  We show that various scalar field models of dark energy predict degenerate
luminosity distance history of the Universe and thus cannot be distinguished by
supernovae measurements alone. In particular, models with a vanishing
cosmological constant (the value of the potential at its minimum) are
degenerate with models with a positive or negative cosmological constant whose
magnitude can be as large as the critical density. Adding information from CMB
anisotropy measurements does reduce the degeneracy somewhat but not
significantly. Our results indicate that a theoretical prior on the preferred
form of the potential and the field's initial conditions may allow to
quantitatively estimate model parameters from data. Without such a theoretical
prior only limited qualitative information on the form and parameters of the
potential can be extracted even from very accurate data.
