Even though robot learning is often formulated in terms of discrete-time Markov decision processes (MDPs), physical robots require near-continuous multiscale feedback control. Machines operate on multiple asynchronous sensing modalities each with different frequencies, e.g., video frames at 30Hz, proprioceptive state at 100Hz, force-torque data at 500Hz, etc. While the classic approach is to batch observations into fixed-time windows then pass them through feed-forward encoders (e.g., with deep networks), we show that there exists a more elegant approach -- one that treats policy learning as modeling latent state dynamics in continuous-time. Specifically, we present 'InFuser', a unified architecture that trains continuous time-policies with Neural Controlled Differential Equations (CDEs). 'InFuser' evolves a single latent state representation over time by (In)tegrating and (Fus)ing multi-sensory observations (arriving at different frequencies), and inferring actions in continuous-time. This enables policies that can react to multi-frequency multi-sensory feedback for truly end-to-end visuomotor control, without discrete-time assumptions. Behavior cloning experiments demonstrate that 'InFuser' learns robust policies for dynamic tasks (e.g., swinging a ball into a cup) notably outperforming several baselines in settings where observations from one sensing modality can arrive at much sparser intervals than others.