C-172 Flight Instructor reported student losing directional control during IFR approach. Flight Instructor assumed control and flight continued.

Narrative

During training flight; the student was flying an instrument approach in IMC. Shortly after crossing the FAF and entered into a cloud; the student began to lose directional control; resulting in increasing lateral deviation. I immediately took the controls when it became clear the aircraft was no longer maintaining the final approach course. At that point; the CDI was fully deflected.My priority was to reestablish aircraft control and ensure safe separation from terrain. While attempting to regain stable flight; the aircraft entered an unplanned 360-degree turn. Once the aircraft was stabilized and under positive control; I initiated the published missed approach procedure.The deviation resulted from a student control loss during training. At no point was safety intentionally compromised; and all actions taken were to regain control of the aircraft and prevent a hazardous situation. After stabilization; the flight continued in accordance with all published and ATC procedures.To prevent this happening again; I'm going to pay closer attention to when my student starts getting task-saturated and take the controls sooner if things begin to drift too much. I'll also make sure we talk about and initiate a missed approach earlier whenever the approach starts becoming unstable.'