  We introduce a new model for understanding AGN continuum variability. We
start from a Shakura--Sunyaev thin accretion disc with a steady-state radial
temperature profile $T(R)$ and assume that the variable flux is due to
axisymmetric temperature perturbations $\delta T(R,t)$. After linearizing the
equations, we fit UV-optical AGN lightcurves to determine $\delta T(R,t)$ for a
sample of seven AGNs. We see a diversity of $|\delta T/T| \sim 0.1$ fluctuation
patterns which are not dominated by outgoing waves traveling at the speed of
light as expected for the "lamppost" model used to interpret disc reverberation
mapping studies. Rather, the most common pattern resembles slow ($v \ll c$)
ingoing waves. An explanation for our findings is that these ingoing waves
trigger central temperature fluctuations that act as a lamppost, producing
lower amplitude temperature fluctuations moving outwards at the speed of light.
The lightcurves are dominated by the lamppost signal -- even though the
temperature fluctuations are dominated by other structures with similar
variability time-scales -- because the discs exponentially smooth the
contributions from the slower moving ($v \ll c$) fluctuations to the observed
lightcurves. This leads to lightcurves that closely resemble the expectations
for a lamppost model but with the slow variability time-scales of the ingoing
waves. This also implies that longer time-scale variability signals will
increasingly diverge from lamppost models because the smoothing of
slower-moving waves steadily decreases as their period or spatial wavelength
increases.
