  Alongside the recent increase in discoveries of tidal disruption events
(TDEs) have come an increasing number of ambiguous nuclear transients (ANTs).
These ANTs are characterized by hot blackbody-like UV/optical spectral energy
distributions (SEDs) and smooth photometric evolution, often with hard
powerlaw-like X-ray emission. ANTs are likely exotic TDEs or smooth flares
originating in otherwise narrow-line active galactic nuclei (AGNs). While their
emission in the UV/optical and X-ray has been relatively well-explored, their
infrared (IR) emission has not been studied in detail. Here we use the NEOWISE
mission and its low-cadence mapping of the entire sky to study mid-infrared
dust reprocessing echoes of ANTs. We study 19 ANTs, finding significant MIR
flares in 18 objects for which we can estimate an IR luminosity and temperature
evolution. The dust reprocessing echoes show a wide range in IR luminosities
($\sim 10^{42} - 10^{45}$ erg s$^{-1}$) with blackbody temperatures largely
consistent with sublimation temperature of graphite grains. Excluding the two
sources possibly associated with luminous supernovae (ASASSN-15lh and
ASASSN-17jz), the dust covering fractions (f$_c$) for detected IR flares lie
between 0.05 and 0.91, with a mean of f$_c$ = 0.29 for all ANTs (including
limits) and f$_c$ = $0.38 \pm 0.04$ for detections. These covering fractions
are much higher than optically-selected TDEs and similar to AGNs. We interpret
the high covering fractions in ANT host galaxies as evidence for the presence
of a dusty torus.
