StreamPhy: Streaming Inference of High-Dimensional Physical Dynamics via State Space Models

Streaming world models predict future visual states online while maintaining physically coherent dynamics over long horizons. However, their rollouts often violate basic physical constraints. A common approach distills pretrained bidirectional DiTs into few-step causal generators. However, this paradigm suffers from two fundamental limitations: generic bidirectional teachers acquire limited physical priors from visually oriented pretraining, and the limited priors suffer further loss during bidirectional-to-causal distillation. We present PhyS, a three-stage framework for distilling physical priors into streaming world models. To acquire physical priors from real-world interactions, we construct PhyS-120K, a dataset of 120K real-world physical-interaction videos spanning rigid-body dynamics, soft-body deformation, fluid phenomena, and phase transitions. Each video is annotated with structured descriptions of object properties and causal state transitions. Physics-aware supervised fine-tuning injects the physical priors into a bidirectional 14B DiT teacher, which we then distill into a lightweight 1.3B causal DiT for few-step autoregressive streaming generation. Finally, we use online reinforcement learning to incentivize the distilled model to generate physically plausible rollouts and further propose Temporal Credit Routing (TCR) to address temporal credit assignment. TCR evaluates physical consistency over overlapping temporal windows and routes the resulting group-relative advantages to temporally aligned denoising actions. On PhysicsIQ, PhyS improves the Wan2.1-14B teacher by 18.2% and the Self Forcing, Rolling Forcing, and Causal Forcing by 23.7%, 14.8%, and 31.4%, respectively. Results also improve the physics-aware video benchmarks VideoPhy, VideoPhy2, and PhyGenBench. The dataset, code, and more sample videos are available on our Project Page.

Reconstructing PDE-governed fields from sparse and irregular measurements is challenging due to their ill-posed nature. Deterministic surrogates are trained on dense fields that struggle with limited measurements and uncertainty quantification. Generative models, by learning distributions over spatiotemporal fields, can better handle sparsity and uncertainty. However, existing generative approaches enforce data consistency and PDE constraints simultaneously via sampling-time gradient guidance, resulting in slow and unstable inference. To this end, we propose PerFlow, a Physics-embedded rectified Flow for efficient sparse reconstruction and uncertainty quantification of spatiotemporal dynamics. PerFlow decouples observation conditioning from physics enforcement, performing guidance-free conditioning by feeding observations into rectified-flow dynamics while embedding hard physics via a constraint-preserving projection (e.g., incompressibility or conservation). Theoretically, we establish invariance guarantees to ensure that trajectories remain on the physics-consistent manifold throughout sampling. Experiments on various PDE systems demonstrate competitive reconstruction accuracy with sound physics consistency, while enabling efficient conditional sampling (e.g., 50 steps) and up to 320x faster inference than 2000-step guided diffusion baselines.

Reconstructing high-fidelity flow fields from low-fidelity observations is a central problem in scientific machine learning, yet recent diffusion and flow-matching models typically rely on iterative sampling, making them costly for latency-sensitive workflows such as ensemble forecasting, real-time visualization, and simulation-in-the-loop inference. We study whether a high-fidelity flow-matching generative model can be compressed into a compact one-step model for fast scientific flow reconstruction. Our approach distills an optimal-transport flow-matching teacher into a one-step consistency model. Low-fidelity observations are incorporated at inference by initializing the generative trajectory from a noised observation along the transport path, allowing an unconditional high-fidelity flow model to perform conditional reconstruction without retraining the teacher. We evaluate this distillation strategy on three fluid benchmarks, Smoke Buoyancy, Turbulent Channel Flow, and Kolmogorov Flow, using coarse-to-fine reconstruction as a controlled testbed at field sizes up to $256 \times 256$. Across these settings, the distilled student retains similar performance of the teacher's model on spectrum metrics, while using roughly half as many parameters and achieving a $12\times$ inference speedup over the flow-matching teacher. Under the same training budget, the distilled student also outperforms a one-step consistency model trained directly from scratch by $23.1\%$ in SSIM, showing that teacher distillation improves training efficiency rather than merely accelerating sampling. These results suggest a promising route for turning future high-capacity scientific generative models into compact reconstruction models that are faster to train, cheaper to run, and easier to deploy.