional ablation studies on **real‑domain mixed reference sets**, revealing a key strength of NSG-VD: **strong generalization to unseen generated video domains** when most real test samples are covered by the reference distribution.\n\nSpecifically, we train on Kinetics-400 (real) and SEINE (generated) videos, and test on MSR-VTT (real) and 10 generated videos using **reference sets with varying ratios of MSR-VTT and Kinetics-400**. From Table III, **even a small proportion (3:7) yields satisfactory performance** (84.19% of Accuray, 81.12% of F1-Score) compared with baselines, which quickly saturates. This confirms that **NSG‑VD needs only modest in‐domain real coverage**, while the fake side can remain highly heterogeneous. These results will be included in our revision. \n\nTable III. Effect of reference set. Training: Kinetics-400 (real) and SEINE (generated); Testing: MSR-VTT (real) and 10 generated videos (%).\n|MSR-VTT: Kinetics-400 (Domain Coverage)|0:10 (Low)|3:7 (Medium)|5:5 (Balanced)|7:3 (High)|10:0 (Full)|DeMamba (Baseline)|TALL (Baseline)\n|-|-|-|-|-|-|-|-|\n|**Average Accuray**|77.82|84.19|85.57|87.06|86.05|84.21|80.20|\n|**Average F1-Score**|75.68|81.12|83.36|85.41|87.45|80.87|74.05|\n\n---\n**We hope our response has clarified the confusion and addressed your concerns. Please feel free to reach out if you have any further questions or require additional details. Thank you.**"}, {"review_id": "HcEBXJ7zij", "reviewer": "Reviewer_iZEA", "summary": "The paper proposes a physics-driven AI-generated video detection paradigm. First, it designs Normalized Spatiotemporal Gradient (NSG), a statistic based on probability flow conservation principles. Then, it proposes an NSG estimator by spatial gradients approximation and motion-aware temporal dynamics modeling using pre-trained diffusion models. Last, it proposes an NSG-based video detection model (NSG-VD) with theoretical and empirical justifications.", "questions": "1. The estimation of spatial gradients and temporal derivations heavily relies on the capabilities of the pretrained diffusion model. The potential impact of the pretrained model's performance ceiling and biases on the final effectiveness of NSG-VD needs discussion.\n2. The impact of the reference set's size and distribution on detection performance remains unclear. Additional experiments are needed to assess the robustness of NSG-VD to different reference set configurations.\n3. A comparative analysis between the model's performance and human-level discrimination accuracy for AI-generated versus natural videos would provide further validation of the method's effectiveness.", "limitations": "Yes.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. The paper is well-motivated, as AI-generated videos become increasingly realistic and it is critically urgent to develop effective video detection methods for preserving societal trust in digital media.\n2. The theoretical analysis for NSG-VD further guarantees the effectiveness of NSG-VD.\n3. The comparisons are comprehensive, evaluating the method on both standard and data-imbalanced scenarios.\n\nWeaknesses:\n1. The ablation study is not sufficient. The paper analyzes the impact of spatial gradients and temporal derivatives for NSG-VD, but some key components (e.g., the reference set and diffusion model) lack systematic analysis. \n2. The distinction between natural and AI-generated videos is not illustrated clearly or intuitively.", "was_revised": true, "final_justification": "Thanks for the detailed response. My concerns about the ablation study, the distinction between natural and AI-generated videos, and the potential impact of the pretrained model have been addressed. Hope the authors can integrages relevant discussion into the final version. I will keep my rate as \"Borderline Accept\".", "rebuttal": "We thank the reviewer for the encouraging comments and detailed suggestions. Responses are below:\n\n>Q1. The ablation study is not sufficient. The paper analyzes the impact of spatial gradients and temporal derivatives for NSG-VD, but some key components (e.g., the reference set) lack systematic analysis.\n\n**A1.** We sincerely thank the reviewer for this valuable suggestion regarding the reference set analysis. We conduct additional ablation studies on **real‑domain mixed reference sets**, revealing a key strength of NSG-VD: **strong generalization to unseen generated video domains** when most real test samples are covered by the reference distribution.\n\nSpecifically, we train our detetor on Kinetics-400 (real) and SEINE (generated) videos, and test on MSR-VTT (real) and other 10 generated videos using **reference sets with varying ratios of MSR-VTT and Kinetics-400** (0:10, 3:7, 5:5, 7:3, 10:0). As shown in Table I, **even a small proportion (3:7)** of in-domain real samples **yields satisfactory performance** (84.19% of Accuray and 81.12% of F1-Score and then performance quickly saturates) compared with baselines. This confirms that **NSG‑VD needs only modest in-domain real coverage** to establish the detector, while the fake side can remain highly heterogeneous. We will include these results in our revised manuscript.  \n\nTable I. Effect of reference set composition, trained on Kinetics-400 (real) and SEINE (generated) videos, and tested on MSR-VTT (real) and the other 10 generated videos (%).\n| **MSR-VTT: Kinetics-400** **(Domain Coverage)**|0:10 (Low)|3:7 (Medium)|5:5 (Balanced)|7:3 (High)|10:0 (Full)|DeMamba (Baseline)|TALL (Baseline)\n|-|-|-|-|-|-|-|-|\n|**Average Accuray**|77.82|84.19|85.57|87.06|86.05|84.21|80.20|\n|**Average F1-Score**|75.68|81.12|83.36|85.41|87.45|80.87|74.05|\n\n>Q2. The key components diffusion model lack systematic analysis. The estimation of spatial gradients and temporal derivations heavily relies on the capabilities of the pretrained diffusion model. The potential impact of the pretrained model's performance ceiling and biases on the final effectiveness of NSG-VD needs discussion.\n\n**A2**. We thank the reviewer for this valuable suggestion regarding the pre-trained diffusion models. We discuss this with three key insights: 1) **framework agnosticism to score function sources**, 2) **diffusion model selection criteria**, and 3) **empirical consistency** across different pretrained diffusion models.\n\n* **Architecture‑agnostic framework**: Our NSG‑VD pipeline requires only access to the score function $\\nabla_{\\mathbf{x}}\\log p(\\mathbf{x},t)$. Once this gradient is obtained, regardless of the underlying diffusion architecture, we compute the NSG features $\\mathbf{g}(\\mathbf{x},t)$ (Eqn. 4) and train a **lightweight deep‑kernel** MMD detector on these features. This design decouples the detection mechanism from any specific diffusion implementation.\n* **Diffusion model selection criteria**: We prioritize **unconditional, pixel-space diffusion** models because they directly estimate $\\nabla_{\\mathbf{x}} \\log p(\\mathbf{x}, t)$ in the pixel domain—critical for capturing spatiotemporal dynamics in videos. In contrast, recent latent-space models (e.g., Stable Diffusion [r3], EDMv2 [r4]) perform diffusion in compressed latents, requiring additional decoding and Jacobian projections to recover pixel-space scores, introducing additional complexity and potential approximation errors. We view this as compelling future work. \n* **Empirical validation across diffusion models**: In our main experiments, we use an ImageNet‑pretrained Guided Diffusion model [r1] and achieve strong detection performance (Tables 1–2). To further validate generalizability, we supplement additional experiments with an Improved DDPM-based pre-trained diffusion model [r2] on the same dataset, obtaining **consistent performance** of 1.79% average Accuracy and 5.46% F1-score (Table II). These results confirm that NSG‑VD’s efficacy stems from the **universal gradient‑estimation capability** of diffusion models, not model‑specific design and that our current pixel‑space diffusion model is **sufficient to capture the spatiotemporal dynamics needed** for robust detection. \n\nWe will include these findings in the revised manuscript to highlight the framework’s generalizability and its current practical scope.\n\nTable II. Effect of different diffusion Models, with the same setting as Table 2 (%). \nTable II. Effect of different diffusion Models, with the same setting as Table 2 (%). \n|Method|Accuracy|F1‑Score|\n|-|-|-|\n|DeMamba (Baseline)|84.21|80.12|\n|NSGVD (Improved DDPM, 64x64)| 84.26|81.99|\n|NSGVD (Guided Diffusion, 256x256)|86.05|87.45|\n\n[r1] Diffusion Models Beat GANs on Image Synthesis.NeurIPS, 2021.\n\n[r2] Improved Denoising Diffusion Probabilistic Models. ICML, 2021.\n\n[r3] Scaling Rectified Flow Transformers for High-Resolution Image Synthesis. ICML, 2024.\n\n[r4] Guiding a Diffusion Model with a Bad Version of Itself. NeurIPS, 2024.\n\n\n>Q3. The distinction between natural and AI-generated videos is not illustrated clearly or intuitively.\n\n**A3**. We appreciate the reviewer's insightful comment. Natural videos typically exhibit **rich, coherent, and physically plausible details**. In contrast, current AI-generated videos, particularly those from diffusion models, often display subtle artifacts in high-frequency regions, such as **oversmoothing, localized blurring, or physically inconsistent lighting and shadows, as well as temporal incoherence**. These discrepancies induce implicit distributional shifts in the feature space, enabling their discrimination. In the revised manuscript, we will further elaborate on the core discriminative features underpinning our method and their representational differences, complemented by visualizations of the underlying distributional divergence.\n\n>Q4. The impact of the reference set's size and distribution on detection performance remains unclear. Additional experiments are needed to assess the robustness of NSG-VD to different reference set configurations.\n\n**A4**. We thank the reviewer for this suggestion. We have already analyzed the impact of the reference set’s distribution in our response to Q1-A1. In Appendix E.4 in the paper, we evaluated NSG‑VD using reference sets of varying sizes (Table III, below). From the table, NSG‑VD maintains consistently high detection accuracy and F1‑Score across varying reference set sizes.\n\nTable III. Effect of reference set size (%). \n|size|10|50|75|100|200|300|400|500|\n|-|-|-|-|-|-|-|-|-|\n|Recall|63.22|90.22|89.22|89.89|88.67|88.33|88.67|88.56|\n|AUROC|94.44|97.41|97.01|97.24|97.20|97.26|97.31|97.22|\n|Accuracy|81.11|94.11|93.61|93.94|93.83|93.67|93.83|93.28|\n|F1|74.37|93.59|92.93|93.36|93.09|92.95|93.15|92.60|\n\n>Q5. A comparative analysis between the model's performance and human-level discrimination accuracy for AI-generated versus natural videos would provide further validation of the method's effectiveness.\n\n**A5**. We thank the reviewer's comments. As discussed in our work, early generative models produced visible artifacts such as **distortions and temporal inconsistencies**, which are easily detectable by both humans and algorithms. However, with the rapid advancement of SOTA generative models, modern AI-generated videos attain near-photorealistic fidelity, where residual **artifacts are subtle and often imperceptible to the human eye**. In such cases, an AI detection model leverages fine-grained, frame-level analysis to detect nuanced deviations beyond human perceptual limits. Furthermore, human observers can outperform algorithms in cases involving semantic or commonsense inconsistencies, even when no visual artifacts are present. We acknowledge the importance of this perspective and will include a human-AI comparative evaluation in the revised manuscript.\n\n---\n**We hope our response has clarified the confusion and addressed your concerns. We would greatly appreciate it if you could kindly reconsider your score. Thank you.**"}]

Author rebuttal:

Meta-review: This paper proposes a physics-inspired approach to detecting AI-generated videos via the Normalized Spatiotemporal Gradient (NSG), derived from probability flow conservation, and introduces NSG-VD using pretrained diffusion models and MMD comparisons. The method is original, theoretically grounded, and shows strong empirical results across diverse datasets, including challenging imbalanced cases. Reviewers praised the motivation and novelty but raised concerns about clarity of the derivation, reliance on assumptions like brightness constancy, and limited ablations on diffusion models and reference sets. During rebuttal, the authors addressed most of the concerns. Overall, while some aspects of clarity and analysis could be improved, the paper is novel, well-motivated, and empirically strong. I recommend acceptance.
Decision: Accept (spotlight)