# Variational Streaming Flow: Probabilistic Forecasting in Physical Time

arXiv: https://arxiv.org/abs/2610.00976 · HTML: https://mlsanity.com/paper/2610.00976/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 48 of its 62 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Builds on (most cited first, 30 of 48)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [World Models](https://mlsanity.com/paper/1803.10122/) (2018)
- [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018)
- [Self-Supervised Learning from Images with a Joint-Embedding Predictive Architecture](https://mlsanity.com/paper/2301.08243/) (2023)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [DeepMind Control Suite](https://mlsanity.com/paper/1801.00690/) (2018)
- [V-JEPA 2: Self-Supervised Video Models Enable Understanding, Prediction and Planning](https://mlsanity.com/paper/2506.09985/) (2025)
- [Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models](https://mlsanity.com/paper/1805.12114/) (2018)
- [Chronos: Learning the Language of Time Series](https://mlsanity.com/paper/2403.07815/) (2024)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [Unified Training of Universal Time Series Forecasting Transformers](https://mlsanity.com/paper/2402.02592/) (2024)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [DINO-WM: World Models on Pre-trained Visual Features enable Zero-shot Planning](https://mlsanity.com/paper/2411.04983/) (2024)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [MCVD: Masked Conditional Video Diffusion for Prediction, Generation, and Interpolation](https://mlsanity.com/paper/2205.09853/) (2022)
- [Flow Matching Guide and Code](https://mlsanity.com/paper/2412.06264/) (2024)
- [Embed to Control: A Locally Linear Latent Dynamics Model for Control from Raw Images](https://mlsanity.com/paper/1506.07365/) (2015)
- [LeWorldModel: Stable End-to-End Joint-Embedding Predictive Architecture from Pixels](https://mlsanity.com/paper/2603.19312/) (2026)
- [OGBench: Benchmarking Offline Goal-Conditioned RL](https://mlsanity.com/paper/2410.20092/) (2024)
- [Chronos-2: From Univariate to Universal Forecasting](https://mlsanity.com/paper/2510.15821/) (2025)
- [Neural Jump Stochastic Differential Equations](https://mlsanity.com/paper/1905.10403/) (2019)
- [Neural Rough Differential Equations for Long Time Series](https://mlsanity.com/paper/2009.08295/) (2020)
- [Lag-Llama: Towards Foundation Models for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2310.08278/) (2023)

## 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.