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Vid-ODE: Continuous-Time Video Generation with Neural Ordinary Differential Equation

Sunghyun Park, Kangyeol Kim, Junsoo Lee, Jaegul Choo, Joonseok Lee, Sookyung Kim, Edward Choi

arXiv:2010.08188v2cs.CV

TL;DR

Fixed-rate video models have difficulty handling irregular inputs and generating frames at arbitrary timesteps, including for scientific data with sparse or missing observations. Vid-ODE combines continuous-time modeling with pixel-level composition to generate frames at requested times. The paper reports state-of-the-art continuous-time video-generation performance on real-world datasets, while noting degradation as autoregressive predictions increase.

  • Problem

    Fixed-interval video models struggle with irregularly sampled inputs and generally cannot generate frames at unseen timesteps, a limitation relevant to scientific data with sparse measurements or missing values.

    Source: §1 · p. 1

  • Method

    Vid-ODE uses an ODE-ConvGRU encoder to learn spatio-temporal dynamics and combines adversarial training with pixel-level optical-flow and difference-map composition.

    Source: §1 · pp. 1–2

  • Results

    Vid-ODE consistently achieves state-of-the-art continuous-time video-generation performance on real-world datasets, with demonstrations spanning interpolation and extrapolation.

    Source: §1 · p. 2, §5 · p. 9

  • Takeaways & Limitations

    Vid-ODE demonstrates ODE-based continuous-time video generation on real-world videos, predicting frames at arbitrary timesteps within or beyond the observed range.

    Source: §1 · p. 2

    Because Vid-ODE is autoregressive, its outcomes tend to degrade as the number of predictions increases.

    Source: §5 · p. 9

Abstract

from arXiv · show

Video generation models often operate under the assumption of fixed frame rates, which leads to suboptimal performance when it comes to handling flexible frame rates (e.g., increasing the frame rate of the more dynamic portion of the video as well as handling missing video frames). To resolve the restricted nature of existing video generation models' ability to handle arbitrary timesteps, we propose continuous-time video generation by combining neural ODE (Vid-ODE) with pixel-level video processing techniques. Using ODE-ConvGRU as an encoder, a convolutional version of the recently proposed neural ODE, which enables us to learn continuous-time dynamics, Vid-ODE can learn the spatio-temporal dynamics of input videos of flexible frame rates. The decoder integrates the learned dynamics function to synthesize video frames at any given timesteps, where the pixel-level composition technique is used to maintain the sharpness of individual frames. With extensive experiments on four real-world video datasets, we verify that the proposed Vid-ODE outperforms state-of-the-art approaches under various video generation settings, both within the trained time range (interpolation) and beyond the range (extrapolation). To the best of our knowledge, Vid-ODE is the first work successfully performing continuous-time video generation using real-world videos.

1 Introduction

Fixed-rate video models struggle with irregularly sampled inputs and frames requested at unseen timesteps, a limitation relevant to scientific data as well as ordinary video. Vid-ODE combines continuous-time dynamics with pixel-level video processing to generate frames at arbitrary times, with strong results on real-world datasets.

1 Introduction

  • Fixed-interval models struggle with irregularly sampled inputs and cannot generally generate frames at unseen times, including intermediate points within a video.For example, models may not produce frames at t = 1.5 or t = 3.8 from a 1-FPS video spanning t = 0 to t = 5.Source: §1 · p. 1
  • Irregular sampling matters for scientific spatio-temporal data, where sparse measurements and missing values can leave important dynamics under-observed.Climate measurements may be minutes to hours apart, while wild-environment datasets can have missing values.Source: §1 · p. 1
  • Vid-ODE uses ODE-ConvGRU to capture spatio-temporal dynamics, with adversarial training and pixel-level optical-flow and difference-map composition to enhance sharpness.The framework learns from regular or irregular frame sequences and synthesizes frames at requested timesteps.Source: §1 · pp. 1–2
  • Vid-ODE predicts frames at any requested timestep, within or beyond the observed range, and is presented as the first ODE-based framework for continuous-time generation on real-world videos.The contribution is demonstrated on sparse climate videos across variants of ConvGRU and neural ODEs.Source: §1 · p. 2
  • Vid-ODE consistently achieves state-of-the-art continuous-time video-generation performance on real-world datasets, and experiments also validate its components' effectiveness and complementary roles.The reported settings include both video generation generally and sparse climate videos.Source: §1 · p. 2

2 Related Work

Prior neural-ODE work addressed continuous-time or irregularly sampled sequences, but its demonstrations did not establish applicability to complicated real-world video. Related video-generation work includes pixel-based and motion-based extrapolation, linear-composition approaches, and supervised or unsupervised interpolation methods.

2 Related Work

  • Earlier neural-ODE approaches showed promise for continuous-time modeling, but successful demonstrations were limited to synthetic or low-resolution sequences, leaving real-world video scalability unresolved.Examples include sinusoids, bouncing balls, and rotating MNIST.Source: §2 · p. 2
  • Pixel-based extrapolation predicts pixels from scratch and often blurs, while motion-based methods produce sharp images but degrade with large motion; linear composition combines generated and transformed frames.The cited linear-composition approach is Hao, Huang, and Belongie (2018).Source: §2 · p. 2
  • Interpolation methods span hand-crafted optical flow, supervised end-to-end neural approaches, and an unsupervised training method.The hand-crafted methods are described as having limited applicability for real-world videos.Source: §2 · p. 2

3 Proposed Method: Video Generation ODE

Vid-ODE encodes input frames into a hidden state with ODE-ConvGRU, then uses an ODE solver and pixel-level composition to generate frames at requested timesteps. Adversarial, reconstruction, and difference losses train the model to produce outputs with spatial and temporal quality.

3 Proposed Method: Video Generation ODE

  • The method encodes input video with ODE-ConvGRU, decodes hidden dynamics at requested times, and uses image- and sequence-level discriminators alongside reconstruction and difference losses.The encoder-decoder can generate frames at arbitrary timesteps, including interpolation and extrapolation.Source: §3 · p. 2, §3.3 · p. 4

3.1 Encoder: ODE-ConvGRU

  • ODE-ConvGRU combines neural ODE integration with ConvGRU updates to capture both temporal and spatial information from video frames.The ODE solver advances the hidden state between observations, while the ConvGRU incorporates each frame.Source: §3.1 · p. 3

3.2 Decoder: ODE Solver + Linear Composition

  • At each target time, an ODE solver advances the encoded state, and the decoder predicts optical flow, image difference, and a composition mask to form the output frame.The mask weights the combination of a warped previous frame and the predicted image difference.Source: §3.2 · pp. 3–4

3.3 Objective Functions

  • Training combines image- and sequence-level adversarial losses with pixel-level reconstruction and image-difference losses.Reconstruction compares predicted and ground-truth frames; the difference loss trains the predicted difference against consecutive-frame differences.Source: §3.3 · p. 4

4 Experiments

Vid-ODE is evaluated on interpolation, extrapolation, and irregularly sampled video prediction, with component ablations assessing its design. Across the reported comparisons, it outperforms baselines in standard and irregular-input settings.

4.1 Experimental Setup

  • Experiments cover interpolation and extrapolation on action, animation, sports, and hurricane videos, plus nonlinear-motion extrapolation on bouncing balls.CAM5 tests irregularly sampled hurricane videos; the evaluation section also describes five-frame inputs and five-frame future predictions for extrapolation.Source: §4.1 · p. 5

4.3 Comparison with Task-specific Models

  • Vid-ODE significantly outperforms neural-ODE-based baselines in both interpolation and extrapolation, and outperforms task-specific baselines across reported extrapolation metrics.For interpolation, it beats UVI in all cases except SSIM on KTH-Action, while supervised DVF remains a stronger comparison.Source: §4.2 · p. 6, §4.3 · p. 7

4.2 Comparison with Neural-ODE-based Models

  • ODE-ConvGRU-based Vid-ODE outperforms neural-ODE variants in both tasks; ODE-Conv also scores higher than ODE-FC.The paper attributes the improvement to ODE-ConvGRU and linear composition preserving spatio-temporal information and output sharpness.Source: §4.2 · p. 6
  • On nonlinear bouncing-ball motion, Vid-ODE predicts reflections and still outperforms baselines.The experiments contrast Vid-ODE with Vid-RNN: interpolating adjacent ConvGRU hidden states produces unrealistic frames at unseen timesteps.Source: §4.2 · p. 7, §4.4 · p. 9

4.3 Comparison with Task-specific Models

  • Vid-ODE outperforms irregular-input baselines on CAM5 in LPIPS and MSE, including when inputs are sparsely sampled.All models worsen as sampling rates decrease, but Vid-ODE remains ahead at irregular rates and at the regular 100% rate.Source: Figure 6 · p. 7, §4.3 · pp. 8–9, Table 5 · p. 9

4.4 Analysis of Individual Components

  • The component ablation reports gains from ODE-ConvGRU, adversarial loss, optical-flow warping, and linear composition.Adversarial loss especially improves LPIPS; linear composition fills disappeared pixels in warped images, improving visual quality.Source: §4.4 · p. 9, Table 4 · p. 9

5 Conclusions

Vid-ODE combines ODE-ConvGRU with optical-flow and image-difference composition for continuous-time video generation, while its autoregressive predictions degrade as their number increases.

5 Conclusions

  • Vid-ODE combines ODE-ConvGRU with optical-flow and image-difference composition to generate high-quality continuous-time video on four real-world datasets for interpolation and extrapolation.The paper presents this as a successful continuous-time video-generation approach.Source: §5 · p. 9
  • Vid-ODE tends to produce degraded outcomes as the number of predictions increases because of its autoregressive nature.Source: §5 · p. 9
  • The authors plan to study a flexible structure to address the degradation as prediction counts increase.Source: §5 · p. 9

Ethical Impact

The proposed model is framed as applicable beyond multimedia to spatio-temporal scientific data, particularly sparse climate observations where denser forecasting may be useful.

Ethical Impact

  • The framework is presented as applicable to spatio-temporal data beyond multimedia.Source: Ethical Impact · p. 10
  • Sparse, costly climate measurements may make denser-rate forecasting useful, including for extreme climate events.Source: Ethical Impact · p. 10
  • The authors suggest the approach could support improved estimation quality at lower cost and help decision-makers plan for extreme climate events.Source: Ethical Impact · p. 10

A. Implementation Details

The appendix reports training settings, an interpolation loss construction, and architecture-table notation for Vid-ODE.

A. Implementation Details

  • Vid-ODE was trained for 500 epochs with batch size 8 and an initially 0.001 learning rate decaying by 0.99 per epoch; KTH Action training took 7 hours on one Titan RTX.The reported run used 6.5GB VRAM; data augmentation included horizontal flips and rotations from -10 to 10 degrees.Source: A. Implementation Details · p. 12

5.1 Adversarial Loss for Interpolation

  • For interpolation, the generated sequence is formed by replacing each intermediate real frame with its prediction when computing the image loss.The modified input concatenates the preceding frames, the predicted intermediate frame, and the following frames; at sequence boundaries, concatenation is only on the available side.Source: §5.1 · p. 12

5.2 Model Architecture

  • Architecture tables 6–8 use N for output channels, K for kernel size, S for stride, P for padding, BN for batch normalization, and Up for 2× bilinear upsampling.Source: §5.2 · p. 12

B. Architectures of Vid-ODE and Vid-RNN

The Vid-ODE and Vid-RNN comparison is designed to isolate the ODE component's role in learning continuous video dynamics; their key difference is how they represent unseen timesteps.

B. Architectures of Vid-ODE and Vid-RNN

C. Additional Experiments

Additional experiments compare Vid-ODE with extrapolation baselines and examine interpolation, extrapolation, flexible frame rates, and higher-resolution video generation.

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