Keyframe Interpolation

• Keyframe Interpolation is a technique that generates smooth transitions between sparse user-specified frames by leveraging mathematical and geometric foundations.
• It employs advanced models such as transformer-based, residual, and diffusion approaches to capture high-dimensional, temporally coherent motion.
• The method integrates physical, semantic, and topological constraints to ensure realistic and consistent reconstruction of intermediate frames.

Keyframe interpolation refers to the synthesis of intermediate data—frames or states—between a set of sparse, user-specified, or algorithmically-extracted keyframes in time-dependent signals such as animation, video, motion capture, or scientific scalar fields. In contemporary research, this task is treated as a complex, high-dimensional interpolation problem, with the additional challenge of maintaining physical plausibility, temporal coherence, semantic consistency, and in certain domains, explicit topological or geometric constraints.

1. Mathematical and Geometric Foundations

The mathematical structure of keyframe interpolation crucially determines the smoothness and realism of the resulting transitions. Classical Euclidean approaches—such as affine or linear interpolation, cardinal and cubic Hermite splines, or subdivision curves—often fail to generalize to non-linear spaces or complex structural domains. For instance, "Smooth Interpolation of Key Frames in a Riemannian Shell Space" (Huber et al., 2017) generalizes spline and subdivision schemes to manifolds of thin shell surfaces, modeling shells as Loop subdivision surfaces and utilizing a Riemannian metric that jointly measures bending and membrane distortions. Discrete geodesic interpolation minimizes the path energy

$$E[(S_0, \ldots, S_K)] = K \sum_{k=1}^K W(S_{k-1}, S_k)$$

where $W(\cdot,\cdot)$ is a smooth approximation of the squared Riemannian distance. Auxiliary constructs—discrete geometric logarithm, exponential map, and parallel transport—enable geodesic "shooting," tangent transfer, and intrinsic cubic Hermite construction, resulting in physically and geometrically coherent animated transitions through keyframe space.

In the context of scientific scalar fields, "Topology Aware Neural Interpolation of Scalar Fields" (Kissi et al., 25 Aug 2025) employs a neural network that maps time $t$ (equipped with positional encoding) to the target field, with losses enforcing not only geometric proximity but also topological consistency using persistence diagrams and Wasserstein distances.

2. Model Architectures and Learning Strategies

Recent advances focus on leveraging data-driven and generative models to overcome limitations of classical schemes, especially in high-dimensional data and articulated motions.

• Transformer-based Interpolators: Systems such as SILK (Akhoundi et al., 9 Jun 2025) and "Continuous Intermediate Token Learning..." (Mo et al., 2023) demonstrate that a single-shot transformer encoder, when provided with carefully structured input (e.g., explicit root space poses, zero-filled missing slots, and velocities), can synthesize plausible in-betweening with minimal architectural complexity.
• Residual and Delta Mode Approaches: The deep $\Delta$-interpolator (Oreshkin et al., 2022) employs a residual learning paradigm, predicting the delta between a robust geometric baseline (SLERP interpolation) and the true intermediate, enhancing accuracy and robustness, and simplifying the learning problem.
• Autoregressive and Non-sequential Sampling: "Shuffled Autoregression for Motion Interpolation" (Huang et al., 2023) eschews left-to-right order, instead treating the interpolation sequence as a DAG where generation proceeds in a "shuffled" fashion, each frame conditioned on arbitrary sets of predecessors, improving error propagation and local continuity.
• Diffusion-based Generative Models: Keyframe interpolation is now dominated by latent diffusion models capable of generating multiple plausible in-between solutions. Dual-directional and bidirectional diffusion strategies, such as Generative Inbetweening (Wang et al., 27 Aug 2024) and ViBiDSampler (Yang et al., 8 Oct 2024), address temporal ambiguity and off-manifold artifacts by sampling forward from the start keyframe and backward from the endpoint, then fusing the results using aligned guidance (CFG++, DDS), cross-attention, or explicit condition paths (FCVG (Zhu et al., 16 Dec 2024)). Lightweight fine-tuning (e.g., only on value/output matrices in temporal attention as in (Wang et al., 27 Aug 2024)) further enables adaptation to backward motion without re-training the entire model.

3. Conditioning, Constraints, and Representational Choices

Effective keyframe interpolation often requires domain-specific structural or topological constraints to achieve consistency and fidelity:

• 3D Human Guidance and Pose Conditioning: PoseFuse3D-KI (Guo et al., 3 Jun 2025) integrates explicit 3D human geometry (via the SMPL-X model) into the conditioning pipeline, transforming pose, shape, and expression parameters into a 2D latent space, and fusing them through attention with 2D keypoint and rendering embeddings. This fusion, via joint and vertex attention,

$$O^J = \text{JointAttn}(Q, K^J, V^J),~~O^P = \text{VertexAttn}(Q, K^P, V^P)$$

provides geometric priors that are critical in handling occlusions, large articulated motions, and ambiguous dynamics.

• Semantic and Structural Conditions: FCVG (Zhu et al., 16 Dec 2024) explicitly interpolates framewise semantic or structural conditions (such as matched lines or poses extracted via models like GlueStick) to resolve ambiguity in the path and promote temporal stability, injecting these signals at each step of the generative diffusion process.
• Domain Adaptation and Skeleton-Agnostic Representations: PC-MRL (Mo et al., 13 May 2024) frames motion as temporally consistent point clouds rather than explicit hierarchical skeletons, facilitating unsupervised learning and retargeting across skeletons by using KNN-based temporal losses and roll-invariant quaternion encodings.
• Spherical Coordinate Interpolation: SIDQL (Zhang et al., 1 Jul 2024) ensures physical consistency (e.g., fixed bone lengths) in motion reconstruction by interpolating in spherical coordinates, with each point's trajectory $\Theta_m(t), \Phi_m(t)$ represented as third-order polynomials fit to the angular position and velocity at the keyframes.

4. Applications and Domains

Keyframe interpolation has far-reaching applications:

• Animation and CGI: Both physical shell surface animation (Huber et al., 2017) and human motion in-betweening (SILK (Akhoundi et al., 9 Jun 2025), delta-interpolator (Oreshkin et al., 2022), SAR (Huang et al., 2023)) focus on synthesizing temporally continuous, physically plausible animation from sparse pose or mesh specifications.
• Audio-driven Animation: KeyFace (Bigata et al., 3 Mar 2025) and KeyVID (Wang et al., 13 Apr 2025) use keyframe localization (from audio cues or optical flow motion scores), followed by generative interpolation for tasks such as lip-synced facial animation, precise alignment of dramatic events, and long-sequence audio-video synthesis.
• Video Generation, Editing, and Enhancement: Bidirectional diffusion samplers (ViBiDSampler (Yang et al., 8 Oct 2024)), and AdaFlow (Zhang et al., 8 Feb 2025) enable scalable video frame synthesis and text-driven editing over thousands of frames by adaptively slimming attention and selecting only the most content-representative keyframes.
• Scientific Visualization and Topological Data Analysis: Neural interpolation frameworks (Kissi et al., 25 Aug 2025) allow reconstruction of dense time-varying scalar field data from sparse keyframes coupled with persistent topological summaries, enabling applications in in-situ scientific computing, medical imaging, and simulation.
• Interactive and User-Guided Synthesis: Framer (Wang et al., 24 Oct 2024) introduces interactive control via keypoint trajectory guidance for frame interpolation, allowing users to explicitly control local motion, correspondences, and morphing paths, supplemented with an autopilot module for automatic estimation of trajectories.

5. Quantitative Evaluation and Benchmarking

Evaluation protocols draw on a diverse set of metrics tailored to the modality:

Metric	Domain	Role
FVD, FID	Video interpolation/generation	Measures overall perceptual/video quality
LPIPS	Visual similarity	Perceptual similarity between generated and real frames
PSNR, SSIM	Image/video quality	Pixel-level and structural similarity
NPSS	Motion interpolation	Normalized power spectrum similarity (temporal realism)
Chamfer, WCD	Line inbetweening	Line structure and continuity
KPE	Motion keyframes	Adherence to user-specified keyframe poses
Wasserstein	Scalar field topology	Topological discrepancy (via persistence diagrams)

Specialized benchmarks, such as CHKI-Video (Guo et al., 3 Jun 2025), LongV-EVAL (Zhang et al., 8 Feb 2025), and task-specific user studies (e.g., facial animation (Bigata et al., 3 Mar 2025)) provide standardization and meaningful comparison across algorithms and modalities.

6. Challenges, Limitations, and Research Trajectories

A common thread in recent advancements is the navigation of inherent ambiguities introduced by sparse constraints, non-Euclidean structure, and motion uncertainty. Ambiguous motion paths, occlusions, and large inter-keyframe gaps require architectures capable of both stochastic sampling and explicit conditioning. Recent methods have addressed these with bidirectional/genetic diffusion schemes, explicit topological and structural losses, and advanced attention/fusion strategies. Ongoing challenges include:

• Scaling efficiently to extremely long video (solved in part via AdaFlow's attention slimming (Zhang et al., 8 Feb 2025)).
• Robustness to imprecise constraints (addressed by time-warping and spatial residuals (Goel et al., 2 Mar 2025)).
• Generalization across domains and skeletons (using skeleton-agnostic, point cloud-based representations (Mo et al., 13 May 2024)).
• Semantic control, interactivity, and interpretability (as in Framer (Wang et al., 24 Oct 2024) and FCVG (Zhu et al., 16 Dec 2024)).

A plausible implication is continued integration of structural, semantic, and topological priors with generative diffusion frameworks, producing controllable, artifact-free, temporally stable interpolation for broad application domains.

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Keyframe interpolation thus stands at the intersection of geometry, learning, and domain-specific constraints, enabling powerful tools for animation, video synthesis, motion retargeting, and scientific data analysis. Current state-of-the-art methodologies leverage manifold-based calculus, advanced transformers, bidirectional generative models, explicit condition interpolation, and topological supervision to achieve high-fidelity, temporally coherent in-betweens from sparse or imprecise keyframes across complex data domains.