TFP: Temporally Conditioned Memory-Fusion Policies for Visuomotor Learning

Vision--Language--Action (VLA) policies such as $\pi_{0.5}$ and OpenVLA perform well on many manipulation tasks, but they are often reactive: the next action is predicted from the current observation, instruction, and proprioceptive state. This assumption breaks down in stage-dependent manipulation, where visually similar states may require different actions depending on latent task progress and previous interaction outcomes. We argue that such tasks require not only memory, but dynamics-aware belief updates: the policy should preserve task progress during stable or occluded phases and revise its belief near contact, release, or subgoal transitions. We introduce Temporally Conditioned Memory-Fusion Policies (TFP), a lightweight memory-action framework for VLA backbones. TFP maintains an episode-local task-progress belief with Liquid Time-Constant dynamics and injects the updated belief directly into the flow-matching action decoder through adaptive modulation. This lets temporally accumulated context shape the generated action chunk, rather than serving only as passive history context. With a 3.3B-parameter model, TFP improves the average success rate from $96.9\%$ to $98.75\%$ on LIBERO and from $91.4\%$ to $93.77\%$ on LIBERO-plus. On the memory-focused MIKASA ShellGameTouch diagnostic, TFP achieves success up to $75.0\%$. Mechanistic analyses show that write-gain changes near manipulation events are about $6\times$ larger than far non-event phases, and hidden-state interventions show that the belief causally modulates generated action chunks. These results suggest that compact, event-sensitive memory dynamics can improve VLA policies under occlusion, visual perturbation, and stage-dependent task structure.