Continuous-Time Trajectory Generation from Discrete Observations with Stochasticity

arXiv:2609.32026 · stat.ML, cs.LG, math.DS · Submitted 2026-09-25 · Read on arXiv

stat.ML, cs.LG, math.DS

Submitted: 2026-09-25

Updated: 2026-09-25

Code: https://github.com/R1fe/PhiBE-Flow

Terminology

• Latent Space — 7× in this paper · explained in 7 episodes
• Transformer — 7× in this paper · explained in 2 episodes
• Adam — 5× in this paper · explained in 2 episodes
• Latent Representation — 5× in this paper · explained in 2 episodes
• Ornstein–Uhlenbeck Process — 5× in this paper · explained in 3 episodes
• Stochastic Dynamics — 5× in this paper · explained in 2 episodes
• Generative Model — 4× in this paper · explained in 2 episodes
• Generative Modeling — 4× in this paper · explained in 3 episodes
• Generative Models — 4× in this paper · explained in 2 episodes
• Consistency — 3× in this paper · explained in 3 episodes
• Convergence Guarantees — 3× in this paper · explained in 3 episodes
• Diffusion Model — 3× in this paper · explained in 8 episodes
• Diffusion Models — 3× in this paper · explained in 6 episodes
• Flow Matching — 3× in this paper · explained in 8 episodes
• Mean Squared Error — 3× in this paper
• Peak Signal-to-Noise Ratio — 3× in this paper
• Benchmark — 2× in this paper · explained in 2 episodes
• Robustness — 2× in this paper · explained in 5 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Diffusion Processes — 1× in this paper · explained in 2 episodes
• Latent Representations — 1× in this paper · explained in 3 episodes
• Normalizing Flow — 1× in this paper · explained in 3 episodes
• Normalizing Flows — 1× in this paper · explained in 4 episodes
• Optimal Transport — 1× in this paper · explained in 5 episodes
• Ordinary Differential Equations (ODEs) — 1× in this paper · explained in 2 episodes
• Probabilistic Forecasting — 1× in this paper · explained in 3 episodes
• Reinforcement Learning — 1× in this paper · explained in 4 episodes
• Representation Learning — 1× in this paper · explained in 2 episodes
• Structural Similarity Index Measure — 1× in this paper
• Theoretical Guarantees — 1× in this paper · explained in 2 episodes

Sources

• Building Normalizing Flows with Stochastic Interpolants
• Likelihood Training of Schr\"odinger Bridge using Forward-Backward SDEs Theory
• Stochastic Adversarial Video Prediction
• Geometry-Preserving Encoder/Decoder in Latent Generative Models
• Video (language) modeling: a baseline for generative models of natural videos
• Score-Based Generative Modeling through Stochastic Differential Equations
• Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit
• Towards Accurate Generative Models of Video: A New Metric & Challenges
• VideoGPT: Video Generation using VQ-VAE and Transformers
• PhiBE: A PDE-based Bellman Equation for Continuous Time Policy Evaluation

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