Air carrier Captain reported that glide slope anomalies on approach to SFO ILS 28R led to an unstabilized approach and a low altitude alert from ATC.

Narrative

Arriving into SFO and still on the DYAMD5 arrival; we were cleared for the ILS 28R approach from ARCHI. The airplane stayed in LNAV/VNAV PTH the whole time until just past CEPIN; when the First Officer (FO) who was pilot flying (PF); armed approach mode and LOC and GS became active. The localizer and glide slope diamonds were right on at the time the modes became active; Autopilot CMD B was engaged; and we were gear down at Flaps 15. At around 1;800' approaching AXMUL just as the FO had called for Flaps 30 and the landing checklist; the airplane had a slight rolling motion and began to pitch up. At first it felt like wake turbulence but then we noticed the glideslope diamond at about half a dot above (airplane below glide slope) and continuing to trend upwards. The next thing we noticed was the airspeed starting to decay; so the FO immediately added thrust. By the time the airspeed came back to a positive trend; the glideslope diamond was at about half a dot below (airplane above glideslope) and trending downwards; and the airplane started to pitch down to chase the glideslope. The FO then turned off the Autopilot; at which point we were at about half a dot low again on the glideslope; and recovered the path. ATC issued a low altitude warning to us around the same time at around 1;300' at which time we were proceeding visually with the PAPIs showing 3 red 1 white. The airplane was fully configured shortly after by the time we reached 1;000' and stable at the 500' gate. We reported the erratic glideslope to ATC and the rest of the approach and landing was uneventful. No low airspeed; stick shaker; or overspeed warnings were activated during the approach.