  Most existing theoretical investigations of the accuracy of diffusion models,
albeit significant, assume the score function has been approximated to a
certain accuracy, and then use this a priori bound to control the error of
generation. This article instead provides a first quantitative understanding of
the whole generation process, i.e., both training and sampling. More precisely,
it conducts a non-asymptotic convergence analysis of denoising score matching
under gradient descent. In addition, a refined sampling error analysis for
variance exploding models is also provided. The combination of these two
results yields a full error analysis, which elucidates (again, but this time
theoretically) how to design the training and sampling processes for effective
generation. For instance, our theory implies a preference toward noise
distribution and loss weighting in training that qualitatively agree with the
ones used in [Karras et al. 2022]. It also provides perspectives on the choices
of time and variance schedules in sampling: when the score is well trained, the
design in [Song et al. 2020] is more preferable, but when it is less trained,
the design in [Karras et al. 2022] becomes more preferable.
