  The nearby dwarf spiral galaxy NGC 4395 contains a broad-lined active
galactic nucleus (AGN) of exceptionally low luminosity powered by accretion
onto a central black hole of very low mass ($\sim10^4-10^5$ M$_\odot$). In
order to constrain the size of the optical continuum emission region through
reverberation mapping, we carried out high-cadence photometric monitoring of
NGC 4395 in the $griz$ filter bands on two consecutive nights in 2022 April
using the four-channel MuSCAT3 camera on the Faulkes Telescope North at
Haleakal\={a} Observatory. Correlated variability across the $griz$ bands is
clearly detected, and the $r$, $i$, and $z$ band light curves show lags of
$8.4^{+1.0}_{-1.1}$, $14.2^{+1.2}_{-1.4}$, and $20.4^{+2.0}_{-2.1}$ minutes
with respect to the $g$ band when measured using the full-duration light
curves. When lags are measured for each night separately, the Night 2 data
exhibit lower cross-correlation amplitudes and shorter lags than the Night 1
light curves. Using the full-duration lags, we find that the lag-wavelength
relationship is consistent with the $\tau\propto\lambda^{4/3}$ dependence found
for more luminous AGN. Combining our results with continuum lags measured for
other objects, the lag between $g$ and $z$ band scales with optical continuum
luminosity as $\tau_{gz} \propto L^{0.56\pm0.05}$, similar to the scaling of
broad-line region size with luminosity, reinforcing recent evidence that
diffuse continuum emission from the broad-line region may contribute
substantially to optical continuum variability and reverberation lags.
