Context. Establishing the origin of the water D/H ratio in the Solar System is central to our understanding of the chemical trail of water during the star and planet formation process. Recent modeling suggests that comparisons of the D 2 O/HDO and HDO/H 2 O ratios are a powerful way to trace the chemical evolution of water and, in particular, determine whether the D/H ratio is inherited from the molecular cloud or established locally. Aims. We seek to determine the D 2 O column density and derive the D 2 O/HDO ratios in the warm region toward the low-mass Class 0 sources B335 and L483. The results are compared with astrochemical models and previous observations to determine their implications for the chemical evolution of water. Methods. We present ALMA observations of the D 2 O 1 1,0 –1 0,1 transition at 316.8 GHz toward B335 and L483 at ≲0.′′5 (≲100 au) resolution, probing the inner warm envelope gas. The column densities of D 2 O, HDO, and H 2 18 O are determined by synthetic spectrum modeling and direct Gaussian fitting, under the assumption of a single excitation temperature and similar spatial extent for the three water isotopologs. Results. D 2 O is detected toward both sources in the inner warm envelope. The derived D 2 O/HDO ratio is (1.0 ± 0.2) × 10 −2 for L483 and (1.4 ± 0.1) × 10 −2 for B335. These values indicate that the D 2 O/HDO ratio is higher than the HDO/H 2 O ratios by a factor of ≳2 toward both sources. Conclusions. The high D 2 O/HDO ratios are a strong indication of chemical inheritance of water from the prestellar phase down to the inner warm envelope. This implies that the local cloud conditions in the prestellar phase, such as temperatures and timescales, determine the water chemistry at later stages and could provide a source of chemical differentiation in young systems. In addition, the observed D 2 O/H 2 O ratios support an observed dichotomy in the deuterium fractionation of water toward isolated and clustered protostars, namely, a higher D/H ratio toward isolated sources.