  We present a comparative study of absolute distances to a sample of very
nearby, bright Type Ia supernovae (SNe) derived from high cadence, high
signal-to-noise, multi-band photometric data. Our sample consists of four SNe:
2012cg, 2012ht, 2013dy and 2014J. We present new homogeneous, high-cadence
photometric data in Johnson-Cousins BVRI and Sloan g'r'i'z' bands taken from
two sites (Piszkesteto and Baja, Hungary), and the light curves are analyzed
with publicly available light curve fitters (MLCS2k2, SNooPy2 and SALT2.4).
When comparing the best-fit parameters provided by the different codes, it is
found that the distance moduli of moderately-reddened SNe Ia agree within ~0.2
mag, and the agreement is even better (< 0.1 mag) for the highest
signal-to-noise BVRI data. For the highly-reddened SN~2014J the dispersion of
the inferred distance moduli is slightly higher. These SN-based distances are
in good agreement with the Cepheid distances to their host galaxies. We
conclude that the current state-of-the-art light curve fitters for Type Ia SNe
can provide consistent absolute distance moduli having less than ~0.1 -- 0.2
mag uncertainty for nearby SNe. Still, there is room for future improvements to
reach the desired ~0.05 mag accuracy in the absolute distance modulus.
