Papers › ODE²VAE: Deep generative second order ODEs with Bayesian neural networks
ODE²VAE: Deep generative second order ODEs with Bayesian neural networks
Çağatay Yıldız, Markus Heinonen, Harri Lähdesmäki
We present Ordinary Differential Equation Variational Auto-Encoder (ODE²VAE), a latent second order ODE model for high-dimensional sequential data. Leveraging the advances in deep generative models, ODE²VAE can simultaneously learn the embedding of high dimensional trajectories and infer arbitrarily complex continuous-time latent dynamics. Our model explicitly decomposes the latent space into momentum and position components and solves a second order ODE system, which is in contrast to recurrent neural network (RNN) based time series models and recently proposed black-box ODE techniques. In order to account for uncertainty, we propose probabilistic latent ODE dynamics parameterized by deep Bayesian neural networks. We demonstrate our approach on motion capture, image rotation and bouncing balls datasets. We achieve state-of-the-art performance in long term motion prediction and imputation tasks.
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Tasks
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Results from the paper archive 2025-07-28
| Task | Dataset | Model | Metric | Value | Rank at snapshot | Leaderboard | Report |
|---|---|---|---|---|---|---|---|
| Video Prediction | CMU Mocap-1 | ODE2VAE-KL | Test Error | 15.99 | #1 of 2 | Archive leaderboard | report |
| Video Prediction | CMU Mocap-1 | ODE2VAE | Test Error | 93.07 | #2 of 2 | Archive leaderboard | report |
| Video Prediction | CMU Mocap-2 | ODE2VAE-KL | Test Error | 8.09 | #3 of 4 | Archive leaderboard | report |
| Video Prediction | CMU Mocap-2 | ODE2VAE | Test Error | 10.06 | #4 of 4 | Archive leaderboard | report |
Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.
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