  Conceptual difficulties in semiclassical and quantum gravity arise from
diffeomorphism invariance of classical general relativity. With a motivation to
shed some light on these difficulties, we study a class of toy models for which
one-dimensional diffeomorphism invariance, namely time-reparametrization
invariance, emerges at the classical level from energy conservation. An attempt
to quantize the models while taking the invariance seriously leads to toy
versions of the problem of time in quantum gravity, of the cosmological
constant problem, and of the black hole firewall problem. Nevertheless, all
these problems are easily resolved by taking into account that the invariance
emerges only at the classical level, while the fundamental theory that needs to
be quantized is not diffeomorphism invariant.
