The endoplasmic reticulum (ER) is a structurally complex, membrane-enclosed compartment that stretches from the nuclear envelope to the extreme periphery of eukaryotic cells. The organelle is crucial for numerous distinct cellular processes, but how these processes are spatially regulated within the structure is unclear. Traditional imaging-based approaches to understanding protein dynamics within the organelle are limited by the convoluted structure and rapid movement of molecular components. Here, we introduce a combinatorial imaging and machine learning-assisted image analysis approach to track the motion of photoactivated proteins within the ER of live cells. We find that simultaneous knowledge of the underlying ER structure is required to accurately analyze fluorescently-tagged protein redistribution, and after appropriate structural calibration we see all proteins assayed show signatures of Brownian diffusion-dominated motion over micron spatial scales. Remarkably, we find that in some cells the ER structure can be explored in a highly asymmetric manner, likely as a result of uneven connectivity within the organelle. This remains true independently of the size, topology, or folding state of the fluorescently-tagged molecules, suggesting a potential role for ER connectivity in driving spatially regulated biology in eukaryotes.