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We provide full theoretical guarantees for the convergence behaviour ofdiffusion-based generative models under the assumption of strongly logconcavedata distributions while our approximating class of functions used for scoreestimation is made of Lipschitz continuous functions. We demonstrate via amotivating example, sampling from a Gaussian distribution with unknown mean,the powerfulness of our approach. In this case, explicit estimates are providedfor the associated optimization problem, i.e. score approximation, while theseare combined with the corresponding sampling estimates. As a result, we obtainthe best known upper bound estimates in terms of key quantities of interest,such as the dimension and rates of convergence, for the Wasserstein-2 distancebetween the data distribution (Gaussian with unknown mean) and our samplingalgorithm.  Beyond the motivating example and in order to allow for the use of a diverserange of stochastic optimizers, we present our results using an $L^2$-accuratescore estimation assumption, which crucially is formed under an expectationwith respect to the stochastic optimizer and our novel auxiliary process thatuses only known information. This approach yields the best known convergencerate for our sampling algorithm.

On diffusion-based generative models and their error bounds: The log-concave case with full convergence estimates