Sequence-Level Interpolation (Seq-Inter)

• Sequence-Level Interpolation (Seq-Inter) is a technique that treats interpolation as a sequence-wise problem, generating intermediate states with global consistency.
• It leverages continuous timestamp parameterization, segment-wise modeling, and sequence-level loss functions to ensure high fidelity and temporal coherence.
• Seq-Inter is applied in areas like video frame interpolation, zero-delay signal reconstruction, and latent trajectory modeling, enhancing scalability and performance.

Sequence-Level Interpolation (Seq-Inter) is a paradigm in signal, image, and video processing in which the interpolation task is formulated and solved at the granularity of entire sequences, rather than as isolated, pairwise, or fixed-step interpolation problems. This approach allows for the generation or reconstruction of intermediate states—whether numerical signal samples, image frames, or multidimensional sensory data—across arbitrarily fine temporal or spatial resolutions, while accounting for dependencies and structural consistency throughout the entire sequence. Seq-Inter enables high-fidelity, temporally-coherent, and scalable interpolation, and serves as a foundation for state-of-the-art methods in generative modeling, zero-delay signal reconstruction, and cross-domain sequence synthesis (Zhang et al., 1 Oct 2025, Ruiz-Moreno et al., 2022, Bose et al., 2021, Mahdi et al., 15 Apr 2026).

1. Defining Sequence-Level Interpolation

Sequence-Level Interpolation generalizes the classical interpolation problem by treating the sequence as a whole, either by optimizing end-to-end objectives over the entire signal or by enabling generation of arbitrary intermediate steps on demand. Unlike conventional methods that assume fixed interpolation steps (e.g., splitting the interval between two observations into evenly spaced frames or samples), Seq-Inter provides the following attributes:

• Continuity: The interpolation is not limited to pre-defined points; any timestamp or spatial location within the domain can be generated.
• Sequence Dependency: Choices at one step influence later steps, optimizing global objectives rather than merely local fits.
• Scalability: The methodology supports long sequences through hierarchical or segment-wise decomposition without incurring prohibitive computational costs.

The paradigm encompasses both generative approaches (as in video frame interpolation or latent trajectory generation) and signal reconstruction settings (as in smoothing splines under streaming or zero-delay constraints) (Zhang et al., 1 Oct 2025, Ruiz-Moreno et al., 2022, Bose et al., 2021).

2. Core Methodological Approaches

The realization of Seq-Inter depends on the application domain, but most state-of-the-art approaches feature:

• Timestamp or Position Parameterization: Each output is explicitly indexed by a continuous variable (e.g., normalized timestamp $t \in [0,1]$) rather than a discrete index (Zhang et al., 1 Oct 2025).
• Sequence-wise or Segment-wise Modeling: For tractability or memory efficiency, especially in deep generative pipelines, long sequences are decomposed into manageable sub-segments, each interpolated with local normalization and stitched back together (Zhang et al., 1 Oct 2025, Ruiz-Moreno et al., 2022).
• Sequence-level Loss Functions: Training objectives are applied across the entire output sequence or involve cumulative losses reflecting global signal quality, consistency, or smoothness (Ruiz-Moreno et al., 2022, Bose et al., 2021).
• Implicit or Explicit Conditioning: Temporal or spatial coherence is enforced not just by fixed endpoints, but by conditioning intermediate steps on appearance, motion tokens, or historical information extracted from previous segments (Zhang et al., 1 Oct 2025, Mahdi et al., 15 Apr 2026).

3. Models and Algorithms

Several algorithmic frameworks exemplify the Seq-Inter principle:

a. Generative Video Interpolation (ArbInterp)

ArbInterp deploys a DiT-based diffusion model augmented by Timestamp-aware Rotary Position Embedding (TaRoPE), enabling synthesis at any target timestamp, not just fixed intervals. For long or high-rate interpolation, a segment-wise generation scheme ("Seq-Inter" decomposition) is used, with appearance-motion decoupled conditioning: appearance consistency is enforced through explicit prefix frames, and motion coherence is preserved by motion tokens extracted via a Motion Semantic Extractor (MSE). This ensures seamless transitions when interpolating sequences of arbitrary length (Zhang et al., 1 Oct 2025).

b. Zero-Delay Smoothing Spline (RNN-Assisted Sequential Policy)

The zero-delay smoothing spline problem is framed as a sequential decision problem, where each piecewise polynomial segment is selected to minimize both instantaneous and expected future cumulative costs. A recurrent neural network (RNN) predicts the "cost-to-go" and informs a differentiable convex optimization layer that enforces smoothness and conformity to streaming data, with cumulative loss minimized over entire training sequences. This enables real-time, sequence-level, globally optimal signal interpolation under causal (zero-delay) constraints (Ruiz-Moreno et al., 2022).

c. Latent Trajectory Interpolation via Neural ODEs (NeurInt)

NeurInt models the interpolation trajectory in latent space as a solution to a second-order Neural ODE. The initial condition (start-point and data-dependent velocity) is set by encoders, and the entire interpolant is generated by numerical integration. Training is performed with a combined endpoint reconstruction and adversarial loss over the whole sequence, enforcing both visual fidelity and continuous-time smoothness. This enables not only precise interpolation, but a distribution over realistic transition paths (Bose et al., 2021).

d. Cross-Domain Sequence Generation (Syn2Seq Forcing, DFoT)

In the context of cross-view video generation, Seq-Inter reframes the synthesis problem as a construction of a continuous sequence, interpolating between disparate domains (e.g., exocentric and egocentric views) by generating a pseudo-ground-truth transition block via specialized interpolators and diffusion models. Self-attention architectures (e.g., Diffusion Forcing Transformers) enable modeling the full temporal sequence, handling spatio-temporal discontinuities at transitions (Mahdi et al., 15 Apr 2026).

4. Conditioning, Consistency, and Segment Stitching

A distinctive challenge in sequence-level interpolation concerns maintaining both global consistency and local smoothness when interpolating or generating long sequences, especially when sub-sequences must be stitched together.

• Appearance Consistency: Prefixing each segment with the final frame of the previous segment ensures that the model's output remains photometrically and texturally consistent.
• Motion Coherence: Motion tokens, extracted by temporally-augmented encoders and projected into the generative backbone (e.g., via cross-attention), allow the model to propagate style and semantic continuity through the sequence.
• Hierarchical Strategies: For particularly long or variable-resolution output, hierarchical anchoring (e.g., interpolating the midpoint then recursively subdividing) improves scalability without sacrificing fidelity (Zhang et al., 1 Oct 2025).
• History Conditioning: In diffusion-based sequence models, the influence of prior frames can be controlled via noise scheduling or fractional guidance, allowing for flexible adaptation of how much historical "memory" the model exploits for each output (Mahdi et al., 15 Apr 2026).

5. Training Strategies and Objectives

Seq-Inter models employ objectives that integrate over entire sequences, rather than optimizing local or pairwise fidelity alone:

• Global (Sequence-Level) Cost: The total loss is the sum over all steps or frames, directly minimizing cumulative error (MSE, MAE, negative log-likelihood, etc.).
• Auxiliary Regularizers: When learnable conditioning (such as appearance or motion tokens) is employed, additional regularization (e.g., cross-attention or controllability losses) stabilizes training and ensures interpretability (Zhang et al., 1 Oct 2025).
• Adversarial and Reconstruction Losses: For generative tasks, adversarial objectives enforce perceptual realism, while reconstruction losses on endpoints (and optionally on intermediate steps) ensure accurate transitions (Bose et al., 2021).
• Robustness to Segment Lengths: Randomized segment lengths during training expose models to a diversity of local and global time scales, improving generalization to any user-specified interpolation factor (Zhang et al., 1 Oct 2025).

6. Benchmarks, Performance, and Empirical Insights

Sequence-level interpolation methods have been validated on a wide spectrum of domains and metrics:

Model/Domain	Key Metrics	Seq-Inter Gains
ArbInterp (VFI) (Zhang et al., 1 Oct 2025)	FID, LPIPS, FVD, VBench	Outperforms prior methods for all scales (2x–32x)
Zero-delay spline (Ruiz-Moreno et al., 2022)	MSE, MAE	50–80% gap closed to batch (oracle) baseline
NeurInt (images) (Bose et al., 2021)	FID, Interpolant-FID, SVM	Substantially lower FID, more realistic diversity
Syn2Seq-Forcing (Mahdi et al., 15 Apr 2026)	PSNR, SSIM, LPIPS	>2.5 dB PSNR gain on Exo2Ego with frame-interp.

Multi-scale and continuous-timestamp benchmarks confirm that Seq-Inter enables arbitrarily fine, high-fidelity interpolation with seamless temporal continuity. In streaming and zero-delay contexts, it bridges much of the gap to offline-optimal solutions. In generative modeling, it delivers realism and diversity unattainable by deterministic or pairwise-only strategies.

7. Broader Impact and Generalization

The sequence-level interpolation paradigm enables unified, principled approaches to tasks such as video frame interpolation at arbitrary frame rates, zero-delay causal signal reconstruction, cross-domain or cross-view video generation, and learned path interpolation in latent spaces. It facilitates flexible temporal/sampling resolutions, fully data-dependent transitions, and modular extensibility to more complex tasks (multi-view, multimodal, etc.). A plausible implication is broad applicability to domains as diverse as time-series imputation, motion planning, and scientific data reconstruction, wherever global sequence structure is relevant for interpolation or generative modeling (Zhang et al., 1 Oct 2025, Ruiz-Moreno et al., 2022, Bose et al., 2021, Mahdi et al., 15 Apr 2026).