Diffusive Dynamics Modeling

Diffusive Dynamics Modeling uses time as the control variable to predict the diffusion of substances at arbitrary future time points based on current images, which provides a foundation for future generation and real-world modeling. However, this task remains challenging due to: (1) Time-controlled generation of dynamics lacks temporal connections between adjacent time points, leading to discontinuities. (2) Prediction deviations across temporal spans violate the macroscopic directionality, leading to inconsistency. The diffusion model generation process follows diffusive dynamics along the noise-level axis, while real diffusive dynamics evolve along the time axis. Taking these two dynamics as the two axes to form a two-dimensional grid enables the establishment of temporal relationships across multiple noise levels. Therefore, we propose Diffusive Grid, a unified diffusive dynamics modeling framework to establish temporal relationships throughout the denoising process. Based on this grid, Dynamics Alignment Learning (DAL) aligns predictions that reach the same grid node through temporal evolution and denoising, thereby constraining the entire generation process with adjacent time points and improving continuity. Moreover, Grid Walk (GW) constructs paths across temporal spans and anchors their endpoints to the target, allowing supervision to propagate through intermediate states and regularize consistency. Experiments covering both natural and physiological diffusive processes demonstrate that our method achieves better overall performance in continuity and consistency.