  We provide full theoretical guarantees for the convergence behaviour of
diffusion-based generative models under the assumption of strongly log-concave
data distributions while our approximating class of functions used for score
estimation is made of Lipschitz continuous functions. We demonstrate via a
motivating example, sampling from a Gaussian distribution with unknown mean,
the powerfulness of our approach. In this case, explicit estimates are provided
for the associated optimization problem, i.e. score approximation, while these
are combined with the corresponding sampling estimates. As a result, we obtain
the best known upper bound estimates in terms of key quantities of interest,
such as the dimension and rates of convergence, for the Wasserstein-2 distance
between the data distribution (Gaussian with unknown mean) and our sampling
algorithm.
  Beyond the motivating example and in order to allow for the use of a diverse
range of stochastic optimizers, we present our results using an $L^2$-accurate
score estimation assumption, which crucially is formed under an expectation
with respect to the stochastic optimizer and our novel auxiliary process that
uses only known information. This approach yields the best known convergence
rate for our sampling algorithm.
