Insects can detect bilateral differences in odor concentration between their two antennae, enabling them to sense odor gradients. While gradients aid navigation in simple odor environments like static ribbons, their role in navigating complex plumes remains unknown. Here, we use a virtual reality paradigm to show that Drosophila use bilateral sensing for a distinct computation: detecting the motion of odor signals. Such odor direction sensing is computationally equivalent to motion detection algorithms underlying motion detection in vision. Simulations of natural plumes reveal that odor motion contains valuable directional information absent from the airflow, which Drosophila indeed exploit when navigating natural plumes. Olfactory studies dating back a century have stressed the critical role of wind sensing for insect navigation; we reveal an entirely orthogonal direction cue used by flies in natural environments, and give theoretical arguments suggesting that this cue may be of broad use across the animal kingdom.