Back to the Future: Reverse-Consequence Modeling for Long-Horizon Particle Dynamics

Accurate prediction of object trajectories is fundamental to mechanical understanding and robotic control. However, autoregressive models inherently suffer from cumulative errors, leading to severe drift in long-horizon rollouts. Observing that in many physical systems with dissipative or convergence-to-rest behavior, the final states are often more predictable than transient dynamics (e.g., a sliding object resting under friction or a pendulum stabilizing at equilibrium), we propose ReStep, a cascaded approach that reverses the conventional forward-prediction paradigm. ReStep first employs a stochastic model to directly predict the final state, then leverages Anchored Diffusion to generate goal-conditioned intermediate trajectories. By conditioning on both ”boundary states”, it effectively constrains dynamics and reduces uncertainty, producing physically plausible and temporally coherent transitions. We further integrate ReStep dynamics as the physical engine within a 3D Gaussian Splatting pipeline, enabling a unified physical-visual framework for intuitive inference from images. Extensive experiments on diverse rigid and non-rigid collision datasets show that ReStep achieves superior long-term accuracy, substantially mitigating error accumulation via reverse-consequence modeling.