Interactive control for video generation is moving from coarse prompts toward fine-grained, physically meaningful manipulation of dynamic scenes. Yet existing controllable methods either require the full control schedule before generation starts, or use pixel-space signals that dictate object positions rather than physical dynamics. To address these limitations, we propose PhysStream, an autoregressive model for physics-grounded image-to-video synthesis that incorporates structured scene memory---positional maps and object tracking maps derived online from previously generated frames---and supports fine-grained motion control via sparse velocity-increment signals that encode physical quantities, letting the model learn the underlying dynamics. We train our model in two stages: a bidirectional model is first finetuned with motion-control conditioning, then a causal autoregressive model is trained with additional structured scene memory, further improving physical consistency. PhysStream enables interactive, mid-generation control over multi-object tabletop rigid-body scenes---a capability not supported by prior methods---reducing motion distribution distance (FVMD) by 33% and trajectory error by 12% over the strongest baselines on synthetic benchmarks, and is preferred by human evaluators in over 85% of in-the-wild comparisons. Please check our website for more details: https://czzzzh.github.io/PhysStream