FlexiClip: Locality-Preserving Free-Form Character Animation
Authors: Anant Khandelwal
Venue: ICML 2025 poster (2025)
Keywords: Text-to-Video generation
Primary area: deep_learning->generative_models_and_autoencoders
TL;DR: clipart animation, temporal Jacobians, probability flow ODEs, flow matching loss, GFlowNet, continuous-time modeling, character animation

Abstract: Animating clipart images with seamless motion while maintaining visual fidelity and temporal coherence presents significant challenges. Existing methods, such as AniClipart, effectively model spatial deformations but often fail to ensure smooth temporal transitions, resulting in artifacts like abrupt motions and geometric distortions. Similarly, text-to-video (T2V) and image-to-video (I2V) models struggle to handle clipart due to the mismatch in statistical properties between natural video and clipart styles. This paper introduces FlexiClip, a novel approach designed to overcome these limitations by addressing the intertwined challenges of temporal consistency and geometric integrity. FlexiClip extends traditional Bézier curve-based trajectory modeling with key innovations: temporal Jacobians to correct motion dynamics incrementally, continuous-time modeling via probability flow ODEs (pfODEs) to mitigate temporal noise, and a flow matching loss inspired by GFlowNet principles to optimize smooth motion transitions. These enhancements ensure coherent animations across complex scenarios involving rapid movements and non-rigid deformations. Extensive experiments validate the effectiveness of FlexiClip in generating animations that are not only smooth and natural but also structurally consistent across diverse clipart types, including humans and animals. By integrating spatial and temporal modeling with pre-trained video diffusion models, FlexiClip sets a new standard for high-quality clipart animation, offering robust performance across a wide range of visual content. Project Page: https://creative-gen.github.io/flexiclip.github.io/

FlexiClip: Eecality-Preservingg Free-Form Character Animation
Anant Khandelwal
Abstract
1. Introduction
Animating static clipart images while preserving their vi- sual integrity and ensuring temporal coherence in motion is a challenging problem in computer graphics. Existing methods, like AniClipart (Wu et al., 2024) address this by modeling key point trajectories with cubic Bézier curves and applying ARAP deformation maintain geometric con- sistency. Gal23 (Gal et al., 2024) is also similar work learning neural displacement field with pre-trained T2V (Text-to-Video) diffusion model on cubic Bézier curves. While AniClipart effectively captures spatial deformations, it struggles with maintaining temporal consistency across frames. Specifically, the method suffers from abrupt transi- tions, geometric distortions, and inconsistencies when gen- erating complex motions or handling rapid pose transitions (Fig. 3). These artifacts arise from rigid parametrization of the motion process that does not fully account for tem- poral noise or its correction over time. Additionally, recent T2V/IVV (Image-to-Videe
Animating clipart images with seamless motion while maintaining visual fidelity and temporal coherence presents significant challenges. Ex- isting methods, such as AniClipart, effectively model spatial deformations but often fail to en- sure smooth temporal transitions, resulting ar- tifacts like abrupt motions and geometric distor- tions. Similarly, text-to-video (T2V) and image- to-video (I2V) models struggle to handle clipart due to the mismatch in statistical properties be- tween natural video and clipart styles. This paper introduces FlexiClip, a novel approach designed to overcome these limitations by addressing the in- tertwined challenges of temporal consistency and geometric integrity. FlexiClip extends traditional Bézier curve-based trajectory modeling with key innovations: temporal Jacobians to correct motion dynamics incrementally, continuous-tin eling via probability flow ODEs (pfODEs) to mitigate temporal noise, and flow matching loss inspired by GFlowNet principles optimize smooth motion transitions. These enhancements ensure coherent animations across complex sce- narios involving rapid movements and non-rigid deformations. Extensive experiments validate the effectiveness FlexiClip generating anima- tions that are not only smooth and natural but also structurally consistent across diverse clipart types, including humans and animals. By inte- grating spatial and temporal modeling with pre- trained video diffusion models, FlexiClip sets a new standard for high-quality clipart animation, offering robust performance across a wide range of visual content. Project Page: https://creative- github.i/
models (Chen et al., 2023; 2024; Xing et al., 2025; Zhang et al., 2023; HaCohen et al., 2024; Wang al., 2024; Lei al., 2023) enable animation from text and images, but struggle to produce high-quality clipart animations due to the significant difference in statistical properties between natural videos and clipart.
mod-
To overcome these limitations, we introduce FlexiClip, a novel approach that extends the state of the art by address- ing the key challenges of temporal coherence and geometric consistency animated clipart. FlexiClip also builds on the basic framework of modeling keypoint trajectories with cubic Bézier curves but introduces significant innovations to improve temporal dynamics and maintain consistent animation pipeline. Central to FlexiClip is the use of tempo- ral Jacobian for incremental temporal corrections, pfODE (Limm al., 2023; de Albuquerque & Pearson, 2024) for continuous-tine integration of these corrections, and flow matching loss inspired by GFlowNet (Bengio al., 2023) to ensure smooth temporal evolution and reduction of temporal noise.
gen.
'Search Technology Center India, Microsoft, IDC, Ben- galuru, India(Bharat), Correspondence to: Anant Khandelwal <anantk microsoft.com, maant.itdd.2085 @0tl:/5@mmml.oomo comi.
Although AniClipart also represents keypoint motion through Bézier curves but employs ARAP (As Rigid As Possible) deformation to model spatial consistency, its tem- poral modeling lacks mechanism for addressing noise accumulation across frames. In contrast, FlexiClip intro-
Proceedings of the ndnd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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FlexiClip: Free-Form Character Animation
Breakdancar performing on inverted freaze with one hand the floor and legs artistically intertwined in the ein
A young girl jumping high up and down
young girl porforms squat
doncing lege
moving down, woving
The parrot fispping its wings.
young boy jumpa up
Figure 1. FlexiClip generates high high-quality clipart animations based on text prompts, ensuring visual consistency and smooth temporal motion. Original clipart images are outlined with dashed boxcs.
duces novel paradigm by learning temporal Jacobians that incrementally correct the spatial Jacobian time. This framework enables precise control over temporal evolution and prevents drift in the motion dynamics, thereby main- taining the animation's naturalness and consistency across longer sequences. Additionally, we leverage probability flow ODE (pfODE) (Sec.2.2) to model the temporal cor- rection process continuous-time function, addressing temporal noise more effectively than discrete-time optimiza- tion methods.
noise introduced by the spatial model is progressively re- duced, facilitating smoother transitions between frames and preventing the accumulation of errors. Unlike earlier ap- proaches, such AniClipart, that do not explicitly model the evolution of temporal noise, FlexiClip provides a robust mechanism for controlling noise accumulation and preserv- ing the underlying motion's coherence.
At last, FlexiClip integrates learning of spatial and tempo- ral modules with the concept of video Score Distillation Sampling (SDS), which allows to distill the knowledge of pre-trained video diffusion models to guide the anima- tion generation process. Extensive experiments and ablation studies demonstrate FlexiClip's 's ability to generate smooth, natural, and temporally consistent clipart animations across wide range of visual content, including humans and ani- mals (see Fig. 1). FlexiClip also supports handling complex animations (Fig. 5) where keypoint transitions involve non- rigid deformations like rotation, complex motion, etc. In summary, our contributions can be summarized as follows:
A critical challenge in temporal animation is the preserva- tion of motion smoothness without introducing geometric distortions. previous works, such as AniClipart, motion dynamics are modeled independently for each frame, which can lead to inconsistent transitions and visual artifacts (Fig 3). In contrast, FlexiClip utilizes pÊODE (Sec.2.2) to model the evolution of temporal Jacobian, which are corrected pro- gressively over time. This continuous correction mechanism ensures that the temporal noise is mitigated, resulting in smoother and more consistent motion transitions. Moreover, this framework provides novel solution to the problem of maintaining structural consistency (locality preserving) during fast spatial transitions, which is often difficult task in motion modeling.
Coherent Temporal Corrections: We introduce the novel concept of temporal Jacobians, which incre- mentally adjust the spatial geometry over time to ac- count for temporal variations. This mechanism ensures smoother and more temporally coherent animations by addressing the issue of noise accumulation across frames.
Another novel contribution of FlexiClip is the flow matching loss, which leverages the principles of GFlowNet (Bengio ct al., 2023) to optimize the temporal noise reduction pro- cess. The flow matching loss operates by comparing the dynamics of the spatial Jacobian and their temporal cor- rections time. This approach ensures that temporal
Locality Preserving Deformation: We propose the use of pFODE to model the continuous time evolu- tion of the temporal Jacobians, This approach allows
2

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FlexiClip: Locality-Preservvi Free-Form Character Animation
for more precise temporal corrections and ensures smoother transitions between frames, improving upon discrete-time methods such as those used in AniClipart.
Once the updated vertex positions V are computed, the corresponding updated Jacobian for each face f is derived by taking the gradient of V over the face:
Flow Matching Loss for Temporal Noise Reduction: We introduce the flow matching loss, inspired by the GFlowNet framework, to optimize the reduction of temporal noise. This loss function ensures that the accumulated temporal noise progressively reduced over time, leading to smoother, more consistent anima- tions.
3 VVV"
(5)
For a triangular face I with vertices {vi, Vj. Va the Ja- cobian matrix captures how the vertex positions within the triangle are influenced by barycentric coordinates:
Qv
av
0v
Bv.
8v
Dv:
J
Qv
bv
dvi
(6)
Jv.
dv.
2. Preliminaries
Ov
Bv:
ävi
8yk
89%
2.1. Representing Shapes as Jacobian Fields
Updated Jacobians give local deformation of each triangle.
Let Mo = (Vo, Fo) denote the initial mesh, where Vo E RVx2 x2 specifies the 2D vertex positions and Fu E R describes the triangular faces. Keypoints are defined us- ing an indicator matrix K. {0, 1) V,V,,, with the cor- responding vertices represented as V. Vo These keypoints are assigned target positions T. = V. + De, where D. E R Vex2 defines the displacements.
2.2. Probability flow ODE (pfODE)
The diffusion process governs the evolution of data points over time via the stochastic differential equation (SDE):
dx = S di + G(x, () dW,
where [(x, 1) is the drift term and G(v, () is the noise coef- ficient. Over time, the distribution transforms from po(x) to an isotropic Gaussian distribution (r To reverse this process, we model the reverse SDE as:
The deformation of the mesh is characterized by Jacobian field Jn {Jo.f f E Fo}. where each face f has an associated Jacobian matrix Jo.f E R2222 This matrix is computed Jo.s v,Vo. which represents the gradient of the vertex positions over the triangle f. To compute the deformed mesh V*, we solve the following optimization problem:
dr = (f(x,t) V (((GEt))
dW. (8) where [(x 1) is the drift term, G(æ, 1) represents the noise diffusion matrix, W is time-reversed Brownian motion and V, (x)) is the score function, approximated by the dif- fusion model. This reverse process reconstructs the data distribution by denoising, guided by the score function V. log Pz().. However, in addition the SDE, Song et al. (Lim et al., 2023) proposed the probability flow ODE (pfODE), which satisfies the same Fokker-Planck equation, but is deterministic (no Brownian term). it is given by:
-G(x, f)G(() t). log)(())) dt G(I, tdW
V = arg min LV V AJ
where L is the cotangent Laplacian operator, A is the mass matrix, and is the specified Jacobian field. To avoid trivial deformations such as global translations, constraints are applied to the keypoints, resulting in the following extended formulation:
V = arg min LV V" AJ + T.I., (2)
= (1(0,1) - v (Gx,)) dx
where A > 0 balances the influence of the constraint term. The solution is obtained by solving the linear system:
dt
2
2 Gla, ([(,,) 1)² Va log
(L'I + KK L AJ
T
AK
Te.
(3)
which can be efficiently solved using techniques such as Cholesky decomposition. Let this be denoted with g as differentiable solver: V* gJJ, Ke, T.). To learn the input shape J, set D. 0 we learn it by minimiz- ing the difference between the J and the identity, i.e., no deformation
This přODE evolves the data points smoothly without the stochastic Brownian motion term. This process is determin- istic, and data points evolve smoothly, resulting in flow that preserves local neighborhoods.
Under the Gaussian noise assumption, the score function V, log (z()) can be trained from a pre-trained diffusion model via score matching, and hence can guide mesh de- formation starting with noisy vertices. However, the key
P
La
Σ
J
I
(4)
3

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FlexiClip: Locality-Peesevving Free-Form Character Animation
challenge in learning the mesh deformation directly with pre-trained diffusion models is that these models reverse the isotropic Gaussian noise, as described in the SDE-based formulation, making it harder to directly match the target dis- tribution (highly structured, like posed mesh). is straight- forward to show (App. C) that the class of time-varying densities satisfies (9) when f = 0 and GG = Ć, similar to (de Albuquerque & Pearson, 2024) we consider the přODE with rescaling avoid variance overflow:
R(r) is an unnormalized reward function.
The flow function F(T) incorporates the normalizing factor, and the state flow function F(s) models the unnormalized probability flow for each state. GFlowNet's training uses the detailed balance (DB) condition, which ensures that for any transition (s + s'), the following holds: FF = F(s') Pp(ss') (ss + s') A. For terminal states x. the condition F()) R(x) is required. Satisfying this DB criterion ensures that the terminal distribution Pr(x) matches the desired target distribution, proportional to R(xx).
di = (-t))---00 Ve log + (A(t)- 1000---1(0)) (t) -
dt
(10)
with C(t) playing the role of injected noise and A(t) the role of the scale schedule. Similar (de Albuquerque & flows
Jo P
parametrized
cubic Bézier
Triangulation
Pearson, 2024) we will leverage cimension-preservve for (tt) and A(t) to learn the exact temporal noise to be reversed. As the noise reduces, the rescaling A(t) induces force in the opposite direction as the force induced by score function. This balance ensures that the distribution stabilizes asymptotically, maintaining local structure while evolving smoothly into the target distribution.
JN
Text Prompt: "woman dancing"
Input
pfODE
Clipart
flour
Differential Rendering
LgDS
T2V
2.3. GelowNets
Figure 2. System Design of FlexiClip: A novel framework for generating temporally coherent and geometrically consistent an- imated clipart. FlexiClip leverages PIODE for continuous- -iime modeling on top of spatial posing, and a flow matching loss for re- ducing temporal noise, cnabling smooth, natural animations across complex motion sequences.
Generative Flow Networks (GFlowNets) (Bengio et al., 2023) enable training generative models with unnormal- directed
ized target densities. GFlowNet is represented acyclic graph G = (S, A), where S is the set of states and A S S x S is the set of actions. Transitions between states are deterministic, with an initial state so and terminal states SN. The forward policy (s' s) defines the transition from s to s', while the backward policy PD (s|s") defines the re- verse. The goal is learn a forward policy such that the terminal state distribution (ar) x R(x)), where R(x) is the unnormalized reward function.
3. FlexiClip
In this section, we introduce our mesh deformation frame- work, FlexiClip (Fig.2). We begin with a method overview (Sec. 3.1), followed by a spatial posing with Jacobian Fields on parameterized Bézier trajectories (Sec. 3.2). Next, we discuss how temporal signals modeled using pfODE to ensure temporally coherent motion (Sec. 3.3). Finally, we outline the loss functions used (Sec. 3.4).
The flow function F(T) includes the normalizing factor, and F(x) models the unnormalized probability flow for each state. Training uses the detailed balance (DB) condition, ensuring (s'(ss)))s = F(s') (ssss') for all transitions (s 8') A. For terminal states æ, the condition F(x)= = R(x) must hold. This ensures the terminal distribution Pr(x) matches the desired target, proportional to R(x).
3.1. Method Overview
In FlexiClip. detect keypoints and construct skeletons using UniPose (Yang et al., 2023) and skeleton generation (Cacciola, 2004), similar to AniClipart (Wu et al., 2024). Cu- bic Bézier trajectories define spatial motion, while PfODE and temporal Jacobian handle temporal noise. Attention networks estimate C(t) and A(t), and flow matching from GFlowNets reduces temporal noise. Video SDS loss enables learning from the single image input.
Generative Flow Networks (GFlowNetts) (Bengio et al., 2023) provide a framework for training generative models with an unnormalized target density function. A GelowNet represented as directed acyelic graph G AS, where S is the set of states and A C S S is the set of actions. The transition between states is deterministie, and the network has an initial state 8n and terminal states 8N. The forward policy PF (s'(s) defines the transition probability from state s to s', while the backward policy P (s(ss') defines the re- verse transition. The goal is to learn a forward policy such that the terminal state distribution (r x R(x), where
3.2. Spatial Posing
We begin by describing the mathematical framework to an- imate a clipart image, zo. characterized by M keypoints
4

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FlexiClip: Locality-Preserri Free-Form Character Animation
(po(t)) and associated cubic Bézier trajectories param- eterized by control points (c(i)) - These trajectories dictate the temporal evolution of the keypoints {pe(t) Jimo M-1 over N timesteps, where t E (0.1..... N
via integration:
J = JJ- + L: fR(J6 Civy c T;;): dr. (13)
-)- At timestep t, keypoint positions (i) are sampled along Bézier trajecto- ries c(i) as: (1) = ーn (2,))), (t), where 24 E [0.1] is the normalized time and (y( = (1 - (111-)))-5m0) un. These updated keypoint positions {pe(t)} anchor the cli- part's deformation for & > 0 and hence they are used as anchor vertices To in (Eq.2) to compute the spatial defor- mation of the object geometry across discrete time steps. Before learning the deformation for f > O, we fix the input shape Jo using (Eq.4). While this method efficiently models the spatial deformation, it often fails to maintain temporal coherence across frames. Prior research (Wu et al., 2024; Gal et al., 2024) highlights that predicting future Bézier control points at discrete timesteps frequently results in dis- torted object identities, loss of geometric consistency, and abrupt transitions between frames. Even with parameterized learning methods (Wu al., 2024), such as those optimized using Score Distillation Sampling (SDS) loss, unseen pose configurations often result in jerky or unnatural motion dy- namics. (Fig.3).
Here, J is initialized zero for the first frame, ensur- ing a neutral starting state. Numerical methods such as Euler's method are used for integration. In comparison to (Eq. 10) we model the time-varying noise C(t) with Civ and rescaling A(t) with C CW is the attention over spatial Jacobians over a time window W i.e. till the cur- rent time step. And, O CW-1 is the attention over temporal Jacobian in time window W 1 i.e. till previous step. In (Eq.10) 10) we need score function which can estimate a de- noised version of a noise-corrupted data sample given noise level Ct)). Comparatively, (Eq.13) also denoise the input noise accumulated over spatial Jacobians Cl - Ctt) and the corrections applied to them - + rescaling A(L) we are estimating the denoised Jacobian which is the correction term for spatial Jacobian. For convergence, as in (Eq.10) as soon as the corrections applied starts to contract it balance the opposing force from the error in spatial Jacobians and finally the corrections term reduced to zero. To ensure this correction term reduces to zero only for temporal noise we apply the flow matching (detailed balance) objective from GFlowNets, detailed subsequently.
3.3. Temporal Smoothing
Lets denote the Jacobians for N time steps obtained from spatial posing is denoted as JJP J.......... J.. - called as spatial Jacobians. We reformulate the temporal smoothing problem to predict temporal Jacobian Jf as cor- rective terms to spatial Jacobian J The total Jacobian at time is given by:
3.4. Loss function
We distill the prior knowledge of a pretrained video diffu- sion model via Video Score Distillation Sampling (SDS). Let J = {J (Eq.11) represent the predicted Jacobian fields over time, and V [V?),
Jt= be the temporally consistent set of vertices computed via differentiable func- tion 9 given J. and T for each time step (Sec...1). For each time step L, the deformed mesh M; = (Vi,F) (P) is used to warp W initial clipart image and then rendered using a differentiable renderer R (Li et al., 2020), producing frames I = R (WV(Lo). M[)) The sequence of frames forms the video X (-)= The pretrained video diffusion model es with the input video X parameters, it produces gra- dient w.r.t @ which are the spatial and temporal parameters driving the animation:
J. = J.P + J
(11)
This decomposition focuses on learning localized correc- tions, enabling precise control and mitigating drift through incremental adjustments.
ODE Formulation: Since the first frame stationary and given as input, we set the first frame's 's temporal Jacobian as, J = 0 E Fx222 Furthermore, we are required to remove only temporal noise from spatial Jacobians and wanted to add only temporal correction term (temporal Jaco- bian), we propose to reformulate the ODE given in (Eq.10) given as:
X) = Ev,c [i((e) (co(Zesy,)) -) ae
0x
V LoLDD( (o.)s
(14)
dJ dt = In(JJ; Ch,, CW-D,1;0R)
where t' U(O,,T)) ~ No I). and ze noisy la- tent embedding of X, ea the U-Net denoising network in the T2V model, conditioned on the text prompt y and the diffusion time step l'. The optimization of SDS loss in- volves back-propagating through the UNet (-), and then to spatial and temporal parameters, which is computationally expensive. Hence we leverage gradients as per (Poole et al., 2022) by omitting the UNet Jacobian. Specifically, in our
(12)
where Jf is the base Jacobian of the first frame, Cf and C#f-1 are attention-encoded features of current-window pose predictions and past-window temporals, respectively. The function fa. parameterized by 0R. outputs temporal corrections. The temporal Jacobian at time 1, JR. is obtained
5

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FlexiClip: Locality-Preserving. Free-Form Character Animation
case gradient updates the Bézier parameters (spatial) and (attention, ODE) parameters (temporal) which refines the geometry of the meshes M' = {M; - For better text- video alignment, classifier-free guidance (Ho & Salimans, 2022) is applied:
correction minimizing loss given as:
flow = =By Vx log pe (X, J1) - Vx logpe Pe (X, )(
+ +EIIJ, 1 (18)
The Overall Loss for FlexiClip is defined as the weighted sum loss in 1q. 16, 17:
Es Es () + ()+)))((ersy))) sea ( (2r;0,()),
(15)
where 8 is the guidance scale, 0 denotes null text prompt.
Lsns + À Lito
(19)
where À is the weight to balance the loss magnitudes. Flex- iClip is end-to-end differentiable to be able to learn the keypoint movement and temporal smoothing required.
Flow Matching Loss Optimizing the mesh deformation with Video SDS loss using Gaussian noise assumption can produce animations with abrupt transitions, exhibit local geometric distortions as the displacement for each keypoint is predicted independently and hence not be able to match the target distribution (as explained in Sec.2.2). In con- clusion, we are required to optimize the temporal noise (Sec.3.3) for smooth evolution of keypoints and maintain local structure, however these pre-trained video diffusion models under isotropic Gaussian noise assumption increase the effective dimensionality of the data, which may begin as a low-dimensional manifold embedded within same dimen- sionality. Thus, maintaining intrinsic data dimensionality requires choice of flow that preserves this dimension. We define the dimensionality as the denoising objective, for example, consider the noise quantified as C(()
4. Experiments
We evaluate FlexiClip through comprehensive experiments. First, we describe the experimental setup (Sec.4.1) and evaluation metrics (Sec.4.2). Next, we compare FlexiClip with AniClipart (Wu et al., 2024), sketch-animation method Gal23 (Gal et al., 2024), as well as leading T2V models (Sec.4.3). Ablation studies (Sec.4.5) validate our design decisions, and we showcase FlexiClip's ability to handle complex animations (Sec.4.6).
4.1. Experimental Setup
FlexiClip enables high-resolution, complex animations by leveraging SVGs, where paths defined by control points are animated via mesh deformation and rendered into bitmaps using DiffVG (Li et al., 2020) for video SDS loss. For bitmap clipart, pixels within each triangle are warped. We used 30 clipart images from AniClipart (Wu et al., 2024) and additional ones from Freepik' across various categories (humans, animals, and objects), resized to 256x256 pixels. First, we learn Ju with Eq.4 for 10K iters. After that, motion trajectories with 8-11 control points were optimized upto 700 steps using Adam (learning rate: 0.5). We applied Mod- elScope T2V (Wang et al., 2023) with a guidance parameter of 50 for SDS loss. For spatial posing, cubic Bézier control points, we use a 4-layer MLP with LeakyReLU activation, with the final layer being linear. Temporal Jacobians from POODE were predicted with 3-layer MLP, while two at- tention networks with 32-dimensional keys/values and two heads modeled motion and deformation effectively. Stan- dard 24-frame animations were rendered on an NVIDIA V100 in 40 minutes using 26 GB.
I (xx-daalEEn D(X n; C(t)) 2
(16)
C(I)
where D-)) de-noised version of noise-corrupted data sam- plc X given noise level C(t). In practice we used the same denoiser es U-Net of pre-trained video diffusion model, hence (Fq.16) is essentially the score function Vx log p( X).
To preserve the dimension for the temporal noise, despite learning the deformation under the Gaussian noise assump- tion, we propose to take the difference between the score function obtained for frames I, produced through overall Jacobian J, and spatial Jacobian J This loss is inspired from the detailed balance (DB) objective from GFlowNets where, the backward process (Spatial Jacobian) keeps on introducing the temporal noise and the forward process keeps on reducing the added temporal noise for each state transition. Since the score function is already normalized and comparable there is no normalizing factor F(s) as in Sec.2.3, thus the loss function is given as:
Lioo = Ex, V log pr (x, - Vx log pr (X, J
4.2. Metrics
(17)
We evaluated FlexiClip on same metrics from AniClipart (Wu et al., 2024), namely, 1) bitmap metrics (cosine similar- ity via CLIP for visual identity and X-CLIP for text-video alignment) and 2) animation metrics (Motion Vibrancy
Here, as well the gradient ing from this loss. Moreover, we wanted the parameterized Bézier to capture temporal movement of keypoints as much as possible and hence we want the temporal Jacobian (cor- rective term) to be as small as possible, hence we add the
ax 36 is taken while back propagat-
hntps//wwww.rrepikccom
6

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FlexiClip: Srcality-Preservinng Free-Form Character Animation
hand deformation (e.g., during dance movements), AniCli- part exhibits noticeable distortions, which negatively impact the naturalness of the animation. FlexiClip, on the other hand, maintains better consistency in object shape and defor- mation, showing smoother transitions without compromis- ing visual identity. In particular, when handling leg folding during jumping and dynamic hand movements, FlexiClip ensures these actions are portrayed realistically (whereas AniClipart shows the distorted hand for girl/boy jumping), which is critical requirement for creating natural anima- tions.
Table 1. Quantitative results of FlexiClip in terms of hitmap met- rics against AniClipart and T2V/1VV models.
Visual Identity Preservation Score 1)
Video
Method
Alignment (X-CLIP Score 1)
DynamiCrafter (Xing et al., 2025)
0.8031
0.1732
Gal23 (Gal 2024)
0,8395
0.1865
VidooCrafter2 (Chen et al., 2024)
0.8410
0.1988
I2VGen-XL XL (Zhong et al., 2023)
0,8798
0,2015
ModelSSoppe (Wang
2013)
018632
0.2037
ToonCrafter (Xing et al., 2024)
0,9280
0.1997
AnimateCMM-I (Wang al., 2024)
0,2030
Pyramid Flow (Lei et 2023)
0,9312
0,2015
LTXVideo (HaCohen al., 20124)
0.9325
0.2054
AniClipart (Wi et al., 2024)
0,5401
0.2075
FlexiClip (Ours)
0.9563
0,2102
Additionally, FlexiClip excels at producing smoother and more realistic deformations, as evidenced by the parrot ani- mation, where the wing flapping looks much more natural and consistent. The wings of the parrot exhibit a smooth, continuous motion, enhancing the visual realism compared to AniClipart's deformation, which is flapping its tail rather than wings showing lack of text alignment. Looking at the quantitative results I and 2), FlexiClip outperforms AniClipart in both the bitmap and animation metrics. Specif- ically, FlexiClip achieves a higher CLIP score (0.9563 vs. 0.9401) and X-CLIP score (0.2102 vs. 0.2075), signifying better visual identity preservation and text-video alignment. Furthermore, FlexiClip's 's animation quality metrics, includ- ing MV, TC, GD, DS, and AE, also surpass AniClipart's 's results, with FlexiClip yielding more motion variation, lower distortions, and higher animation efficacy. Notably Flexi- Clip GD has increased but DS decreased showing smoother animations. FlexiClip versus I2V Models: See App.B.
Table 2. Quantitative results of FlexiClip in terms of animation metries against AniClipart.
Method
MVt
TCJ
GDJ
DSL
AE (x10")t
AniClipart
20.87
8,51
50.98
18.49
75.23
FlexiClip (Ours)
25.33
8.14
52.34
13.76
113.44
(MV), Temporal Consistency (TC), and Geometric Devia- tion (GD)). To better evaluate methods for free- rre-ffooing and smooth animation we propose the following metries:
Deformation Smoothness(DS): This metric evaluates how smoothly the control points deform along Bézier paths. It computes the average difference in displacement vectors of consecutive frames:
N-IM-1
DS (N 1N M
1
Σ
Σ
where d(0) is the displacement of control point i at frame t. Lower values indicate smoother deformation.
User Study To assess the improvements made by Flexi- Clip, we conducted a subjective user study with 55 static cli- part images animated by six methods: FlexiClip (Ours), An- iClipart, LTXVideo, PyramidFlow, AnimateLCM-I22 and DynamiCrafter. Participants were asked to rate the anima- tions visual identity preservation, text- vidto alignment, and smoothness using a six-point scale from O (strongly disagree) to 1.0 (strongly agree). The study was conducted online with 30 participants, and ratings were averaged across the 55 clipart images. The results in Tab.3 show that Flexi- Clip significantly outperforms the other methods.
Animation (AEr: To evaluate the energy dis- tributed across control points, we calculate the mean squared displacement across all frames:
N
M-1
AE N.
1
Σ
Σ
(
Po
(4)
12.
M
Higher values indicate more dynamic animations.
4.3. Comparison to State-of-the-Art Methods
FlexiClip versus AniClipart: We compare FlexiClip with AniClipart based on the results observed in the tables (Tab. I, 2 && 3) and visual examples (Fig.3). One of the key dif- ferences between the two models lies in their ability to preserve visual identity and create more coherent text-video animations. While AniClipart demonstrates impressive per- formance in visual identity preservation and text-video align- ment, it encounters challenges when it comes to handling complex deformations. For instance (Fig.3), in the case of
Table 3. Subjective user study results
User Selection & f
Identity Preservation
Video Alignment
Smoothness
FlexiClip (Ours)
94,90
94.54
93.81
AniClipart
83.63
80.72
76.36
L.TXVidoo
61.82
60.36
58.18
PyramidFlow
56.36
54.90
$2.36
Animatel CC-12V
49.09
48.72
45.09
DynumiCratter
7

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FlexiClip: Free-Form Character Animation
womon doncer dancing Cia-
The parrot flapping its wings.
boy jumping to hit shutrlecock
jumping throw the handball
AniClipart
FlexiClip
AniClipart
FlexiClip
AniClipart
FlexiClip
AniClipart
FlexiClip
Four consccutive frames shown for comparison. AniClipart distorts the objects (c.g.. boy/girl jumping, woman dancing), lacks proper text conditioning (e.g.. parrot), and shows poor temporal consistency (e.g.. boy jumping). In contrast, FlexiClip preserves the visual identity, maintaining consistent shapes and producing high-quality, smooth, and text-aligned animations. Detailed animations can he seen at: https:/creattiv--enn. htwpriieeeeeeggtuuuooo/eeiiiiiee www.llxxiciiiiiihbb.o.o...
Figure 3. FlexiClip AniClipart:
4.4. Effect on Motion Quality and Convergence
looking animations. Thus, À serves as an effective default for balancing alignment, smoothness, and training efficiency.
In our experiments, we found that parameter plays critical role in balaneing the aligmment of generated motion with the text prompt and ensuring smooth, natural motion trajectories. Specifically, tuning À influences both the qual- ity of the animation and the convergence behavior during training. We set À = 15 for all reported results to maintain consistency across examples.
4.5. Ablation Study
We conducted an ablation study validate the significance of each critical component in FlexiClip. The quantitative re- sults of the study are detailed in Table 4, while Figure and 7 showcases qualitative comparison of the different variants. We performed ablation to describe importance of tempo- ral Jacobian obtained from pfODE and the flow matching loss, which constitute the core our system. Notably, geometric deviation (GD) in FlexiClip higher compared to AniClipart due to the absence of ARAP deformation, which inherently minimizes shape distortion observed from reduced deformation Smoothness(DS).
When is set too low, such as around 1, model struggles generate coherent motion aligned with the textual descrip- tion, often requiring up 1000 gradient descent steps to produce acceptable outputs. Increasing À incrementally to values up to 5 does not result in a significant reduction in the required number of training steps, indicating limited benefit in that range. However, a more noticeable impact emerges when À is raised values between 5 and 10, where we ob- serve variability convergence, some animations achieve satisfactory quality in as few as 600 steps, while others still require up to 900 steps.
Temporal Jacobian To evaluate the effectiveness of in- corporating temporal Jacobian, we removed this component and instead used baseline keypoint transformation with- out considering the continuous dynamics provided by the POODE framework. Without temporal Jacobian, the ani- mation exhibited noticeable artifacts (Fig.6), including lack of smoothness in movements and unnatural keypoint transitions, as seen the parrot, ghost, and cloud exam- ples in (Fig.6). The quantitative results corroborate these findings: the "w/o Temporal Jacobian" variant exhibited a
At A 15, the motion generation becomes consistently more reliable, with most animations aligning well with the text prompt after approximately 700 training steps. This value represents a practical trade-off between convergence speed and motion quality. Pushing À beyond 15 leads noticeably sharper and faster motions, but this comes at the expense of temporal smoothness, resulting less natural-
8

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FlexiClip: Locality- Locality-Peeserving Free-Form Character Animation
lower motion variance (MV= 23.00) and higher temporal inconsistency (TC= 8.80). Additionally, the geometric dis- tortion (GD) score for this variant decreased to 51.50 (vs Default) showing rigid transformation as seen from ghost, parrot example it failed to show movement of hands and wings flapping respectively. In contrast, the default setting, with temporal Jacobians, yielded superior results across all metries, highlighting its necessity for realistic and accurate animations.
bility animate based on complex textual conditions. Here, she dances and folds her hands in rhythm with the descrip- tion, reflecting the system's ability to integrate fine-tuned motion semantics with precise keypoint dynamics.
Multiple Objects Demonstrated coordinated interactions. The couple dancing exemplifies FlexiClip'ss 's support for ani- mating multiple objects simultancously. The synchronized movements of the man and woman highlight the system's 's proficiency in managing interactions between objects while maintaining spatial and temporal coherence.
Table Ablation Study with FlexiClip variants.
FlexiClip Variant
MV f
TC 4
GD 4
4
AE
w/o Temporal Jacobian
23.00
8.80
51.50
14.00
105.00
Layered Animations FlexiClip supports layered anima- tions (see in Fig.l Breakdancer animation) for depth and complexity. This allows for the creation of dynamic ani- mations enhancing its applicability for interactive media.
woo Flow Match. Loss
24.50
8.40
53,00
14.20
95,00
Default
25.33
8.14
52.34
13.76
113.44
Flow Matching Loss The flow matching loss plays a cru- cial role in aligning the generated motion trajectories with the temporal coherence and dynamics inferred from text de- scriptions. To assess its impact, we omitted the flow match- ing loss from the total loss. As shown in the man and woman dance examples in Fig.7, this substitution led to erratic and exaggerated movements, deviating significantly from the in- tended motion semantics. Quantitatively, "w/o Flow Match. Loss" variant showed increased geometric distortion (GD= = 53.00) and reduced average energy (AE = 95,00), indicative of less expressive and abrupt motion dynamics. Addition- ally, temporal consistency (TC) degraded slightly (TC = 8.40), reinforcing the importance of this loss in maintain- ing stable frame-to-frame transitions. The absence of flow matching loss caused inconsistencies visible in the chaotic limb movements and unstable/abrupt posture transitions in the dancing examples. The default setting, which incorpo- rates flow matching loss, demonstrated balanced trade-off between dynamism and coherence, achieving the highest average energy (AE = 113.44) and competitive motion variance (MV = 25.33) with smooth animation.
Table 5. FlexiClip: Diverse and Complex Animations.
Input
Complex Animation Illustrations
sways breeze.
(a)
women in green
dets and blac bornd
famcs fokling
(8)
damin
5. Conclusion
We introduced FlexiClip, a cutting-edge framework for text- to-animation generation, excelling in visual identity preser- vation, text-video alignment, and animation smoothness. Extensive evaluations, including user studies, demonstrate that FlexiClip outperforms existing methods like AniClipart and LTXVideo, particularly in handling complex deforma- tions, maintaining temporal consistency, and producing re- alistic motions. Ablation studies validated the importance of temporal Jacobians and flow matching loss, essential for smooth transitions and accurate motion dynamics. FlexiClip supports diverse scenarios, including rotational dynamics, multi-object interactions, and layered animations, making it versatile for interactive media and entertainment. By setting a new standard in text-to- an-matimm frameworks, FlexiClip paves the way for future advancements in real-time applica- tions, 3D integration, and personalized animations.
4.6. More Results
FlexiClip has been able to support diverse and complex animations (Tab.5), broadening its applications in creating visually captivating and textually coherent animations.
Rotation Demonstrated rotational movements. The flower swaying its petals in the breeze showcases FlexiClip's ss ability to handle smooth rotational dynamics. Without any rota- tional mechanism explicitly, the system captures the gentle oscillation of petals, creating lifelike representation of natural motion.
Demonstrated complex mo- tions via multiple text conditioning. The woman in a green dress with black polka dots demonstrates FlexiClip's 's capa-
Multiple Text Conditions

---

FlexiClip: Locality- Free-Form Character Animation
Impact Statement
References
This paper introduces FlexiClip, a novel framework for ani- mating static clipart images with enhanced temporal coher- ence and geometric integrity. By integrating temporal Jaco- bians, continuous-time modeling via probability flow ODEs (pfODEs), and flow matching loss inspired by GelowNet principles, FlexiClip addresses longstanding challenges in clipart animation, such as abrupt motions and geometric distortions.
Bengio, Y., Lahlou, S., Deleu, T., Hu, E. J., Tiwari, M., and Bengio, E. Gflownet foundations. The Journal of Machine Learning Research, 24(1):0000610066 2023.
Cacciola, F. A egal implementation of the straight skeleton of simple 2d polygon with holes. In 2nd CGAL user workshop, volume 1. Citeseer, 2004.
Chen, H., Xia, M., He, Y., Zhang, Y., Cun, X., Yang, S., Xing, J., Liu, Y., Chen, Q., Wang, X., et al. Videocrafterl: Open diffusion models for high-quality video generation. arXiv preprint arXiv:2310.19511 2023.
Potential Positive Impacts
Advancement in Digital Animation: FlexiClip's methodology can significantly benefit industries in- volved in digital animation, including education, en- tertainment, and digital marketing, by enabling the creation of smooth and natural animations from static images.
Chen, H., Zhang, Y., Cun, X., Xia, M., Wang, X., Weng, C., and Shan, Y. Videocrafter2: Overcoming data limitations for high-quality video diffusion models. In Proceedings of the IEEE/CVF Conference Computer Vision and Pattern Recognition, pp. 7310-7320 2024.
Accessibility for Content Creators: By simplifying the animation process for clipart images, FlexiClip can empower individual creators and small businesses to produce high-quality animations without extensive resources.
de Albuquerque, D. and Pearson, J. Inflationary flows: Cal- ibrated bayesian inference with diffusion-based models. In Globerson, A., Mackey, L., Belgrave, D., Fan, A., Pa- quet, U., Tomczak, J., and Zhang, C. (eds.), Advances in Neural Information Processing Systems, volume 37, pp. 96847-96891. Curran Associates, Inc., 2024.
Educational Tools Enhancement: The ability to imate educational clipart can lead to more engaging learning materials, potentially improving educational outcomes.
Gal, R., Vinker, Y., Alaluf, Y., Bermano, A., Cohen-Or, D., Shamir, A., and Chechik, G. Breathing life into sketches using text-to-video priors. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 1325-4336, 2024.
Potential Negative Impacts and Mitigations
The case of animating static images could be misused to create deceptive content. To mitigate this, it's essential to develop and integrate detection tools that can identify Al-generated anima- tions.
Misinformation Risks:
HaCohen, Y., Chiprut, N., Brazowski, B., Shalem, D., Moshe, D., Richardson, E., Levin, E., Shiran, G., Zabari, N., Gordon, O., et al. Ltx-video: Realtime video latent diffusion. arXiv preprint XXXx:2500.00103, 2024.
Ho, J. and Salimans, T. Classifier-free diffusion guidance. arXiv preprint arXiv:2207. 12598, 2022.
Intellectual Property Concerns: Animating copy- righted clipart without proper authorization could in- fringe on intellectual property rights. Users should be educated copyright laws, and systems should include checks to prevent unauthorized use.
Lei, J., Hu, X., Wang, Y., and Liu, D. Pyramidflow: High- resolution defect contrastive localization using pyramid normalizing flow. In Proceedings of the IEEE/CVF Con- ference on Computer Vision and Pattern Recognition (CVPR), pp. 14143-14152, June 2023.
Bias in Animation Outputs: If the training data for FlexiClip contains biased representations, the anima- tions produced might perpetuate these biases. It's cru- cial to use diverse and representative datasets and im- plement bias detection mechanisms.
Li, T.-M,, Lukáë, M., Gharbi, M., and Ragan- Kelley, J. Differentiable vector graphics rasterization for editing and learning. ACM Transactions on Graphics (TOG), 39 16):1-15,22
Ethical Considerations
Lim, S., Yoon, E., Byun, T., Kang, T., Kim, S., Lee, K., and Choi, S. Score-based generative modeling through stochastic evolution equations in hilbert spaces. In Pro- ceedings of the 37th International Conference on Neural Information Processing Systems, NIPS '23, Red Hook, NY, USA, 2023. Curran Associates Inc.
While FlexiClip primarily aims to advance the field of ma- chine learning and animation, it is important to remain vig- ilant about its applications. Developers and users should adhere to ethical guidelines, ensuring that the technology is used responsibly and does not contribute to societal harm.
10

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FlexiClip:
Free-Form Character Animation
Poole, B., Jain, A., Barron, J. T., and Mildenhall, B. Dream- fusion: Text-to-3d using 2d diffusion. arXiv preprint arXiv: 1488, 2022.
Wang, F.-Y., Huang, Z.,, Bian, W., Shi, X., Sun, K., Song, G., Liu, Y., and Li, H. Animatelcm: Computation-efficien personalized style video generation without personalized video data. In SIGGRAPH Asia 2024 Technical Commu- nications, pp. 1-5. 2024.
Wang, J. Yuan, H., Chen, D., Zhang, Y. Wang, X., and Zhang, Modelscope text-to-video technical report. arXiv preprint arXiv:2308.06571, 2023.
Wu, R., Su, W., Ma, K., and Liao, Aniclipart: Clipart animation with text-to-video priors. International Journal of Computer Vision, pp. 1-17, 2024.
Xing, J., Liu, H., Xia, M., Zhang, Y., Wang, X., Shan, Y., and Wong, T.-T. Tooncrafter: Generative cartoon interpolation. ACM Transactions on Graphics (TOG), 43 (6):1-11, 2024.
Xing, J., Xia, M., Zhang, Y., Chen, H., Yu, W., Liu, H., Liu, G., Wang, X., Shan, Y., and Wong, T.-T. Dynamicrafter: Animating open-domain images with video diffusion pri- ors. In European Conference on Computer Vision, pp. 399 417. Springer, 2025.
Yang, J., Zeng, A., Zhang, R., and Zhang, L. Unipose: De- tecting any keypoints. arXiv preprint arXiv:2310.08530, 2023.
Zhang, S., Wang, J., Zhang, Y., Zhao, K., Yuan, H., Qin, Z., Wang, X., Zhao, D., and Zhou, J. 12vgen-xl: High-quality image-to-viee synthesis via cascaded diffusion models. arXiv preprint arXiv:2311.04155 2023.

---

FlexiClip: Locality-Preserri Free-Form Character Animation
A. Ablation Studies
Input
(w/o Flow Matching Loss)
Vs Default
Input
(w/o Temporal Jacobian) Vs Default
The porrot flapping its wings.
nenon doncer denerg
(a) Ablation
(a) Ablation
(b) Default
(b) Default
The Helloacen phost vorig
(a) Ablation
y
penann weoring a upchand
in in on & and
(b) Default
Paisoe suns wha siona aammu yeutt an
(a) Ablation
dky
(a) Ablation
(b) Default
(b) Default
Table Ablation: w/o Temporal Jacobian Default- This figure compares animations with and without the temporal Jacobian. With- it, noticeable artifacts such jerky movements and unnatural keypoint transitions appear (e.g.. parrot, ghost, cloud). In contrast, the temporal Jacobian yiclds smoother, more consistent, and rcalis- tic animations.
Table Ablation: w/o Flow Matching Loss vs Default Removing the flow matching loss leads erratic, exaggerated motion with chaotic limb movements and unstable transitions. Including the flow matching loss preserves smooth, dynamic, and coherent animations, ensuring stable frame-to come-to-franc to-frame transitions
w/o Temporal Jacobian: To evaluate the effectiveness of incorporating temporal Jacobian, we removed this component and instead used baseline keypoint transformation without considering the continuous dynamics provided by the pfODE framework. Without temporal Jacobian, the animation exhibited noticeable artifacts (Fig.6), including lack of smoothness in movements and unnatural keypoint transitions, seen in the parrot, ghost, and cloud examples in Fig.6. The quantitative results corroborate these findings: the "w/o Temporal Jacobian" variant exhibited a lower motion variance (MV 23.00) and higher temporal inconsistency (TC = 8.80). Additionally, the geometric distortion (GD) score for this variant decreased to 51.50 (vs Default) showing rigid transformation as seen from ghost, parrot example it failed to show movement of hands and wings flapping respectively. In contrast, the default setting, with temporal Jacobians, yielded superior results across all metries, highlighting its necessity for realistic and accurate animations.
The flow matching loss plays a crucial role in aligning the generated motion trajectories with the temporal coherence and dynamics inferred from text descriptions. To assess its impact, omitted the flow matching loss from the total loss. As shown in the man and woman dance examples in Fig.7, this substitution led to erratic and exaggerated movements, deviating significantly from the intended motion semantics. Quantitatively, the "w/o Flow Match. Loss" variant showed increased geometric distortion (GD 53.00) and reduced average energy (AE = 95.00), indicative of less expressive and abrupt motion dynamics. Additionally, temporal consistency (TC) degraded slightly (TC 8.40), reinforcing the importance of this loss in maintaining stable come-tto-frame transitions. The absence of flow matching loss caused inconsistencies visible in the chaotic limb movements and unstable/abrupt posture transitions in the dancing examples. The default setting, which incorporates flow matching loss, demonstrated a balanced trade-off between dynamism and coherence, achieving the highest average energy (AE 113.44) and competitive motion variance (MV = =25.33) with
w/o Flow Matching Loss:
12

---

FlexiClip: Locality Free-Form Character Animation
smooth animation.
B. FlpxiClip Vs T2V/I2V Models
nonon doncen Che-Che
The parnot flopping its wings.
boy Jumping chuttlacock
m
h
TT
to the
handball
Input Clipart
DynamiCrafter
Animatte.CCM-12V
LTXVideo
Pyramid Flow
Figure 4. FlexiClip vs T2V/12V Models:
LTXVideo and PyramidFlow show moderate performance, with scores higher than methods like DynamiCrafter and Animatel (CM CCM-1VV, but still lagging behind FlexiClip. While these methods manage basic identity preservation, they struggle with animation movement and text alignment, resulting in lower ratings. DynamiCrafter, in particular, performs poorly across all metrics, reflecting its inability to preserve visual details and adapt effectively to text prompts.
The methods evaluated in this study exhibit varying performance levels when it comes to key animation quality aspects, such as identity preservation, text-video alignment, and smoothness. While certain techniques are successful in preserving the overall semantics of the input clipart, they often fall short in maintaining finer details, leading to lower identity preservation scores. These methods tend to produce animations that are static or lack significant motion, which negatively impacts the alignment with the given text prompts, ultimately resulting in less engaging and less accurate animations. Other methods, such AniClipart and LTXVideo, perform relatively well but still struggle with capturing finer details and translating text prompts into dynamic animations with sufficient movement. These approaches yield more static animations, which limits their ability accurately reflect the intended transformations and reduces the overall visual appeal.
On the other hand, methods like DynamiCrafter exhibit the weakest performance in all areas, with noticeably poor identity preservation and minimal alignment with text descriptions. The animations generated by these techniques tend to lack both the required detail and movement, making them less suitable for generating high-quality, contextually accurate animations.
Overall, the comparison highlights the significant improvements offered by FlexiClip over other methods, demonstrating its ability generate high-quality, detailed, and smooth animations that align more effectively with input prompts.
C. Derivation of the Fokker-Planck Equation Under time varying densities
We start with the smoothing kernel defined as:
1 x(x, t) = N(x; p. C(t)) = (2m)d/2 (C) exp (-2(0- - 1) - mi)
where:
13

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FlexiClip: SncalityPPreserving Free-Form Character Animation
/ is the mean,
(t) is the covariance matrix,
C.1. Derivatives the Kernel
C. 1. TIME DERIVATIVE
The time derivative of k(2, t) is given by:
-) ())l==))TT--- -T Ōx (0) + (0-
x(x,t)
1.2. GRADIENT
The gradient of k<x, () is:
VK= -0- - m)
1.3.3. SECOND DERIVATIVE
The second derivative is:
0%x
= ri (x- ()) n)); [c]
0r,0n,
C.2. Evolution of the Probability Density
The time varying probability density p(a, t) evolves as:
p(x, t) = po(x) * k(2, t),
where * denotes convolution. The evolution is governed by:
C.2.1. TIME DERIVATIVE OF p(x,
Pp Ōk po(x)
Øl 01
Substituting the time derivative of τi, we have:
dp
po()) K 1r-C-10)+ + 2 tr
1
(c-1(x - p)(x -))==-))T00 -)(o-())
C.2.2. DIVERGENCE OF THE DRIFT TERM
For drift vector field f(x), the divergence term is:
-V (fp) -po(x)) V (fn),
where:
V. (fR) = (V f) f Vn.
C.2.3. DIFFUSION TERM
The diffusion term, assuming the diffusion matrix G(z, t), becomes:
V.V, Σ Gup = (o(x))
V.V, Σ Gu
14

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FlexiClip: Locality Free-Form Character Animation
C.3. Simplifications and Final Form
Assume f(x) 0 (no drift) and J, (spatially homogeneous diffusion). The condition simplifies to:
- + 2
1
1 1 tr (c- - (x - 1) --10)) - (r(C-IGGT) 2
1 tr (c- 4) -2) ()TC-
+ 2
This condition is satisfied when:
GG (x,t)= C(t).
15


Reviews:
[{"review_id": "hzcz9UiM8Z", "reviewer": "Reviewer_GNpb", "summary": "This paper addresses several key challenges in the the problem of clipart animation. To address the noise accumulation along the animation, the paper proses the novel concept of temporal Jacobians to correct the temporal noise. To ensure the smooth temporal transitions between frames, the paper proposes pfODE to model the temporal Jacobians. A novel flow matching loss is introduced to optimize the temporal noise. The result: high quality clipart animation with great temporal coherence. The experiments are quite comprehensive. The major technical claims from the paper are all well validated.\n\nUpdate after rebuttal: after reading other reviewers' comments and the authors' rebuttal, my rating of acceptance remains unchanged.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Many thanks for reviewing our paper and for your detailed and thoughtful evaluation. I truly appreciate the time and effort you put into this, as well as your unbiased rating of our work.\n\nRegarding your question about the 3D extension, FlexiClip can easily be adapted for 3D animation. This requires adding just one extra coordinate and learning the Bézier trajectory over it, which is straightforward for our approach. In fact, we plan to release the code with configurable 2D and 3D settings.\n\nTo specifically address your question—yes, our method can be extended to 3D mesh deformation, and we will include the 3D extension in our code release.\n\nLet me know if you need any further refinements!", "claims_and_evidence": "I find that all the major technical claims are supported by intuitions and experimental validation.\nClaim 1: the temporal Jacobians idea is novel and it is the base to a solution to temporal noise accumulation. To my knowledge, this novelty claim is true, and the effectiveness is validated in experiment Sec. 4.4  - removing this part leads to noticeable temporal artifacts.\n\nClaim 2: the pfODE formulation and the flow matching loss enables temporal smoothness. This claim is supported by the change in several metrics after removing this loss from training (Sec. 4.4).\n\nClaim 3: the proposed method suits multiple scenarios including multi-object, layered objects and rotation. These are demonstrated in experiment Sec. 4.5\n\nOverall, I find this paper solid in making and validating the claims.", "methods_and_evaluation_criteria": "Overall the method makes a lot of sense to me. The paper first identifies the key problem with previous clipart animation methods -- using rigid parameterization (such as the ARAP prior in AniClipart) for motion, and do not explicitly account for the noise accumulation over time. It is a great idea to decompose the deformation Jacobian into the spatial one and per-time-step corrective Jacobians, with the latter being optimized using flow matching loss -- treating the spatial Jacobian as the backward process that introduces temporal noise and the forward process reduces such noise. The formulation is elegant and effective.\n\nAs for evaluation, the paper compares with a number of recent methods on the same (clipart animation) or neighboring (video generation) tasks. The metrics are chosen to well reflect the major improvements brought by this paper -- temporal coherency, deformation smoothness, and the capability to preserve identity. These design make the evaluation results convincing.", "theoretical_claims": "The major theoretical claims (implicitly made) are that (1) The spatial + temporally corrective Jacobians are suitable representation for this task; (2) the probability flow ODE is suitable to model the evolution of the temporal Jacobians, and (3) the flow matching loss can effectively minimize the temporal noise. These theories are outside of my major research domain, but I tried to understand them reading through Sec. 2 and 3 and the analysis and derivations make sense to me. Would love to discuss and learn from other reviewers to give a solid assessment on this part.", "experimental_designs_or_analyses": "I appreciate the well-organized experiment section. The metrics are clearly defined and they are well-designed to reflect different aspects of animation -- the extent of the motion (AE, MV), temporal coherency (TC, DS) and visual identity preservation. The new method is in-depth compared with the most recent baseline, AniClipart (Sec. 4.3). The findings in this section well align with the motivations and claims in the paper introduction. User study further corroborates the superior perceptual quality of the new method. The ablation study is the key evaluation -- confirming that the three major components in the proposed method are effective and necessary.\nIn all, the experiment section is strong.", "relation_to_broader_scientific_literature": "The paper proposes a novel and effective method for clipart animation from single image input. It can be of great interest to the computer graphics community as a novel alternative for automatic character animation.", "essential_references_not_discussed": "N.A.", "other_strengths_and_weaknesses": "I find this paper very solid: practical problem, clever idea, and extensive experiments that validates all the major technical novolties. The paper is self-contained and well written. I'd recommend acceptance.", "other_comments_or_suggestions": "I do not have other major comments.", "questions_for_authors": "Is the method applicable for 3D mesh deformation?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "Gji4mUlta5", "reviewer": "Reviewer_Ry9s", "summary": "The paper proposes FlexiClip, a novel method for animating clipart images while preserving temporal coherence and geometric integrity. It extends existing approaches by incorporating temporal Jacobians for incremental motion correction, probability flow ODEs (pfODEs) for continuous-time modeling, and flow matching loss inspired by GFlowNet principles. The paper claims that these enhancements lead to smoother, more consistent animations while avoiding the geometric distortions and temporal artifacts found in previous methods like AniClipart. The experimental results showcase the advantages of FlexiClip in producing better animations across diverse clipart types.\n\nThis paper doesn't include Impact Statements, which are required by ICML. Therefore, I suggest rejection.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks for your review we will include the following impact statement, basically we did'nt included the impact statement since we thought that it will count towards page limit during review process and can be added easily when accepted since 1 page extra will be given to submit the accepted paper to address the reviewer comments. Also, if you read this https://icml.cc/Conferences/2025/CallForPapers, that reviewer does not have authority to reject submission based on missing impact statement only program chairs can do that. Also there is this FAQ also there is this FAQ which clarifies that we did not desk-reject any papers for missing impact statements: https://icml.cc/Conferences/2025/PeerReviewFAQ. \n\nPlease find the below the detailed impact statement for our work, we request you to please revise your acceptance score for this paper: \n\nThe innovations in FlexiClip have significant implications for multiple domains:\n\n**Animation Industry**\nFlexiClip could streamline production processes for 2D animation, potentially reducing the labor-intensive nature of traditional animation while maintaining artistic quality. The technology could be particularly valuable for independent animators and small studios without access to extensive resources.\n\n**Digital Content Creation**\nAs online platforms continue to prioritize dynamic content, FlexiClip's approach could enable creators to efficiently produce engaging animated content from static images, expanding creative possibilities for digital storytelling, marketing, and educational resources.\n\n**User Interface Design**\nThe locality-preserving aspects of FlexiClip could inform new approaches to animated user interfaces, where maintaining visual coherence during transitions between states is crucial for user experience.\n\n**Broader Implications**\nBeyond its immediate technical contributions, FlexiClip represents a significant step toward bridging traditional animation principles with modern computational techniques. By addressing the intertwined challenges of temporal consistency and geometric integrity, the research sets a new standard for character animation that respects both the artistic qualities of the original image and the physical plausibility of movement.\n\nThe paper \"FlexiClip: Locality-Preserving Free-Form Character Animation\" introduces transformative advancements in the field of clipart animation, addressing critical challenges such as maintaining visual fidelity and ensuring temporal coherence in character motion. FlexiClip achieves smooth, natural-looking animations while preserving the structural integrity of clipart images. Additionally, its integration with pre-trained video diffusion models through methods like Video Score Distillation Sampling (SDS) bridges traditional animation principles with cutting-edge machine learning frameworks.\n\nThese innovations have far-reaching implications for the animation industry, enabling streamlined workflows for animators and reducing the labor-intensive nature of traditional animation processes. FlexiClip's ability to generate high-quality animations from static clipart images expands creative possibilities for digital content creation, marketing, and educational applications. Furthermore, its locality-preserving approach holds promise for enhancing animated user interfaces, improving transitions and user experiences.\n\nBeyond practical applications, FlexiClip sets a new benchmark in character animation by addressing intertwined challenges of temporal smoothness and geometric fidelity. Its robust framework not only advances artistic expression but also paves the way for future developments in computer graphics, animation technology, and related fields such as robotics and biomechanics. By redefining standards for seamless motion generation, FlexiClip establishes itself as a foundational contribution to the evolution of animation techniques in the digital age.", "claims_and_evidence": "Most of the claims are proved via experiments and results. While there are some geometric distortions that occur in the results.", "methods_and_evaluation_criteria": "Yeah, the methods make sense to me.", "theoretical_claims": "None", "experimental_designs_or_analyses": "Yes, the experiments looks sound to me, and this paper follows the experiment setup of an existing work.", "relation_to_broader_scientific_literature": "I'm not familiar with this area, so it's hard for me to write this part.", "essential_references_not_discussed": "I'm not familiar with this area, so it's hard for me to write this part.", "other_strengths_and_weaknesses": "Strengths: The use of probability flow ODEs (pfODEs) provides a mathematically grounded way to ensure temporal smoothness.\nThe flow matching loss based on GFlowNet principles is a reasonable adaptation.\n\nWeakness: Some results show noticeable distortions, particularly in human characters (e.g., hands, faces, and body parts deform unnaturally). While motion smoothness is analyzed, the paper lacks a quantitative evaluation of motion accuracy.", "other_comments_or_suggestions": "None", "questions_for_authors": "None", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "8M8qknZSuv", "reviewer": "Reviewer_LSdo", "summary": "The paper proposes FlexiClip,  a novel approach designed to overcome these limitations by addressing the in\u0002tertwined challenges of temporal consistency and geometric integrity, which extends traditional Bezier curve-based trajectory modeling with (1) temporal Jacobians to correct motion dynamics incrementally, (2) continuous-time modeling via pfODEs to mitigate temporal noise, and (3) a flow matching loss inspired by GFlowNet principles to optimize smooth motion transitions. The method sets a new standard for clipart animation.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Sensitivity of λ in Balancing SDS Loss and Flow Matching Loss**\n\nThank you for your thoughtful review and for raising this important question regarding the sensitivity of our method to the hyperparameter $\\lambda$, which balances the SDS loss and flow matching loss.\n\nThrough our experiments, we observed that tuning $\\lambda$ is crucial for balancing trajectory alignment with text and ensuring smooth motion. In our setup, we set $\\lambda$ = 15 for consistency across all examples.\n\n1. When $\\lambda=1$, the model requires significantly more gradient updates—often up to 1000 steps—to generate acceptable motion.\n2. Increasing $\\lambda$ up to 5 does not significantly reduce the number of required steps.\n3. Raising $\\lambda$ from 5 to 10 introduces some variability, where good results can sometimes be achieved in 600 steps, but in other cases, up to 900 steps are needed.\n4. At $\\lambda=15$, nearly all generated motions align well with the text prompt at around 700 steps.\n5. Further increasing $\\lambda$ results in sharper and faster motion, which appears less smooth.\n\nWe appreciate this insightful question and will use the additional page allowance in the final paper to provide further details and examples.\n\nAdditionally, we invite you to explore our GitHub page (https://creative-gen.github.io/flexiclip.github.io/), where we showcase more complex motion examples beyond those currently visible in our paper which are deemed to be simpler animations.\n\nWe sincerely appreciate your valuable feedback. We kindly request you to consider our responses and, if appropriate, please increase your score accordingly.", "claims_and_evidence": "Yes. The paper's core claims about FlexiClip are well-supported by compelling evidence. Visual identity preservation is validated through higher CLIP scores (0.9563 vs 0.9401) and 94.90% user preference.Temporal consistency improvements are demonstrated via lower TC scores (8.14 vs 8.51) and effective ablation studies. Text-video alignment claims are substantiated by improved X-CLIP scores (0.2102 vs 0.2075) and 94.54% user preference in alignment ratings.", "methods_and_evaluation_criteria": "Yes, the FlexiClip method makes sense to me. The bitmap metrics, animation metrics used and the proposed deformation smoothness and animation energy also make sense to me.", "theoretical_claims": "Yes. The main theoretical foundation in Section 2.2 and Appendix C, where the authors develop their continuous-time modeling approach using probability flow ODEs. I didn't find any obvious errors in their mathematical derivations.", "experimental_designs_or_analyses": "Yes, the comparison and ablation study are efficient. The sample size (30 participants) for the user study is moderate but acceptable.", "relation_to_broader_scientific_literature": "The FlexiClip paper makes three key innovative contributions to animation research: (1) It introduces temporal Jacobians that incrementally correct spatial deformations, addressing the frame-to-frame inconsistency problems in prior works like AniClipart (Wu et al., 2024); (2) It adapts probability flow ODEs (originally from generative modeling by Song et al., 2020) to animation contexts, creating a continuous-time framework that preserves geometric structure during complex movements; and (3) It implements a flow matching loss inspired by GFlowNet principles (Bengio et al., 2023) that optimizes smooth transitions between frames.The significance lies in FlexiClip's mathematical formulation that unifies spatial and temporal modeling, effectively solving long-standing challenges in clipart animation where visual identity preservation must be balanced with natural motion dynamics.", "essential_references_not_discussed": "N/A", "other_strengths_and_weaknesses": "Other strengths:\nThe development of novel metrics (DS and AE) shows thoughtfulness in how animation quality should be measured.\nThe paper clearly identifies and addresses a specific limitation in prior work, the trade-off between spatial coherence and temporal consistency in clipart animation. \n\nOther weaknesses:\nThe evaluation focuses on relatively simple character animations.", "other_comments_or_suggestions": "N/A", "questions_for_authors": "How sensitive is the method to the choice of hyperparameters, particularly the λ weight balancing the SDS loss and flow matching loss?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "LvAiDSij1s", "reviewer": "Reviewer_3qmH", "summary": "In this paper, the authors propose a new method, named as FlexiClip, to achieve better temporal coherence and geometric consistency in animated clipart. To better preserve motion smoothness without introducing geometric distortions, FlexiClip utilizes Probability flow ODE (pfODE) to model the evolution of temporal Jacobian which incrementally adjust the spatial geometry over time to account for temporal variations. As a key technical contribution, a flow matching loss is further used to optimize the reduction of temporal noise. Qualitative and quantitative comparisons are performed to validate the effectiveness of the proposed method.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your thoughtful review. Below, we provide detailed responses to each of the weaknesses you raised:\n\n1. **Figure 3 Analysis**: Upon closer inspection, you can observe that AniClipart distorts objects (e.g., hand distortion in the boy/girl jumping and woman dancing examples), lacks proper text conditioning (e.g., the parrot), and exhibits poor temporal consistency (e.g., the boy jumping). If the figures are unclear, we encourage you to view the detailed versions on our anonymous webpage: https://creative-gen.github.io/flexiclip.github.io/.\n\n2. **Additional Results**: The webpage contains more extensive results, showcasing a variety of motion complexities, including couple dancing and two-object interactions. We are also in the process of adding more results, including 3D motion animations.\n\n3. **3D Extension**: Thank you for your question regarding 3D extensions. FlexiClip can be easily adapted for 3D animation, as it only requires adding one extra coordinate and learning the Bézier trajectory over it. This modification is straightforward for our approach. We will release the code with configurable 2D and 3D settings.\n\n4. **User Studies on Ablation Results**: We will conduct user studies on the ablated results as well. However, if you are referring to minor differences between the ablated and full models, we recommend checking the videos on our webpage. While the images may not clearly highlight these differences, the video outputs of the full and ablated models exhibit significant variations. We will include these results in the final draft for further user study.\n\n5. **Typographical Errors**: We appreciate your feedback regarding typos and will carefully proofread the final revision to ensure all errors are corrected.\n\nOnce again, we sincerely appreciate your time and effort in reviewing our paper. We kindly request you to consider our responses and, if appropriate, please increase your score accordingly.", "claims_and_evidence": "Please see the comments below.", "methods_and_evaluation_criteria": "Yes. I think the proposed method is technically sound.", "theoretical_claims": "I have checked the proofs in Section C.", "experimental_designs_or_analyses": "Yes, please see the **Claims And Evidence** part.", "relation_to_broader_scientific_literature": "I think this submission has already listed sufficient related papers.", "essential_references_not_discussed": "I think the current related work part is okay.", "other_strengths_and_weaknesses": "**Strengths**:\n1. This paper is well written. I can follow it easily.\n2. From my understanding, I like the basic idea of FlexiClip which is simple and clear.\n3. The authors perform sufficient experiments to verify the effectiveness of the proposed method.\n\n**Weakness**:\n\nI am not an expert in this area so I just have some ideas to help authors refine this work.\n1. The visual improvement over AniClipart is limited. For example, in Figure 3, both AniClipart and FlexiClip can synthesize good shapes with adaptive details. I also cannot perceive meaningful differences between these two methods in the supplementary website.\n2. The current experimental results can only support rigid motion rather than non-rigid complicated motions. Could you please provide more challenging demo results in the revision?\n3. Can the key contribution of FlexiClip be extended to 3D shapes? Can the authors share some insights for it?\n4. Could you also conduct some user studies for the ablation study? For some examples shown in Table 6-7, the visual differences between the ablated model and the full model are minor. Adding some user study results could help to achieve comprehensive conclusions.\n5. Typos: L22-L23: \"Additionally, Recent\" -> \"Additionally, recent\";\n\n---\n## Update After Rebuttal\n\nI thank the authors for providing such detailed response which address most of my concerns. Thus I will remain a positive tone towards this submission.", "other_comments_or_suggestions": "No.", "questions_for_authors": "No.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: The paper proposes an innovative framework FlexiClip to address the challenges of maintaining visual fidelity and temporal coherence in animated clipart.  The technical contributions include: (1) temporal Jacobians for incremental motion correction, (2) continuous-time modeling through probability flow ODEs, and (3) a flow matching loss for reducing temporal noise. The proposed FlexiClip outperforms previous methods, achieving better scores in visual identity and animation quality. While the technical contributions and potential impact of the work are acknowledged, there are concerns about the extent of visual improvements and the limited scope of the evaluation. 


During the rebuttal phase, the authors have made efforts to address the reviewers' concerns during the rebuttal phase, particularly by clarifying the differences in their results compared to existing methods and explaining their evaluation methodology. They have also provided additional resources, such as a project page with detailed animations, to help reviewers better assess the quality of their results. These efforts lead to a consensus voting for the paper acceptance.


Given the positive feedback from all the reviewers and potentially impactful approach to animated clipart, the AC is happy to recommend accepting this paper for publication in ICML 2025. Congratulations! Please be aware that the authors are strongly encouraged to address the aforementioned points in their camera-ready version.
Decision: Accept (poster)