Cessna 172 pilot reported the engine began to severely vibrate during descent. Pilot diverted and landed safely.

Narrative

Current Mission: Flight Training in pursuance of Commercial ASELNo. Aboard: 2Fuel Aboard: ~3 hoursThis was a training mission in which several landings were conducted at ZZZ airport. Following these practice landings; the next focus was maneuvers. The maneuvers conducted were lazy eights; chandelles; and steep spirals. Following steep spirals; I began to prepare for eights-on-pylons; a low-level maneuver. We were still about 3;000 ft MSL when I started to set up for this maneuver. As this happened my instructor gave me a simulated engine failure as part of training by reducing the throttle to idle. At this point; I ran through my proper checklists and glided the airplane to a position from which an off-field landing could be made. At about 600' AGL (800' MSL); my instructor told me to recover from this maneuver and commence a climb. I added power; pushed carb heat to cold; and reduced flaps initially to 20 degrees. Right as the flaps reached 20 degrees a very severe and distinct vibration from the engine commenced. This vibration lasted for approximately 15-20 seconds and felt that the engine might be losing power. The instructor swiftly acted and [requested assistance] with ZZZ Approach on the frequency. Due to being low-level at the time; authority was exercised almost immediately. We initially attempted to proceed southeast and climb with what felt like reduced engine power.At this point; the approach controller advised that ZZZ1 Airport was closer to our position than ZZZ2. Thus; we continued the turn northeast and also continued to climb. By the time we were heading northeast; it felt as if the vibration intensity had reduced significantly. However; given the potential severity of the situation; we continued to climb until we were assured were within the gliding range of ZZZ1. We then glided the airplane to ZZZ1; due to less altitude loss than predicted we joined a left downwind and landed on runway XX at ZZZ1. After this; we taxied into the FBO and met with maintenance personnel at the airport to discuss the situation. One other consideration I want to mention is the location and timing of how the incident occurred. When practicing the simulated engine failure just before this event; we were within gliding distance of an open field. However; the time between when power was added to when the significant vibration occurred meant that we were no longer in a position to glide to the field. Had the engine completely failed; the airplane likely would have been forced to land in trees. Luckily the airplane had enough power still to climb out of that situation. I want this situation to bring to light the hazard of the situation being at a low altitude with a potential engine failure. There is a lot of training that involves ground reference maneuvers where altitudes below 1000' are required. While some of these maneuvers can be great for training and developing piloting skills; there is certainly a hazard to be noted about low-altitude maneuvers.