Latent Dynamics · 2026-10-02
Variational Streaming Flow: Probabilistic Forecasting in Physical Time
Hans Hao-Hsun Hsu, Minseon Gwak, Soon Hoe Lim, Pan Li, N. Benjamin Erichson
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TL;DR
Variational Streaming Flow (VSF) extends Streaming Flow (SF) for probabilistic forecasting in physical time. SF uses a deterministic velocity field and outputs a single future from a fixed history. VSF adds a latent variable sampled once per rollout and kept fixed, producing multiple plausible futures while retaining SF’s physical-time efficiency. The authors report improved long-horizon predictive accuracy and distributional fidelity on deterministic and stochastic dynamical systems, and better goal-directed success when used as a JEPA-based world-model predictor.
Why it matters
VSF addresses a limitation of non-latent physical-time flow models near settings like bifurcations, where deterministic velocity fields produce only one future from an observed history. By conditioning the physical-time velocity field on a rollout-level latent, the model can represent multiple futures. The paper also shows integration as a plug-and-play predictor for JEPA-based world models, improving goal-directed planning success.
Method
- Extend physical-time streaming flow with a latent-conditioned velocity field: d x̂_s / ds = v_θ(x̂_s, s, h, z), where one latent sample z is held fixed for the entire rollout.
- Train with a variational framework: an encoder infers a Gaussian latent posterior from local future transition information, regularized toward a fixed prior via KL; use a generalized energy reconstruction across multiple latent samples.
- At inference, sample z ~ p(z) once, then roll out through discretized physical-time dynamics; refresh history while keeping z unchanged.
Abstract (from arXiv)
Probabilistic forecasting is important for predicting complex dynamical systems because intrinsic randomness and incomplete observations can cause the same observed state to evolve into multiple plausible futures. While flow matching is a flexible approach for probabilistic forecasting, it is computationally expensive. Streaming flow (SF) reformulates this approach to model temporal evolution efficiently by learning a continuous velocity field directly in physical time. However, SF learns a deterministic velocity field. Thus, it provides only a single future trajectory for a given fixed initial state and observation history. To overcome this limitation, we introduce Variational Streaming Flow (VSF). Our approach learns a latent distribution that is conditioned on the dynamics of interest. In turn, this enables probabilistic forecasting. Importantly, we retain the computational efficiency of SF by generating in physical time. Across deterministic and stochastic dynamical systems, VSF demonstrates superior predictive accuracy and distributional fidelity. We demonstrate the advantage for both long-horizon rollouts exceeding 1,000 steps, and settings with bifurcating dynamics. Moreover, VSF can be integrated into existing Joint-Embedding Predictive Architecture (JEPA)-based world models as a plug-and-play predictor to improve temporal dynamics and goal-directed success rate in navigation, motion planning, and manipulation.
Related papers
- EpicWorldModel: Exploration-driven Planning with Latent World Models
- MDN-VJEPA: Multimodal Probabilistic Joint-Embedding World Models
- WorldFlow: Joint Video and 3D Motion Prediction via Large-Scale Pretraining
- Time-JEPA: Grounding Video World Models with Physical Time Series
- From Suboptimal to Optimal: One-Step Latent Flow Policies for Offline Reinforcement Learning
Publication record
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First public release: 2026-10-01 · Indexed by Pub-AI: 2026-10-02 UTC
Variational Streaming Flow: Probabilistic Forecasting in Physical Time
Preprint posted: 2026-10-01 · Original record ↗
- arxiv
- 2610.00976
Explicit source versions (1)
- v2 · 2026-10-03
- Preprint available
Source date: 2026-10-01 · First detected: 2026-10-25 UTC · Historical baseline
Source evidence (1)
- Official evidence ↗ · atom:published (official metadata)
- Explicit source version detected · v2
Source date: 2026-10-03 · First detected: 2026-10-25 UTC · Historical baseline
Source evidence (1)
- Official evidence ↗ · atom:id explicit version (official metadata)
Abstract · arxiv
Probabilistic forecasting is important for predicting complex dynamical systems because intrinsic randomness and incomplete observations can cause the same observed state to evolve into multiple plausible futures. While flow matching is a flexible approach for probabilistic forecasting, it is computationally expensive. Streaming flow (SF) reformulates this approach to model temporal evolution efficiently by learning a continuous velocity field directly in physical time. However, SF learns a deterministic velocity field. Thus, it provides only a single future trajectory for a given fixed initial state and observation history. To overcome this limitation, we introduce Variational Streaming Flow (VSF). Our approach learns a latent distribution that is conditioned on the dynamics of interest. In turn, this enables probabilistic forecasting. Importantly, we retain the computational efficiency of SF by generating in physical time. Across deterministic and stochastic dynamical systems, VSF demonstrates superior predictive accuracy and distributional fidelity. We demonstrate the advantage for both long-horizon rollouts exceeding 1,000 steps, and settings with bifurcating dynamics. Moreover, VSF can be integrated into existing Joint-Embedding Predictive Architecture (JEPA)-based world models as a plug-and-play predictor to improve temporal dynamics and goal-directed success rate in navigation, motion planning, and manipulation.